We investigate an effect that an ideal Lorenz number $L_{\rm i}$ of correlated metal shows peculiar Fermi surface dependence, which is caused by the onset of a particular channel of Umklapp scattering. We evaluate $L_{\rm i}$ for some simple models and transition metals, and note that $L_{\rm i}$ for Na$_x$CoO$_2$ decreases sensitively as $x$ approaches an Umklapp threshold around $x_c \simeq 0.6$.
The Lorenz ratio serves as a measure to compare thermal and electric conductivities of metals. Recent experiments observed small Lorenz ratios in the compensated metal WP$_2$, indicating that charge flow is strongly favored over heat conduction. Motivated by these findings, we study transport properties of compensated metals in the presence of electron-electron collisions and electron-impurity scattering. We focus on intermediate temperatures, where the phonon contributions to transport are weak and elastic and inelastic scattering rates are comparable. Our exact solution for the kinetic equat…
In this article we study the thermal response functions for two one-dimensional models, namely the Hubbard and spin-less fermion $t$-$V$ models. By exactly diagonalizing finite sized systems we calculate dynamical electrical, thermoelectrical, and thermal conductivities via the Kubo formalism. The thermopower (Seebeck coefficient), Lorenz number, and dimensionless figure of merit are then constructed which are quantities of great interest to the physics community both theoretically and experimentally. We also geometrically frustrate these systems and destroy integrability by the inclusion of a…
The temperature dependent properties of heat capacity, heat conductivity and Hall-Lorenz ratio have been solved numerically after taking the previously proposed ionization energy based Fermi-Dirac statistics and the coexistence of Fermi and charge-spin separated liquid into account. The thermo-magneto-electronic properties are entirely for spin and charge carriers, hence the phonon contribution has been neglected. A linear dependence between the Hall-Lorenz ratio and temperature ($T$) is also obtained in accordance with the experimental results for overdoped YBa$_2$Cu$_3$O$_{7-δ}$, if these co…
The 2D models of heat capacity, its conductivity ($κ$), Hall resistance ($R_H$) and the Lorenz ratio ($\mathcal{L}$) have been derived using the ionization energy ($E_I$) based Fermi-Dirac statistics (iFDS). These models reproduce the experimentally measured $ρ(T)$ and $R_H(T)$. The variation of $\mathcal{L}$ is proportional to 1/T due to electron-phonon ($e$-$ph$) scattering in $κ$. However, the $e$-$ph$ coupling in the electrical resistivity has the polaronic effect that complies with iFDS, rather than the $e$-$ph$ scattering that satisfies the Bloch-Grüneisen formula. These models are purel…
We analyze the effect of contact resistance on the Lorenz number measurement based on direct electronic thermal conductivity experiments. The contact resistance can significantly limit the experimental measured value when the Lorenz number is enhanced, but not as much so when it is suppressed, should the Wiedemann-Franz law be violated. The result provides the conditions of the potential false negative error and highlights the importance of improving the contact resistance in studying non-Fermi liquid behavior in thermal transport experiments.
Thermal response functions of strongly correlated electron systems are of appreciable interest to the larger scientific community both theoretically and technologically. Here we focus on the infinitely correlated t-J model on a geometrically frustrated two-dimensional triangular lattice. Using exact diagonalization on a finite sized system we calculate the dynamical thermal response functions in order to determine the thermopower, Lorenz number, and dimensionless figure of merit. The dynamical thermal response functions is compared to the infinite frequency limit and shown to be very weak func…
We introduce and analyze two different scenarios for violation of the Wiedemann-Franz law in strongly correlated electron systems of solids, close to a topological quantum critical point (TQCP) where the density of states $N(0)$ diverges. The first, applicable to the Fermi-liquid (FL) side of the TQCP, involves a transverse zero-sound collective mode that opens a new channel for the thermal conductivity, thereby enhancing the Lorenz number $L(0)$ relative to the value $L_0=π^2k^2_B/3e^2$ dictated by conventional FL theory. The second mechanism for violation of the WF law, relevant to the non-F…
Correlated density matrix theory is generalized to investigate equilibrium properties of normal Fermi Liquids such as 3He and nuclear matter at nonzero temperatures. The results also generalize the Fermi-hypernetted-chain technique that is familiar from studies of the ground state of correlated fermions. By employing the concept of renormalized bosons and fermions the formal results are cast in a form that permits the direct evaluation of the statistical properties of the correlated liquid such as the entropy and the specific heat at constant volume among other quantities.
A topological crossover, associated with the collapse of the Fermi surface in strongly correlated Fermi systems, is examined. It is demonstrated that in these systems, the temperature domain where standard Fermi liquid results hold dramatically narrows, because the Landau regime is replaced by a classical one. The impact of the collapse of the Fermi surface on pairing correlations is analyzed. In the domain of the Lifshitz phase diagram where the Fermi surface collapses, splitting of the BCS superconducting phase transition into two different ones of the same symmetry is shown to occur.
A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point is studied within the Fermi liquid approach. The transition occurs between two topologically equivalent states, each with three sheets of the Fermi surface. One of these states possesses a quasiparticle halo in the quasiparticle momentum distribution $n(p)$, while the other, the hole pocket. The transition is found to be of the first order with respect to both the coupling constant $g$ and the temperature $T$. The phase diagram of the system in the vicinity of this transition is constr…
Basing on the density functional theory of fermion condensation, we analyze the non-Fermi liquid behavior of strongly correlated Fermi-systems such as heavy-fermion metals. When deriving equations for the effective mass of quasiparticles, we consider solids with a lattice and homogeneous systems. We show that the low-temperature thermodynamic and transport properties are formed by quasiparticles, while the dependence of the effective mass on temperature, number density, magnetic fields, etc gives rise to the non-Fermi liquid behavior. Our theoretical study of the heat capacity, magnetization, …
The reason for the appearance of two distinct bands in the photoemission of the single CuO$_2$ plane Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+δ}$ near the Fermi level is discussed on the basis of the self-consistent solution of the two-dimensional t-J model.
The low-temperature kinetics of the strongly correlated electron liquid inhabiting a solid is analyzed. It is demonstrated that a softly damped branch of transverse zero sound emerges when several bands cross the Fermi surface simultaneously near a quantum critical point at which the density of states diverges. Suppression of the damping of this branch occurs due to a mechanism analogous to that affecting the phonon mode in solids at room temperature, giving rise to a classical regime of transport at extremely low temperatures in the strongly correlated Fermi system.
A number of recent experiments have highlighted a remarkable transformation of a large cuprate Fermi surface into small pockets in the underdoped region signalling a breakdown of a conventional Fermi liquid theory in the PG phase. A few phenomenological models have been recently put forward to account for this transformation. However, none of those models have been derived microscopically nor are totally compatible with experimental data. In the present work we show that the observed Fermi-surface reconstruction can be accounted for directly within a standard microscopic $t-J$ model of correla…
We present theoretical results for the optical conductivity and the non-resonant Raman susceptibilities for three principal polarization geometries relevant to the square lattice. The susceptibilities are obtained using the recently developed extremely correlated Fermi liquid theory for the two-dimensional t-t'-J model, where t and t' are the nearest and second neighbor hopping. Our results are sensitively depending on t, t'. By studying this quartet of related dynamical susceptibilities, and their dependence on t, t', doping and temperature, we provide a useful framework for interpreting and …
We characterize the electron doping evolution of (Sr$_{1-x}$La$_x$)$_3$Ir$_2$O$_7$ by means of angle-resolved photoemission. Concomitant with the metal insulator transition around $x\approx0.05$ we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume $3x/2$, where $x$ is the independently measured La concentration. The quasiparticle weight $Z$ remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion. This indicates a conventional, weakly correlated Fermi liquid state with a momentum ind…
Strongly correlated Fermi systems are fundamental systems in physics that are best studied experimentally, which until very recently have lacked theoretical explanations. This review discusses the construction of a theory and the analysis of phenomena occurring in strongly correlated Fermi systems such as heavy-fermion (HF) metals and two-dimensional (2D) Fermi systems. It is shown that the basic properties and the scaling behavior of HF metals can be described within the framework of a fermion condensation quantum phase transition (FCQPT) and extended quasiparticle paradigm that allow us to e…
