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arXiv:2112.07654 · Physical review. B./Physical review. B

Topological chiral currents in the Gross-Neveu model extension

Emanuele Tirrito, Maciej Lewenstein, A. Bermúdez

Published Jul 28, 2022• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.106.045147

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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.
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 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 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.
Understanding the robustness of topological phases of matter in the presence of interactions poses a difficult challenge in modern condensed matter, showing interesting connections to high-energy physics. In this work, we leverage these connections to present a complete analysis of the continuum long-wavelength description of a generic class of correlated topological insulators: Wilson-Hubbard topological matter. We show that a Wilsonian renormalization group (RG) approach, combined with the so-called topological Hamiltonian, provide a quantitative route to understand interaction-induced topological phase transitions that occur in Wilson-Hubbard matter. We benchmark two-loop RG predictions for a quasi-1D Wilson-Hubbard model by means of exhaustive numerical simulations based on matrix product states (MPS). The agreement of the RG predictions with MPS simulations motivates the extension of the RG calculations to higher-dimensional topological insulators.
We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model in (1+1) dimensions using matrix product state (MPS) simulations. At zero temperature and along the symmetry line of the phase diagram, we find a sequence of inhomogeneous ground states that arise through a real-space version of the mechanism of Hilbert-space fragmentation. For weak interactions, doping the symmetry-protected topological (SPT) phase of the GNW model leads to localised charges or holes at periodic arrangements of immobile topological defects separating the fragmented subchains: a topological crystal. Increasing the interactions, we observe a transition into a parity-broken phase with a pseudoscalar condensate displaying a modulated periodic pattern. This soliton lattice is a sequence of topological charges corresponding to anti-kinks, which also bind the doped fermions at their respective centres. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density k = 2\pi\rho k = 2 π ρ , providing non-perturbative evidence for chiral spirals beyond the large- N N limit. These results demonstrate that various exotic inhomogeneous phases can arise in lattice field theories, and motivate the use of quantum simulators to confirm such QCD-inspired phenomena in future experiments.
We investigate the emergence of bond-directional spin-spin interactions in a synthetic Fermi-Hubbard bilayer that can be realized with ultracold fermions in Raman optical lattices. The model exploits synthetic dimensions to couple two honeycomb layers, each corresponding to a different hyperfine atomic state, via Raman-assisted tunneling and, moreover, via an inter-layer Hubbard repulsion due to the cold-atom scattering. In the strong-coupling regime at half filling, we derive effective spin Hamiltonians for the kinetic exchange featuring Kitaev, Heisenberg, off-diagonal exchange ( \Gamma Γ -couplings), as well as tunable Dzyaloshinskii-Moriya interactions. We identify specific configurations that generate both ferromagnetic and antiferromagnetic Kitaev couplings with various perturbations of relevance to Kitaev materials, providing a tunable platform that can explore how quantum spin liquids emerge from itinerant fermion systems. We analyze the Fermi-liquid and Mott-insulating phases, highlighting a correspondence between Dirac and Majorana quasi-particles, with possible phase transitions thereof. In an extreme anisotropic limit, we show that the model reduces to an inter-layer ribbon in a quasi-1D ladder, allowing for a numerical study of the correlated ground state using matrix product states. We find a transition from a symmetry-protected topological insulator to a Kitaev-like regime characterized by nonlocal string order. Our results establish that cold-atom quantum simulators based on Raman optical lattices can be a playground for extended Kitaev models, bridging itinerant fermionic systems and spin-liquid physics.