@article{Assaad,
  title = {Depleted Kondo lattices: Quantum Monte Carlo and mean-field calculations},
  author = {Assaad, F. F.},
  journal = {Phys. Rev. B},
  volume = {65},
  issue = {11},
  pages = {115104},
  numpages = {11},
  year = {2002},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.65.115104},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.65.115104}
}

@article{EsslingerReview,
author = {Esslinger, Tilman},
title = {Fermi-Hubbard Physics with Atoms in an Optical Lattice},
journal = {Annual Review of Condensed Matter Physics},
volume = {1},
number = {1},
pages = {129-152},
year = {2010},
doi = {10.1146/annurev-conmatphys-070909-104059},

URL = { 
        https://doi.org/10.1146/annurev-conmatphys-070909-104059
    
},
eprint = { 
        https://doi.org/10.1146/annurev-conmatphys-070909-104059
    
}
,
    abstract = { The Fermi-Hubbard model is a key concept in condensed matter physics and provides crucial insights into electronic and magnetic properties of materials. Yet, the intricate nature of Fermi systems poses a barrier to answering important questions concerning d-wave superconductivity and quantum magnetism. Recently, it has become possible to experimentally realize the Fermi-Hubbard model using a fermionic quantum gas loaded into an optical lattice. In this atomic approach to the Fermi-Hubbard model, the Hamiltonian is a direct result of the optical lattice potential created by interfering laser fields and short-ranged ultracold collisions. It provides a route to simulate the physics of the Hamiltonian and to address open questions and novel challenges of the underlying many-body system. This review gives an overview of the current efforts in understanding and realizing experiments with fermionic atoms in optical lattices and discusses key experiments in the metallic, band-insulating, superfluid, and Mott-insulating regimes. }
}


@article{WuHomobilayer,
  title = {Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers},
  author = {Wu, Fengcheng and Lovorn, Timothy and Tutuc, Emanuel and Martin, Ivar and MacDonald, A. H.},
  journal = {Phys. Rev. Lett.},
  volume = {122},
  issue = {8},
  pages = {086402},
  numpages = {5},
  year = {2019},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.122.086402},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.122.086402}
}

@article{Mak,
  title={Quantum anomalous Hall effect from intertwined moir{\'e} bands},
  author={Li, Tingxin and Jiang, Shengwei and Shen, Bowen and Zhang, Yang and Li, Lizhong and Tao, Zui and Devakul, Trithep and Watanabe, Kenji and Taniguchi, Takashi and Fu, Liang and others},
  journal={Nature},
  volume={600},
  number={7890},
  pages={641--646},
  year={2021},
  publisher={Nature Publishing Group}
}

@article{hulet,
	abstract = {Ultracold atomic gases in optical lattices potentially offer simulations of condensed-matter phenomena beyond what theory and computations can access; compensated optical lattice techniques applied to the Hubbard model now enable unprecedented low temperatures to be reached for fermions ---only 1.4 times that of the antiferromagnetic phase transition, approaching the limits of present modelling techniques.},
	author = {Hart, Russell A. and Duarte, Pedro M. and Yang, Tsung-Lin and Liu, Xinxing and Paiva, Thereza and Khatami, Ehsan and Scalettar, Richard T. and Trivedi, Nandini and Huse, David A. and Hulet, Randall G.},
	da = {2015/03/01},
	date-added = {2022-07-01 10:42:30 -0500},
	date-modified = {2022-07-01 10:42:30 -0500},
	doi = {10.1038/nature14223},
	id = {Hart2015},
	isbn = {1476-4687},
	journal = {Nature},
	number = {7542},
	pages = {211--214},
	title = {Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms},
	ty = {JOUR},
	url = {https://doi.org/10.1038/nature14223},
	volume = {519},
	year = {2015},
	Bdsk-Url-1 = {https://doi.org/10.1038/nature14223}}


@article{flat,
  title = {Nearly flat Chern bands in moir\'e superlattices},
  author = {Zhang, Ya-Hui and Mao, Dan and Cao, Yuan and Jarillo-Herrero, Pablo and Senthil, T.},
  journal = {Phys. Rev. B},
  volume = {99},
  issue = {7},
  pages = {075127},
  numpages = {19},
  year = {2019},
  month = {Feb},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.99.075127},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.99.075127}
}


@article{kee,
	abstract = {The topological Haldane model on a honeycomb lattice is a prototype of systems hosting topological phases of matter without external fields. It is the simplest model exhibiting the quantum Hall effect without Landau levels, which motivated theoretical and experimental explorations of topological insulators and superconductors. Despite its simplicity, its realization in condensed matter systems has been elusive due to a seemingly difficult condition of spinless fermions with sublattice-dependent magnetic flux terms. While there have been theoretical proposals including elaborate atomic-scale engineering, identifying candidate topological Haldane model materials has not been successful, and the first experimental realization was recently made in ultracold atoms. Here, we suggest that a series of Fe-based honeycomb ferromagnetic insulators, AFe2(PO4)2 (A=Ba, Cs, K, La) possess Chern bands described by the topological Haldane model. How to detect the quantum anomalous Hall effect is also discussed.},
	author = {Kim, Heung-Sik and Kee, Hae-Young},
	da = {2017/04/03},
	date-added = {2022-07-01 18:16:28 -0500},
	date-modified = {2022-07-01 18:16:28 -0500},
	doi = {10.1038/s41535-017-0021-z},
	id = {Kim2017},
	isbn = {2397-4648},
	journal = {npj Quantum Materials},
	number = {1},
	pages = {20},
	title = {Realizing Haldane model in Fe-based honeycomb ferromagnetic insulators},
	ty = {JOUR},
	url = {https://doi.org/10.1038/s41535-017-0021-z},
	volume = {2},
	year = {2017},
	Bdsk-Url-1 = {https://doi.org/10.1038/s41535-017-0021-z}}

@article{haldaneexp,
	abstract = {The Haldane model, which predicts complex topological states of matter, has been implemented by placing ultracold atoms in a tunable optical lattice that was deformed and shaken.},
	author = {Jotzu, Gregor and Messer, Michael and Desbuquois, R{\'e}mi and Lebrat, Martin and Uehlinger, Thomas and Greif, Daniel and Esslinger, Tilman},
	da = {2014/11/01},
	date-added = {2022-06-21 09:56:52 -0500},
	date-modified = {2022-06-21 09:56:52 -0500},
	doi = {10.1038/nature13915},
	id = {Jotzu2014},
	isbn = {1476-4687},
	journal = {Nature},
	number = {7526},
	pages = {237--240},
	title = {Experimental realization of the topological Haldane model with ultracold fermions},
	ty = {JOUR},
	url = {https://doi.org/10.1038/nature13915},
	volume = {515},
	year = {2014},
	Bdsk-Url-1 = {https://doi.org/10.1038/nature13915}}


@article{Blankenbecler,
  title = {Monte Carlo calculations of coupled boson-fermion systems. I},
  author = {Blankenbecler, R. and Scalapino, D. J. and Sugar, R. L.},
  journal = {Phys. Rev. D},
  volume = {24},
  issue = {8},
  pages = {2278--2286},
  numpages = {0},
  year = {1981},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevD.24.2278},
  url = {https://link.aps.org/doi/10.1103/PhysRevD.24.2278}
}

@article{Hirsch,
  title = {Two-dimensional Hubbard model: Numerical simulation study},
  author = {Hirsch, J. E.},
  journal = {Phys. Rev. B},
  volume = {31},
  issue = {7},
  pages = {4403--4419},
  numpages = {0},
  year = {1985},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.31.4403},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.31.4403}
}

@article{White,
  title = {Numerical study of the two-dimensional Hubbard model},
  author = {White, S. R. and Scalapino, D. J. and Sugar, R. L. and Loh, E. Y. and Gubernatis, J. E. and Scalettar, R. T.},
  journal = {Phys. Rev. B},
  volume = {40},
  issue = {1},
  pages = {506--516},
  numpages = {0},
  year = {1989},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.40.506},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.40.506}
}


@misc{Mai,
  doi = {10.48550/ARXIV.2205.08545},
  
  url = {https://arxiv.org/abs/2205.08545},
  
  author = {Mai, Peizhi and Huang, Edwin W. and Yu, Jiachen and Feldman, Benjamin E. and Phillips, Philip W.},
  
  keywords = {Strongly Correlated Electrons (cond-mat.str-el), FOS: Physical sciences, FOS: Physical sciences},
  
  title = {Interaction-driven Spontaneous Ferromagnetic Insulating States with Odd Chern Numbers},
  
  publisher = {arXiv},
  
  year = {2022},
  
  copyright = {Creative Commons Attribution 4.0 International}
}

@misc{qf2,
      title={Itinerant topological magnons in Haldane Hubbard model with a nearly-flat electron band}, 
      author={Zhao-Long Gu and Zhao-Yang Dong and Shun-Li Yu and Jian-Xin Li},
      year={2019},
      eprint={1908.09255},
      archivePrefix={arXiv},
      primaryClass={cond-mat.str-el}
}

@article{qf1,
  title = {Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model},
  author = {Leite, Leonardo S. G. and Doretto, R. L.},
  journal = {Phys. Rev. B},
  volume = {104},
  issue = {15},
  pages = {155129},
  numpages = {17},
  year = {2021},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.104.155129},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.104.155129}
}

@article{senechal,
  title = {Quarter-filled Kitaev-Hubbard model: A quantum Hall state in an optical lattice},
  author = {Hassan, S. R. and Goyal, Sandeep and Shankar, R. and S\'en\'echal, David},
  journal = {Phys. Rev. B},
  volume = {88},
  issue = {4},
  pages = {045301},
  numpages = {7},
  year = {2013},
  month = {Jul},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.88.045301},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.88.045301}
}


@article{herbut,
  title = {Topological Mott Insulator in Three-Dimensional Systems with Quadratic Band Touching},
  author = {Herbut, Igor F. and Janssen, Lukas},
  journal = {Phys. Rev. Lett.},
  volume = {113},
  issue = {10},
  pages = {106401},
  numpages = {5},
  year = {2014},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.113.106401},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.113.106401}
}
@article{peierls,
	abstract = {Es wird untersucht, wann sich in der Quantenstatistik die freie Energie ohne Kenntnis der station{\"a}ren Zust{\"a}nde des Systems berechnen l{\"a}{\ss}t. Mit den hierbei entwickelten Methoden wird die diamagnetische Suszeptibilit{\"a}t von freien Elektronen, ihre Beeinflussung durch die Zusammenst{\"o}{\ss}e und das magnetische Verhalten gebundener Elektronen untersucht. Es wird festgestellt, bis zu welchen Feldst{\"a}rken die Suszeptibilit{\"a}t feldunabh{\"a}ngig ist.},
	author = {Peierls, R. },
	da = {1933/11/01},
	date-added = {2022-04-11 11:14:48 -0500},
	date-modified = {2022-04-11 11:15:02 -0500},
	doi = {10.1007/BF01342591},
	id = {Peierls1933},
	isbn = {0044-3328},
	journal = {Zeitschrift f{\"u}r Physik},
	number = {11},
	pages = {763--791},
	title = {Zur Theorie des Diamagnetismus von Leitungselektronen},
	ty = {JOUR},
	url = {https://doi.org/10.1007/BF01342591},
	volume = {80},
	year = {1933},
	Bdsk-Url-1 = {https://doi.org/10.1007/BF01342591}}


@article{pesinbalents,
	abstract = {Recent theory and experiment have revealed that strong spin--orbit coupling can have marked qualitative effects on the band structure of weakly interacting solids, leading to a distinct phase of matter, the topological band insulator. We show that spin--orbit interaction also has quantitative and qualitative effects on the correlation-driven Mott insulator transition. Taking Ir-based pyrochlores as a specific example, we predict that for weak electron--electron interaction Ir electrons are in metallic and topological band insulator phases at weak and strong spin--orbit interaction, respectively. We show that by increasing the electron--electron interaction strength, the effects of spin--orbit coupling are enhanced. With increasing interactions, the topological band insulator is transformed into a `topological Mott insulator'phase having gapless surface spin-only excitations. The proposed phase diagram also includes a region of gapless Mott insulator with a spinon Fermi surface, and a magnetically ordered state at still larger electron--electron interaction.},
	author = {Pesin, Dmytro and Balents, Leon},
	da = {2010/05/01},
	date-added = {2022-06-02 22:52:23 -0500},
	date-modified = {2022-06-02 22:52:23 -0500},
	doi = {10.1038/nphys1606},
	id = {Pesin2010},
	isbn = {1745-2481},
	journal = {Nature Physics},
	number = {5},
	pages = {376--381},
	title = {Mott physics and band topology in materials with strong spin--orbit interaction},
	ty = {JOUR},
	url = {https://doi.org/10.1038/nphys1606},
	volume = {6},
	year = {2010},
	Bdsk-Url-1 = {https://doi.org/10.1038/nphys1606}}