The spin susceptibility $χ(T)$ of strongly correlated Fermi systems is investigated in the density region where Fermi-liquid theory fails. We attribute this failure to a specific quantum phase transition associated with a rearrangement of the Landau state at low temperatures $T$, retaining the assumption that the Landau quasiparticle picture survives in a generic sense. Taking into account the resulting modification of the quasiparticle istribution function, the spin susceptibility $χ(T)$ is shown to contain a Curie-Weiss component $χ_{\rm CW}(T)\sim (T-Θ_{\rm W})^{-1}$, with the Weiss tempera…
Three-dimensional Fermi surfaces at a high temperature have been clarified for a strongly correlated Ce compound, ferromagnet CeRu$_2$Ge$_2$ in the paramagnetic phase, by virtue of a soft x-ray $hν$-dependent (700-860 eV) ARPES. Although the observed Fermi surfaces as well as quasiparticle dispersions are partly explained by a band-structure calculation based on a localized $4f$ model, qualitative discrepancy in experiments, between our APRES in the paramagnetic phase and de Haas-van Alphen measurement in the ferromagnetic phase, is revealed. This suggests a fundamental change in the $4f$ cont…
We derive the effective low-energy theory for single-wall carbon nanotubes including the Coulomb interactions among electrons. The generic model found here consists of two spin-1/2 fermion chains which are coupled by the interaction. We analyze the theory using bosonization, renormalization-group techniques, and Majorana refermionization. Several experimentally relevant consequences of the breakdown of Fermi liquid theory observed here are discussed in detail, e.g., magnetic instabilities, anomalous conductance laws, and impurity screening profiles.
We examine theoretically the effects caused by a periodic external potential on the correlated motion of a two-dimensional electron system under strong magnetic fields corresponding to a filling factor 1/2. To describe the resulting complex dynamics, we adopt a composite fermion approach and we determine in a two loop approximation the density-response function $K_{00}(\bfq,ω)$ and the compressibility. We show explicitly that the long-wavelength limit of $K_{00}(\bfq,ω)$ exhibits substantial anisotropic behavior induced by the modulation, and that the system tends to be incompressible in a dir…
While an ordinary Fermi sea is perturbatively robust to interactions, the paradigmatic composite-fermion (CF) Fermi sea arises as a non-perturbative consequence of emergent gauge fields in a system where there was no Fermi sea to begin with. A mean-field picture suggests two Fermi seas, of composite fermions made from electrons or holes in the lowest Landau level, which occupy different areas away from half filling and thus appear to represent distinct states. We show that in the microscopic theory of composite fermions, which satisfies particle-hole symmetry in the lowest Landau level to an e…
We show that a strongly correlated Fermi system with the fermion condensate, which exhibits strong deviations from Landau Fermi liquid behavior, is driven into the Landau Fermi liquid by applying a small magnetic field $B$ at temperature T=0. This field-induced Landau Fermi liquid behavior provides the constancy of the Kadowaki-Woods ratio. A reentrance into the strongly correlated regime is observed if the magnetic field $B$ decreases to zero, then the effective mass $M^*$ diverges as $M^*\propto 1/\sqrt{B}$. At finite temperatures, the strongly correlated regime is restored at some temperatu…
We show that the presence of Fermi or non-Fermi liquid behavior in the SU(N) x SU(M) Anderson impurity models may be read off the infrared threshold exponents governing the spinon and holon dynamics in a slave boson representation of these models. We construct a conserving T-matrix approximation which recovers the exact exponents with good numerical accuracy. Our approximation includes both coherent spin flip scattering and charge fluctuation processes. For the single-channel case the tendency to form bound states drastically modifies the low energy behavior. For the multi-channel case in the …
Using ultra-high quality SiGe/Si/SiGe quantum wells at millikelvin temperatures, we experimentally compare the energy-averaged effective mass, $m$, with that at the Fermi level, $m_F$, and verify that the behaviours of these measured values are qualitatively different. With decreasing electron density (or increasing interaction strength), the mass at the Fermi level monotonically increases in the entire range of electron densities, while the energy-averaged mass saturates at low densities. The qualitatively different behaviour reveals a precursor to the interaction-induced single-particle spec…
Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics. We show that the herbertsmithite ZnCu3(OH)6Cl2 can be viewed as a new type of strongly correlated electrical insulator that possesses properties of heavy-fermion metals with one exception: it resists the flow of electric charge. We demonstrate that herbertsmithite's low temperature properties are defined by a strongly correlated quantum spin liquid made with such hypothetic particles as fermionic spinons which carry spin 1/2 and no charge. Our calculations of its thermodynamic and relaxation pro…
We study the one dimensional t-t'-J model for generic couplings using two complementary theories, the extremely correlated Fermi liquid theory and time-dependent density matrix renormalization group over a broad energy scale. The two methods provide a unique insight into the strong momentum dependence of the self-energy of this prototypical non-Fermi liquid, described at low energies as a Tomonaga-Luttinger liquid. We also demonstrate its intimate relationship to spin-charge separation, i.e. the splitting of Landau quasiparticles of higher dimensions into two constituents, driven by strong qua…
We study the two-dimensional $t$-$J$ model with second neighbor hopping parameter $t'$ and in a broad range of doping $δ$ using a closed set of equations from the {\em Extremely Correlated Fermi Liquid} (ECFL) theory. We obtain asymmetric energy distribution curves and symmetric momentum distribution curves of the spectral function, consistent with experimental data. We further explore the Fermi surface and local density of states for different parameter sets. Using the spectral function, we calculate the resistivity, Hall number and spin susceptibility. The curvature change in the resistivity…
In strongly correlated electron systems the constraint which prohibits the double electron occupation at local sites can be realized by either the infinite Coulomb interaction or the correlated hopping interaction described by the Hubbard operators, but they both render the conventional field theory inapplicable. Relaxing such the constraint leads to a class of correlated hopping models based on the deformed Hubbard operators which smoothly interpolate the locally free and strong coupling limits by a tunable interaction parameter $0\leq λ\leq 1$. Here we propose a coherent state path integral …
Self-consistent dynamical approximations for strongly correlated fermion systems are particularly successful in capturing the dynamical competition of local correlations. In these, the effect of spatially extended degrees of freedom is usually only taken into account in a mean field fashion or as a secondary effect. As a result, critical exponents associated with phase transitions have mean field character. Here, we demonstrate that diagrammatic multi-scale methods anchored around local approximations are indeed capable of capturing the non mean-field nature of the critical point of the lattic…
In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Ferm…
The classic composite fermion field theory (Ref. 1) builds up an excellent framework to uniformly study important physical objects and globally explain anomalous experimental phenomena in fractional quantum Hall physics while there are also inherent weaknesses. We present a nonperturbative emergent Dirac fermion theory from this strongly correlated composite fermion field theory, which overcomes these serious long-standing shortcomings. The particle-hole symmetry of Dirac equation resolves this particle-hole symmetry enigma in the composite fermion field theory. With the help of presented nume…
Systematic deviations from standard Fermi-liquid behavior have been widely observed and documented in several classes of strongly correlated metals. For many of these systems, mounting evidence is emerging that the anomalous behavior is most likely triggered by the interplay of quenched disorder and strong electronic correlations. In this review, we present a broad overview of such disorder-driven non-Fermi-liquid behavior, and discuss various examples where the anomalies have been studied in detail. We describe both their phenomenological aspects as observed in experiment, and the current the…
The self-consistent theory of the fermion condensation, a specific phase transition which results in a rearrangement of the single particle degrees of freedom in strongly correlated Fermi systems is developed. Beyond the phase transition point, the single particle spectra are shown to be flat. The interplay between the flattening and the damping of the single particle spectra at $T\to 0$ is investigated. The width $γ(ε)$ of the single particle states is found to grow up linearly with $ε$ over a wide range of energy as in a marginal Fermi liquid. Our results gain insight into the success of the…
In quantum materials, electrons that have strong correlations tend to localize, leading to quantum spins as the building blocks for low-energy physics. When strongly correlated electrons coexist with more weakly-correlated conduction electrons, multiple channels of effective interactions develop and compete with each other. The competition creates quantum fluctuations having a large spectral weight, with the associated entropies reaching significant fractions of $R\ln 2$ per electron. Advancing a framework to understand how the fluctuating local moments influence unconventional superconductivi…
The doping-induced metal-insulator transition in two-chain systems of correlated fermions is studied using a solvable limit of the t-J model and the fact that various strong- and weak-coupling limits of the two-chain model are in the same phase, i.e. have the same low-energy properties. It is shown that the Luttinger-liquid parameter K_ρtakes the universal value unity as the insulating state (half-filling) is approached, implying dominant d-type superconducting fluctuations, independently of the interaction strength. The crossover to insulating behavior of correlations as the transition is app…
Whether a spin-1/2 Fermi gas will become ferromagnetic as the strength of repulsive interaction increases is a long-standing controversial issue. Recently this problem is studied experimentally by Jo et al, Science, 325, 1521 (2009) in which the authors claim a ferromagnetic transition is observed. This work is to point out the results of this experiment can not distinguish whether the system is in a ferromagnetic state or in a non-magnetic but strongly short-range correlated state. A conclusive experimental demonstration of ferromagnetism relies on the observation of ferromagnetic domains.
We demonstrate the existence of novel interaction effects in hole-doped semiconductor quantum wells which are connected to dramatic changes in the Fermi surface geometry occurring upon variation of the doping. We present band structure calculations showing that quantum wells formed in $p$-type cubic semiconductors develop nested Fermi surfaces at a critical hole density set by the width $d$ of the quantum well $k_F\sim π/d$. Nesting gives rise to competing superconducting and charge or spin density wave order, which we analyze using the perturbative renormalization group method. The correlated…
We study strongly correlated ground and excited states of rotating quasi-2D Fermi gases constituted of a small number of dipole-dipole interacting particles with dipole moments polarized perpendicular to the plane of motion. As the number of atoms grows, the system enters {\it an intermediate regime}, where ground states are subject to a competition between distinct bulk-edge configurations. This effect obscures their description in terms of composite fermions and leads to the appearance of novel composite fermion quasi-hole states. In the presence of dipolar interactions, the principal Laughl…
By developing a quantum virial expansion theory, we quantitatively calculate the dynamic density response function of a trapped strongly interacting Fermi gas at high temperatures near unitarity. A clear transition from atomic to molecular responses is identified in the spectra when crossing from the BCS to BEC regimes, in qualitative agreement with recent Bragg spectroscopy observations. Our virial expansion method provides a promising way to solve the challenging strong-coupling problems and is applicable to other dynamical properties of strongly correlated Fermi gases.
In the previous paper, we studied the random-mass Dirac fermion in one dimension by using the transfer-matrix methods and by introducing an imaginary vector potential in order to calculate the localization lengths. Especially we considered effects of the nonlocal but short-range correlations of the random mass. In this paper, we shall study effects of the long-range correlations of the random mass especially on the delocalization transition. The results depend on how randomness is introduced in the Dirac mass.
We study a two species fermion mixture with different populations on a square lattice modeled by a Hubbard Hamiltonian with on-site inter-species repulsive interaction. Such a model can be realized in a cold atom system with fermionic atoms in two different hyperfine states loaded on an optical lattice and with tunable inter-species interaction strength via external fields. For a two-dimensional square lattice, when at least one of the fermion species is close to half-filling, the system is highly affected by lattice effects. With the majority species near half-filling and varying densities fo…
We use scaling and renormalization-group techniques to analyze the leading nonanalyticities in a Fermi liquid. We show that a physically motivated scaling hypothesis reproduce the results known from perturbation theory for the density of states, the density-of-states fluctuations, the specific heat, the spin susceptibility, and the nematic magnetic susceptibility. We also discuss the absence of nonanalytic terms in the density susceptibility. We then use a recent effective field theory for clean electron systems to derive the scaling hypothesis by means of renormalization-group techniques. Thi…
A quasiparticle pattern advanced in Landau's first article on Fermi liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exception…
Recent experiments on quantum degenerate gases give an opportunity for simulating strongly-correlated electronic systems in optical lattices. It may shed light on some long-standing puzzles in condensed-matter physics, like the nature of high-temperature superconductivity in cuprates that had baffled people over two decades. It is believed that the two-dimensional fermionic Hubbard model, or t-J model, contains the key to this problem; but the difficulty of unveiling the mystery of a strongly-interacting fermionic system is also generally acknowledged. Here, as a substitute, we systematically …
We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but their moments exhibit critical behavior, and characterize quantum statistical properties of the system. Moreover, more detailed characterizations are obtained with experimentally feasible spatially resolved counting distributions.
We consider a class of strongly correlated Fermi systems that exhibit an interaction-induced flat band pinned to the Fermi surface, and generalize the Landau strategy to accommodate a flat band and apply the more comprehensive theory to electron systems of solids. The non-Fermi-liquid behavior that emerges is compared with relevant experimental data on heavy-fermion metals and electron-doped high-$T_c$ compounds. We elucidate how heavy-fermion metals have extremely low superconducting transition temperature $T_c$, its maximum reached in the heavy-fermion metal CeCoIn$_5$ does not exceed 2.3 K,…
We show how Fermi liquid theory can be applied to ultra-cold Fermi gases, thereby expanding their "simulation" capabilities to a class of problems of interest to multiple physics sub-disciplines. We introduce procedures for measuring and calculating position dependent Landau parameters. This lays the ground work for addressing important controversial issues: (i) the suggestion that thermodynamically, the normal state of a unitary gas is indistinguishable from a Fermi liquid (ii) that a fermionic system with strong repulsive contact interactions is associated with either ferromagnetism or local…
We consider a holographic theory as a Ginzberg-Landau theory working for strongly interacting system near the quantum critical point: we take the bulk matter field $Φ^I(r,x)$, the dual of the fermion bilinear, as the order parameter. We calculate and classify the fermion spectral functions in the presence of such orders. Depending on the symmetry, we found spectral features like the gap, pseudo-gap, flat disk bands and the Fermi-arc connecting the two Dirac cones, which are familiar in Dirac material and Kondo lattice. Many of above features are associated with the zero modes whose presence is…
A theory of strongly correlated electron or hole liquids with the fermion condensate is presented and applied to the consideration of quasiparticle excitations in high temperature superconductors, in their superconducting and normal states. This theory describes maximum values of the superconducting gap which can be as big as $Δ_1\sim 0.1ε_F$, with $ε_F$ being the Fermi level. We show that the critical temperature $2T_c\simeqΔ_1$. If there exists the pseudogap above $T_c$ then $2T^*\simeqΔ_1$, and $T^*$ is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at…
Recent breakthroughs in the creation of ultra-cold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, high-temperature…
We present the theory of an extremely correlated Fermi liquid (ECFL) with $U\to \infty$. This liquid has an underlying Fermi liquid (FL) Greens function that is further caparisoned. The theory leads to two parallel hierarchies of equations that permit iterative approximations in a certain parameter. Preliminary results for the spectral functions display a broad background and a distinct $T$ dependent left skew. An important energy scale $Δ(\vec{k},x)$ emerges as the average inelasticity of the FL Greens function, and influences the photoemission spectra profoundly. A duality is identified wher…
We show that ultra-cold atoms with synthetic spin-orbit coupling in Raman lattices can be used as versatile quantum simulators to explore the connections between correlated Chern insulators and strongly-coupled four-Fermi field theories related to the Gross-Neveu model in (2+1) dimensions. Exploiting this multidisciplinary perspective, we identify a large-$N$ quantum anomalous Hall (QAH) effect in absence of any external magnetic field, and use it to delimit regions in parameter space where these correlated topological phases appear, the boundaries of which are controlled by strongly-coupled f…
