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.
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.
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.
Higher-order topological states that possess gapped bulk energy bands and exotic topologically protected boundary states with at least two dimensions lower than the bulk have opened a significant and new perspective for understanding topological quantum matter. Here, we propose to generate two-dimensional (2D) topological boundary states for implementing a synthetic magnetic flux of ultracold atoms trapped in bilayer optical lattices. It is shown that a Chern insulator, Dirac semimetals, and a second-order topological phase (SOTP) are generated by the interplay of the two-photon detuning and effective Zeeman shift. These observed topological phases can be well characterized by the energy gap of the bulk, the Wilson loop spectra, and the spin textures at the high-symmetry points of the system. We show that the SOTP exhibits a pair of 0D boundary states. Meanwhile, the phases of the Dirac semimetals and Chern insulator support the conventional 1D boundary states due to the principle of bulk-boundary correspondence. Strikingly, the boundary states that emerge for Dirac semimetals and the SOTP are topologically protected by PT symmetry and chiral-mirror symmetry (${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{M}}}_{\ensuremath{\alpha}}$), respectively. In particular, the location of 0D corner states for the SOTP which are associated with ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\mathcal{M}}}_{\ensuremath{\alpha}}$ symmetry are highly manipulable by tuning the magnetic flux. Our scheme herein provides a platform for emerging exotic topological boundary states, which may facilitate the study of higher-order topological phases in ultracold atomic gases.
We show that a Wilson-type discretization of the Gross–Neveu model, a fermionic N-flavor quantum field theory displaying asymptotic freedom and chiral symmetry breaking, can serve as a playground to explore correlated symmetry-protected phases of matter using techniques borrowed from high-energy physics. A large-N study, both in the Hamiltonian and Euclidean formalisms, yields a phase diagram with trivial, topological, and symmetry-broken phases separated by critical lines that meet at a tri-critical point. We benchmark these predictions using tools from condensed matter and quantum information science, which show that the large-N method captures the essence of the phase diagram even at N=1. Moreover, we describe a cold-atom scheme for the quantum simulation of this lattice model, which would allow to explore the single-flavor phase diagram.
Ultracold atoms provide a controllable platform to explore topological matter induced by spin-orbit (SO) coupling. This thesis reports an experimental realization of topological matter with Ytterbium atoms implemented by a Raman (or SO coupling) lattice - an optical lattice dressed by SO coupling, where internal atomic states are coupled by Raman beams. Remarkably, the lattice simultaneously serves as one of the Raman beams. As the building block of the Raman lattice, SO coupling is first studied in a one-dimensional (1D) bulk system and manifested by two hallmarks, the locking between the atomic spin and momentum and the dephasing in the Rabi oscillation. SO coupling in a periodic lattice renders topological matter. 1D Raman lattice show-cases a novel symmetry-protected topological (SPT) phase beyond the tenfold Altland-Zirnbauer classification. SPT phases distinguished by the Z2 invariant are determined from spin-textures. We highlight textures not only in equilibrium, but also of far-from-equilibrium dynamics after a quench between distinct phases, reflecting the band topology. Higher dimensional Raman lattices are richer. A three-dimensional (3D) topological nodal line semimetal structure has been observed for the first time with ultracold atoms, and reconstructed by a well-designed (pseudo-)tomography - extraction of Dirac points on different momentum layers, owing to the emergence of a crystalline symmetry. Similarly, topological features, such as band inversion lines that are bulk counterparts of Fermi arc states and connect Dirac points, are also uncovered from quench dynamics. "More is different." The SU(N) symmetric spin-independent interaction is investigated by Tan's contact and collective modes. Enhanced by the (orbital) Feshbach resonance, the Raman lattice with tunable interactions can be applied to engineer elusive topological many-body phases, which is envisaged for unveiling the attractive topological superfuilds.
The Dirac fermion is an important fundamental particle appearing in high-energy physics and topological insulator physics. In particular, a Dirac fermion in a one-dimensional lattice system exhibits the essential properties of topological physics. However, the system has not been quantum simulated in experiments yet. Herein, we propose a one-dimensional generalized lattice Wilson-Dirac fermion model and study its topological phase structure. We show the experimental setups of an atomic quantum simulator for the model, in which two parallel optical lattices with the same tilt for trapping cold fermion atoms and a laser-assisted hopping scheme are used. Interestingly, we find that the model exhibits nontrivial topological phases characterized by gapless edge modes and a finite winding number in the broad regime of the parameter space. Some of the phase diagrams closely resemble those of the Haldane model. We also discuss topological charge pumping and a lattice Gross-Neveu model in the system of generalized Wilson-Dirac fermions.
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.