@article{Kuno,
	doi = {10.1088/1367-2630/aa99d0},
	url = {https://doi.org/10.1088/1367-2630/aa99d0},
	year = 2017,
	month = {dec},
	publisher = {{IOP} Publishing},
	volume = {19},
	number = {12},
	pages = {123025},
	author = {Yoshihito Kuno and Keita Shimizu and Ikuo Ichinose},
	title = {Various topological Mott insulators and topological bulk charge pumping in strongly-interacting boson system in one-dimensional superlattice},
	journal = {New Journal of Physics},
	abstract = {In this paper, we study a one-dimensional boson system in a superlattice potential. This system is experimentally feasible by using ultracold atomic gases, and attracts much attention these days. It is expected that the system has a topological phase called a topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with a non-vanishing integer Chern number. Compared to the hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization, we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., the topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefore the Chern number is to be observed in feasible experiments.}
}

@article{sri,
  title = {Topological Mott Insulators},
  author = {Raghu, S. and Qi, Xiao-Liang and Honerkamp, C. and Zhang, Shou-Cheng},
  journal = {Phys. Rev. Lett.},
  volume = {100},
  issue = {15},
  pages = {156401},
  numpages = {4},
  year = {2008},
  month = {Apr},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.100.156401},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.100.156401}
}

@article{Haldane,
  title = {Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the "Parity Anomaly"},
  author = {Haldane, F. D. M.},
  journal = {Phys. Rev. Lett.},
  volume = {61},
  issue = {18},
  pages = {2015--2018},
  numpages = {0},
  year = {1988},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.61.2015},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.61.2015}
}

@article{spinhallscz,
  title = {Spin-Hall Insulator},
  author = {Murakami, Shuichi and Nagaosa, Naoto and Zhang, Shou-Cheng},
  journal = {Phys. Rev. Lett.},
  volume = {93},
  issue = {15},
  pages = {156804},
  numpages = {4},
  year = {2004},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.93.156804},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.93.156804}
}

@article{asym,
	author = {Yu, Yijun and Ma, Liguo and Cai, Peng and Zhong, Ruidan and Ye, Cun and Shen, Jian and Gu, G. D. and Chen, Xian Hui and Zhang, Yuanbo},
	da = {2019/11/01},
	date-added = {2022-02-27 13:51:29 -0600},
	date-modified = {2022-02-27 14:04:27 -0600},
	doi = {10.1038/s41586-019-1718-x},
	id = {Yu2019},
	isbn = {1476-4687},
	journal = {Nature},
	number = {7781},
	pages = {156--163},
	title = {High-temperature superconductivity in monolayer {B}i$_2${S}r$_2${C}a{C}u$_2${O}$_{8+\delta}$},
	ty = {JOUR},
	url = {https://doi.org/10.1038/s41586-019-1718-x},
	volume = {575},
	year = {2019},
	Bdsk-Url-1 = {https://doi.org/10.1038/s41586-019-1718-x}}

@article{lanzarapha,
	author = {Miller, Tristan L. and Zhang, Wentao and Eisaki, Hiroshi and Lanzara, Alessandra},
	date-added = {2020-12-14 12:47:32 -0600},
	date-modified = {2020-12-14 12:47:54 -0600},
	doi = {10.1103/PhysRevLett.118.097001},
	issue = {9},
	journal = {Phys. Rev. Lett.},
	month = {Feb},
	numpages = {6},
	pages = {097001},
	publisher = {American Physical Society},
	title = {Particle-Hole Asymmetry in the Cuprate Pseudogap Measured with Time-Resolved Spectroscopy},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.118.097001},
	volume = {118},
	year = {2017},
	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.118.097001},
	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.118.097001}}

@article{pickettpha,
	author = {Ghosh, Soham S. and Quan, Yundi and Pickett, Warren E.},
	date-added = {2020-12-14 12:46:31 -0600},
	date-modified = {2020-12-14 12:46:40 -0600},
	doi = {10.1103/PhysRevB.100.094521},
	issue = {9},
	journal = {Phys. Rev. B},
	month = {Sep},
	numpages = {7},
	pages = {094521},
	publisher = {American Physical Society},
	title = {Strong particle-hole asymmetry in a 200 Kelvin superconductor},
	url = {https://link.aps.org/doi/10.1103/PhysRevB.100.094521},
	volume = {100},
	year = {2019},
	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevB.100.094521},
	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevB.100.094521}}

@article{singhpha,
	abstract = {We investigate the temperature evolution of the electronic states in the vicinity of the Fermi level of a non-Fermi-liquid (NFL) system, CaRuO3 using ultra high-resolution photoemission spectroscopy; isostructural SrRuO3 exhibiting Fermi-liquid behavior despite similar electron interaction parameters as that of CaRuO3, is used as a reference. High-energy resolution in this study helps to reveal particle-hole asymmetry in the excitation spectra of CaRuO3 in contrast to that in SrRuO3. In addition, we observe signature of phonon excitations in the photoemission spectra of CaRuO3 at finite temperatures while these are weak in SrRuO3.},
	author = {K Maiti and R. S Singh and V. R. R Medicherla},
	date-added = {2020-12-14 12:40:00 -0600},
	date-modified = {2020-12-14 12:40:12 -0600},
	doi = {10.1209/0295-5075/78/17002},
	journal = {Europhysics Letters ({EPL})},
	month = {mar},
	number = {1},
	pages = {17002},
	publisher = {{IOP} Publishing},
	title = {Observation of particle hole asymmetry and phonon excitations in non-Fermi-liquid systems: A high-resolution photoemission study of ruthenates},
	url = {https://doi.org/10.1209%2F0295-5075%2F78%2F17002},
	volume = {78},
	year = 2007,
	Bdsk-Url-1 = {https://doi.org/10.1209%2F0295-5075%2F78%2F17002},
	Bdsk-Url-2 = {https://doi.org/10.1209/0295-5075/78/17002}}

@article{jwilkins,
	author = {Silva, J. B. and Lima, W. L. C. and Oliveira, W. C. and Mello, J. L. N. and Oliveira, L. N. and Wilkins, J. W.},
	date-added = {2020-12-13 23:42:45 -0600},
	date-modified = {2020-12-13 23:42:53 -0600},
	doi = {10.1103/PhysRevLett.76.275},
	issue = {2},
	journal = {Phys. Rev. Lett.},
	month = {Jan},
	numpages = {0},
	pages = {275--278},
	publisher = {American Physical Society},
	title = {Particle-Hole Asymmetry in the Two-Impurity Kondo Model},
	url = {https://link.aps.org/doi/10.1103/PhysRevLett.76.275},
	volume = {76},
	year = {1996},
	Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevLett.76.275},
	Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.76.275}}


@article{davis2004,
	abstract = {The phase diagram of hole-doped copper oxides shows four different electronic phases existing at zero temperature. Familiar among these are the Mott insulator, high-transition-temperature superconductor and metallic phases. A fourth phase, of unknown identity, occurs at light doping along the zero-temperature bound of the `pseudogap'regime1. This regime is rich in peculiar electronic phenomena1, prompting numerous proposals that it contains some form of hidden electronic order. Here we present low-temperature electronic structure imaging studies of a lightly hole-doped copper oxide: Ca2-xNaxCuO2Cl2. Tunnelling spectroscopy (at energies {$|$}E{$|$} > 100 meV) reveals electron extraction probabilities greatly exceeding those for injection, as anticipated for a doped Mott insulator. However, for {$|$}E{$|$} < 100 meV, the spectrum exhibits a V-shaped energy gap centred on E = 0. States within this gap undergo intense spatial modulations, with the spatial correlations of a four CuO2-unit-cell square `checkerboard', independent of energy. Intricate atomic-scale electronic structure variations also exist within the checkerboard. These data are consistent with an unanticipated crystalline electronic state, possibly the hidden electronic order, existing in the zero-temperature pseudogap regime of Ca2-xNaxCuO2Cl2.},
	author = {Hanaguri, T. and Lupien, C. and Kohsaka, Y. and Lee, D. -H. and Azuma, M. and Takano, M. and Takagi, H. and Davis, J. C.},
	da = {2004/08/01},
	date-added = {2020-12-13 15:48:15 -0600},
	date-modified = {2020-12-13 15:48:44 -0600},
	doi = {10.1038/nature02861},
	id = {Hanaguri2004},
	isbn = {1476-4687},
	journal = {Nature},
	number = {7003},
	pages = {1001--1005},
	title = {A `checkerboard'electronic crystal state in lightly hole-doped Ca2-xNaxCuO2Cl2},
	ty = {JOUR},
	url = {https://doi.org/10.1038/nature02861},
	volume = {430},
	year = {2004},
	Bdsk-Url-1 = {https://doi.org/10.1038/nature02861}}

@article{AHO4,
	abstract = {We point out that the quasiparticle spectrum of the Landau Fermi liquid theory has an extra Z2 symmetry, local in momentum space, which is not generic to the Hamiltonian with interactions. Thus the Fermi liquid is in this sense a (quantum) zero-temperature critical point.},
	author = {Anderson, Philip W. and Haldane, F. Duncan M.},
	da = {2001/05/01},
	date-added = {2020-12-15 14:12:54 -0600},
	date-modified = {2020-12-15 14:13:33 -0600},
	doi = {10.1023/A:1010324912515},
	id = {Anderson2001},
	isbn = {1572-9613},
	journal = {Journal of Statistical Physics},
	number = {3},
	pages = {425--428},
	title = {The Symmetries of Fermion Fluids at Low Dimensions},
	ty = {JOUR},
	url = {https://doi.org/10.1023/A:1010324912515},
	volume = {103},
	year = {2001},
	Bdsk-Url-1 = {https://doi.org/10.1023/A:1010324912515}}
	
@article{Thouless,
  title = {Quantized Hall Conductance in a Two-Dimensional Periodic Potential},
  author = {Thouless, D. J. and Kohmoto, M. and Nightingale, M. P. and den Nijs, M.},
  journal = {Phys. Rev. Lett.},
  volume = {49},
  issue = {6},
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  numpages = {0},
  year = {1982},
  month = {Aug},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.49.405},
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}
@article{L0,
  title = {Quantized Hall conductivity in two dimensions},
  author = {Laughlin, R. B.},
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  numpages = {0},
  year = {1981},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.23.5632},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.23.5632}
}
@article{bhz,
	doi = {10.1126/science.1133734},
  
	url = {https://doi.org/10.11262Fscience.1133734},
  
	year = 2006,
	month = {dec},
  
	publisher = {American Association for the Advancement of Science ({AAAS})},
  
	volume = {314},
  
	number = {5806},
  
	pages = {1757--1761},
  
	author = {B. Andrei Bernevig and Taylor L. Hughes and Shou-Cheng Zhang},
  
	title = {Quantum Spin Hall Effect and Topological Phase Transition in {HgTe} Quantum Wells},
  
	journal = {Science}
}

@article{haldanesym,
  title = {Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States},
  author = {Haldane, F. D. M.},
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  issue = {7},
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  numpages = {0},
  year = {1983},
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  doi = {10.1103/PhysRevLett.51.605},
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}

@ARTICLE{xsede,
  author={Towns, John and Cockerill, Timothy and Dahan, Maytal and Foster, Ian and Gaither, Kelly and Grimshaw, Andrew and Hazlewood, Victor and Lathrop, Scott and Lifka, Dave and Peterson, Gregory D. and Roskies, Ralph and Scott, J. Ray and Wilkins-Diehr, Nancy},
  journal={Computing in Science   Engineering}, 
  title={XSEDE: Accelerating Scientific Discovery}, 
  year={2014},
  volume={16},
  number={5},
  pages={62-74},
  doi={10.1109/MCSE.2014.80}}

@article{semenoff,
  title = {Condensed-Matter Simulation of a Three-Dimensional Anomaly},
  author = {Semenoff, Gordon W.},
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  issue = {26},
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  numpages = {0},
  year = {1984},
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  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.53.2449},
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}


