Topological chiral currents in the Gross-Neveu model extension

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 regularisation of the former and, as hereby discussed, explored with current quantum simulators based on ultra-cold atoms in optical Raman lattices. In particular, we present a complete analysis of the Creutz-Hubbard ladder under a generic magnetic flux, which regularises a Gross-Neveu model extension, and presents a characteristic circulating chiral current whose non-zero value arises from a specific violation of Lorentz invariance. We present a complete phase diagram with trivial insulators, ferromagnetic and anti-ferromagnetic 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 methods capture the essence of the phase diagram in different regimes, which is further explored using extensive numerical simulations based on matrix-product states.

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Cited by in corpus (9)

• Quantum Simulation of the N flavor Gross-Neveu Model
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Chiral Spin-Chain Interfaces Exhibiting Event-Horizon Physics
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Large-$S$ and tensor-network methods for strongly-interacting topological insulators
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• The Schwinger and Chiral Schwinger Models in a Non-perturbative Spectral Regularization
• The large $|U|$ expansion for a half-filled asymmetric Hubbard model on a triangular ladder in the presence of spin-dependent magnetic flux
• Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation