We show that synthetic spin-orbit coupling for ultracold atoms in optical Raman potentials can be exploited to build versatile quantum simulators of correlated Chern insulators connected to strongly coupled four-Fermi field theories similar 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 fixed points of these four-Fermi relativistic field theories.We further show how, for strong interactions, the QAH effect gives way to magnetic phases described by a two-dimensional quantum compass model in a transverse field.We present a detailed description of the phase diagram using the large-N effective potential, and variational techniques such as projected entangled pairs.
We show that synthetic spin-orbit coupling for ultracold atoms in optical Raman potentials can be exploited to build versatile quantum simulators of correlated Chern insulators connected to strongly coupled four-Fermi field theories similar 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 fixed points of these four-Fermi relativistic field theories.We further show how, for strong interactions, the QAH effect gives way to magnetic phases described by a two-dimensional quantum compass model in a transverse field.We present a detailed description of the phase diagram using the large-N effective potential, and variational techniques such as projected entangled pairs.
Four-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.
The study of correlation effects in topological phases of matter can benefit from a multidisciplinary approach that combines techniques drawn from condensed matter, high-energy physics and quantum information science. In this work, we exploit these connections to study the strongly-interacting limit of certain lattice Hubbard models of topological insulators, which map onto four-Fermi quantum field theories with a Wilson-type discretisation and have been recently shown to be at reach of cold-atom quantum simulators based on synthetic spin-orbit coupling. We combine large-S and tensor-network techniques to explore the possible spontaneous symmetry-breaking phases that appear when the interactions of the topological insulators are sufficiently large. In particular, we show that varying the Wilson parameter r of the lattice discretisations leads to a novel Heisenberg–Ising compass model with critical lines that flow with the value of r.
We propose to realize and observe Chern Kondo insulators in an optical superlattice with laser-assisted s and p orbital hybridization and a synthetic gauge field, which can be engineered based on the recent cold atom experiments. Considering a double-well square optical lattice, the localized s orbitals are decoupled from itinerant p bands and are driven into a Mott insulator due to the strong Hubbard interaction. Raman laser beams are then applied to induce tunnelings between s and p orbitals, and generate a staggered flux simultaneously. Because of the strong Hubbard interaction of s orbital states, we predict the existence of a critical Raman laser-assisted coupling, beyond which the Kondo screening is achieved, and then a fully gapped Chern Kondo phase emerges, with the topology characterized by integer Chern numbers. Being a strongly correlated topological state, the Chern Kondo phase is different from the single-particle quantum anomalous Hall state, and can be identified by measuring the band topology and double occupancy of s orbitals. The experimental realization and detection of the predicted Chern Kondo insulator are also proposed.
Ultracold Fermi gases of spin-3/2 atoms provide a clean platform to realise SO( 5 5 ) models of 4-Fermi interactions in the laboratory. By confining the atoms in a two-dimensional Raman lattice, we show how this system can be used as a flexible quantum simulator of Dirac quantum field theories (QFTs) that combine Gross-Neveu and Thirring interactions with a higher-order topological twist. We show that the lattice model corresponds to a regularization of this QFT with an anisotropic twisted Wilson mass. This allows us to access higher-order topological states protected by a discrete SO( 5 5 ) group, a remnant of the continuous rotational symmetry of the 4-Fermi interactions that is not explicitly broken by the lattice discretization. Using large- N N methods, we show that the 4-Fermi interactions lead to a rich phase diagram with various competing fermion condensates. Our work opens a route for the implementation of correlated higher-order topological states with tunable interactions that has interesting connections to non-trivial relativistic QFTs of Dirac fermions in D=2+1 D = 2 + 1 dimensions.
The present chapter discusses methods by which topological Bloch bands can be prepared in cold-atom setups. Focusing on the case of Chern bands for two-dimensional systems, we describe how topological properties can be triggered by driving atomic gases, either by dressing internal levels with light or through time-periodic modulations. We illustrate these methods with concrete examples, and we discuss recent experiments where geometrical and topological band properties have been identified. Introduction Ultracold atoms constitute a promising physical platform for the preparation and exploration of novel states of matter [1, 2, 3]. In particular, the engineering of topological band structures with cold-atom systems, together with the capability of tuning interactions between the particles, opens an interesting route toward the realization of intriguing strongly correlated states with topological features, such as fractional topological insulators and quantum Hall liquids [4]. This chapter is dedicated to the preparation and the detection of topological band structures characterized by nonzero Chern numbers [5]. Such Chern bands , which constitute the building blocks for realizing (fractional) Chern insulators [6, 7], arise in two-dimensional (2D) systems presenting time-reversal-symmetry (TRS) breaking effects. For instance, nontrivial Chern bands naturally appear in the Harper-Hofstadter model [8], a lattice penetrated by a uniform flux, where they generalize the (nondispersive) Landau levels to the lattice framework. Additionally, Chern bands also appear in staggered flux configurations, such as in Haldane's honeycomb-lattice model [9] or in lattice systems combining Rashba spin-orbit coupling and Zeeman (exchange) fields. The atoms being charge neutral, “magnetic” fluxes cannot be simply produced by subjecting optical lattices to “real” magnetic fields. It is the aim of this chapter to review several schemes that have been recently implemented in laboratories with the goal of realizing synthetic magnetic fields leading to Chern bands for cold atoms. Our presentation is complementary to that of Chapter 15, as we focus on synthetic magnetic fields in lattice-based systems for which the flux density can be made very large (with magnetic length comparable to interparticle spacing). The chapter is structured as follows: Section 14.2 describes how the Chern number is related to physical observables defined in a lattice framework. In particular, it clarifies the link between recent Chern-number measurements performed in cold bosonic gases and the more conventional (electronic) quantum Hall effect.
We unveil an interesting connection of Lorentz-violating quantum field theories, studied in the context of the standard model extension, and Hubbard-type models of topological crystalline phases. These models can be interpreted as a regularization of the former and, as hereby discussed, explored with current quantum simulators based on ultracold atoms in optical Raman lattices. In particular, we present a complete analysis of the Creutz-Hubbard ladder under a generic magnetic flux, which regularizes a Gross-Neveu model extension and presents a characteristic circulating chiral current whose nonzero value arises from a specific violation of Lorentz invariance. We present a complete phase diagram with trivial insulators, ferromagnetic and antiferromagnetic phases, and current-carrying topological crystalline phases. These predictions are benchmarked using tools from condensed matter and quantum-information science, showing that self-consistent Hartree-Fock and strong-coupling Dzyaloshinskii-Moriya (D-M) methods capture the essence of the phase diagram in different regimes, which is further explored using extensive numerical simulations based on matrix-product states.