@article{ong,
title = {Theory of asymmetric tunneling in the cuprate superconductors},
journal = {Journal of Physics and Chemistry of Solids},
volume = {67},
number = {1},
pages = {1-5},
year = {2006},
note = {Spectroscopies in Novel Superconductors 2004},
issn = {0022-3697},
doi = {https://doi.org/10.1016/j.jpcs.2005.10.132},
url = {https://www.sciencedirect.com/science/article/pii/S0022369705004063},
author = {P.W. Anderson and N.P. Ong},
abstract = {We explain quantitatively, within the Gutzwiller-Resonating Valence Bond theory, the puzzling observation of tunneling conductivity between a metallic point and a cuprate high-Tc superconductor which is markedly asymmetric between positive and negative voltage biases. The asymmetric part does not have a âcoherence peakâ but does show structure due to the gap. The fit to data is satisfactory within the over-simplifications of the theory; in particular, it explains the marked âpeak-dip-humpâ structure observed on the hole side and a number of other qualitative observations. This asymmetry is strong evidence for the projective nature of the ground state and hence for ât-Jâ physics.}
}
@article{laughlin,
  title = {Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations},
  author = {Laughlin, R. B.},
  journal = {Phys. Rev. Lett.},
  volume = {50},
  issue = {18},
  pages = {1395--1398},
  numpages = {0},
  year = {1983},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.50.1395},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.50.1395}
}
@misc{rahulroy2,
  doi = {10.48550/ARXIV.COND-MAT/0603271},
  
  url = {https://arxiv.org/abs/cond-mat/0603271},
  
  author = {Roy, Rahul},
  
  keywords = {Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Physical sciences, FOS: Physical sciences},
  
  title = {Integer Quantum Hall Effect on a Square Lattice with Zero Net Magnetic Field}}
  
  @article{jmoore,
  title = {Topological invariants of time-reversal-invariant band structures},
  author = {Moore, J. E. and Balents, L.},
  journal = {Phys. Rev. B},
  volume = {75},
  issue = {12},
  pages = {121306},
  numpages = {4},
  year = {2007},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.75.121306},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.75.121306}
}

@article{rahulroy1,
  title = {${Z}_{2}$ classification of quantum spin Hall systems: An approach using time-reversal invariance},
  author = {Roy, Rahul},
  journal = {Phys. Rev. B},
  volume = {79},
  issue = {19},
  pages = {195321},
  numpages = {4},
  year = {2009},
  month = {May},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.79.195321},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.79.195321}
}

@article{parameswaran,
title = {Fractional quantum Hall physics in topological flat bands},
journal = {Comptes Rendus Physique},
volume = {14},
number = {9},
pages = {816-839},
year = {2013},
note = {Topological insulators / Isolants topologiques},
issn = {1631-0705},
doi = {https://doi.org/10.1016/j.crhy.2013.04.003},
url = {https://www.sciencedirect.com/science/article/pii/S163107051300073X},
author = {Siddharth A. Parameswaran and Rahul Roy and Shivaji L. Sondhi},
keywords = {Chern insulators, Flat bands, Fractional quantum Hall effect, Topological order, Isolants de Chern, Bandes plates, Effet Hall fractionnaire, Ordre topologique},
abstract = {We present a pedagogical review of the physics of fractional Chern insulators with a particular focus on the connection to the fractional quantum Hall effect. While the latter conventionally arises in semiconductor heterostructures at low temperatures and in high magnetic fields, interacting Chern insulators at fractional band filling may host phases with the same topological properties, but stabilized at the lattice scale, potentially leading to high-temperature topological order. We discuss the construction of topological flat band models, provide a survey of numerical results, and establish the connection between the Chern band and the continuum Landau problem. We then briefly summarize various aspects of Chern band physics that have no natural continuum analogs, before turning to a discussion of possible experimental realizations. We close with a survey of future directions and open problems, as well as a discussion of extensions of these ideas to higher dimensions and to other topological phases.
RÃ©sumÃ©
Nous prÃ©sentons une revue didactique sur la physique des isolants de Chern, qui se concentre plus particuliÃšrement sur lÊŒeffet Hall quantique fractionnaire. Habituellement, cet effet apparaÃ®t typiquement dans des hÃ©tÃ©rostructures semiconductrices Ã  basse tempÃ©rature et sous champ magnÃ©tique fort. En revanche, les isolants de Chern peuvent abriter des phases topologiques aux propriÃ©tÃ©s similaires, mais stabilisÃ©es Ã  lÊŒÃ©chelle du paramÃštre de rÃ©seau, ce qui peut conduire un ordre topologique Ã  haute tempÃ©rature. Nous dÃ©crivons la construction des modÃšles avec bande(s) plate(s), passons en revue les rÃ©sultats numÃ©riques et Ã©tablissons une comparaison entre les isolants de Chern sur rÃ©seau et le problÃšme de Landau dÃ©fini dans le continuum. Nous discutons alors briÃšvement les aspects de la physique des isolants de Chern qui nont pas dÊŒanalogues dans le continuum, avant de passer aux possibles rÃ©alisations expÃ©rimentales. Nous concluons par une liste de perspectives et de problÃšmes encore ouverts dans ce domaine, ainsi que par une discussion des extensions de ces idÃ©es Ã  des dimensions supÃ©rieures et Ã  dÊŒautres phases topologiques.}
}

