Ziegler, L.Tirrito, E.Lewenstein, M.Hands, S.Bermúdez Carballo, Alejandro2023-06-222023-06-222022-040003-491610.1016/j.aop.2022.168763https://hdl.handle.net/20.500.14352/71560CRUE-CSIC (Acuerdos Transformativos 2022). © 2022 The Author(s). His is an open access article under the CC BY-NC-ND license. The ICFO group acknowledges support from ERC AdG NOQIA, State Research Agency AEI (‘‘Severo Ochoa’’ Center of Excellence CEX2019-000910-S) Plan National FIDEUA PID2019-106901GB-I00 project funded by MCIN/AEI /10.13039/501100011033, FPI, QUANTERA MAQS PCI2019-111828-2 project funded by MCIN/AEI /10.13039/501100011033, Proyectos de I+D+I ‘‘Retos Colaboración’’ RTC2019-007196-7 project funded by MCIN/AEI /10.13039/501100011033, Fundació Privada Cellex, Fundació Mir-Puig, Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341, CERCA program, QuantumCAT U16-011424, co-funded by ERDF Operational Program of Catalonia 2014–2020), EU Horizon 2020 FET-OPEN OPTOLogic (Grant No 899794), and the National Science Centre, Poland (Symfonia Grant No. 2016/20/W/ST4/00314), Marie Skłodowska-Curie grant STREDCH No 101029393, ‘‘La Caixa’’ Junior Leaders fellowships (ID100010434), and EU Horizon 2020 under Marie Skłodowska-Curie grant agreement No. 847648 (LCF/BQ/PI19/11690013, LCF/BQ/PI20/11760031, LCF/BQ/PR20/11770012).). A.B. acknowledges support from the Ramón y Cajal program RYC- 2016-20066, CAM/FEDER Project S2018/TCS- 4342 (QUITEMADCM), and PGC2018-099169-B-I00 (MCIU/AEI/FEDER, UE). S.J.H. acknowledges the support of STFC grant ST/T000813Four-Fermi quantum field theories in (2+1) dimensions lie among the simplest models in high-energy physics, the understanding of which requires a non-perturbative lattice formulation addressing their strongly-coupled fixed points. These lattice models are also relevant in condensed matter, as they offer a neat playground to explore strong correlations in the quantum anomalous Hall (QAH) effect. We give a detailed description of our multidisciplinary approach to understand the fate of the QAH phases as the four-Fermi interactions are increased, which combines strong-coupling and effective-potential techniques, unveiling a rich phase diagram with large -N Chern insulators and Lorentz breaking fermion condensates. Moreover, this toolbox can be enlarged with recent advances in quantum information science, as we show that tensor-network algorithms based on projected entangled pairs can be used to improve our understanding of the strong-coupling limit. We also present a detailed scheme that uses ultra-cold atoms in optical lattices with synthetic spin- orbit coupling to build quantum simulators of these four-Fermi models. This yields a promising alternative to characterize the strongly-coupled fixed points and, moreover, could also explore real-time dynamics and finite-fermion densities.(c) 2022 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).engAtribución-NoComercial-SinDerivadas 3.0 Españahttps://creativecommons.org/licenses/by-nc-nd/3.0/es/journal articlehttps://doi.org/10.1016/j.aop.2022.168763https://www.sciencedirect.comopen access53Correlated Chern insulatorsQuantum anomalous Hall effectFour-Fermi lattice field theoriesLarge-N methods tensor networksFísica (Física)22 Física