@article{chamonprl,
  title = {Fractional Quantum Hall States at Zero Magnetic Field},
  author = {Neupert, Titus and Santos, Luiz and Chamon, Claudio and Mudry, Christopher},
  journal = {Phys. Rev. Lett.},
  volume = {106},
  issue = {23},
  pages = {236804},
  numpages = {4},
  year = {2011},
  month = {Jun},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.106.236804},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.106.236804}
}

@article{neupert,
  title = {Fractional topological liquids with time-reversal symmetry and their lattice realization},
  author = {Neupert, Titus and Santos, Luiz and Ryu, Shinsei and Chamon, Claudio and Mudry, Christopher},
  journal = {Phys. Rev. B},
  volume = {84},
  issue = {16},
  pages = {165107},
  numpages = {13},
  year = {2011},
  month = {Oct},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevB.84.165107},
  url = {https://link.aps.org/doi/10.1103/PhysRevB.84.165107}
}


@article{fukanemele,
  title = {Topological Insulators in Three Dimensions},
  author = {Fu, Liang and Kane, C. L. and Mele, E. J.},
  journal = {Phys. Rev. Lett.},
  volume = {98},
  issue = {10},
  pages = {106803},
  numpages = {4},
  year = {2007},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.98.106803},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.98.106803}
}


@article{kanemele,
  title = {${Z}_{2}$ Topological Order and the Quantum Spin Hall Effect},
  author = {Kane, C. L. and Mele, E. J.},
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  volume = {95},
  issue = {14},
  pages = {146802},
  numpages = {4},
  year = {2005},
  month = {Sep},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.95.146802},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.95.146802}
}

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  title = {Universal Intrinsic Spin Hall Effect},
  author = {Sinova, Jairo and Culcer, Dimitrie and Niu, Q. and Sinitsyn, N. A. and Jungwirth, T. and MacDonald, A. H.},
  journal = {Phys. Rev. Lett.},
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  numpages = {4},
  year = {2004},
  month = {Mar},
  publisher = {American Physical Society},
  doi = {10.1103/PhysRevLett.92.126603},
  url = {https://link.aps.org/doi/10.1103/PhysRevLett.92.126603}
}

@article{HK,
author = {Hatsugai ,Yasuhiro and Kohmoto ,Mahito},
title = {Exactly Solvable Model of Correlated Lattice Electrons   in Any Dimensions},
journal = {Journal of the Physical Society of Japan},
volume = {61},
number = {6},
pages = {2056-2069},
year = {1992},
doi = {10.1143/JPSJ.61.2056},
URL = {https://doi.org/10.1143/JPSJ.61.2056},
eprint = {https://doi.org/10.1143/JPSJ.61.2056}}



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	volume = {16},
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	author = {Philip W. Phillips and Luke Yeo and Edwin W. Huang},
	title = {Exact theory for superconductivity in a doped Mott insulator},
	journal = {Nature Physics}}
	
@article{HKnp2,
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	url = {https://doi.org/10.1038%2Fs41567-022-01529-8},
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	publisher = {Springer Science and Business Media {LLC}},
	volume = {18},
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	author = {Edwin W. Huang and Gabriele La Nave and Philip W. Phillips},
	title = {Discrete symmetry breaking defines the Mott quartic fixed point},
	journal = {Nature Physics}}
	
	
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}

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}

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  title = {Statistical analysis of the Chern number in the interacting Haldane-Hubbard model},
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}
