Topological crystals and soliton lattices in a Gross-Neveu model with Hilbert-space fragmentation

Abstract

We explore the finite-density phase diagram of the single-flavour Gross-Neveu-Wilson (GNW) model 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 localized 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 centers. Out of this symmetry line, we show that quasi-spiral profiles appear with a characteristic wavevector set by the density $k=2\pi \rho$, providing non-perturbative evidence for chiral spirals beyond the large-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.

26 pages, 17 figures

References in corpus (44)

• The density-matrix renormalization group in the age of matrix product states
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Color superconductivity in dense quark matter
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• The ITensor Software Library for Tensor Network Calculations
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Matrix product states represent ground states faithfully
• Criticality, the area law, and the computational power of PEPS
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Generalized Symmetries in Condensed Matter
• Quantum Simulation for High Energy Physics
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
• Tensor network states and algorithms in the presence of a global U(1) symmetry
• A cold-atom quantum simulator for SU(2) Yang-Mills lattice gauge theory
• Inhomogeneous chiral condensates
• Simplified topological invariants for interacting insulators
• Algorithms for finite Projected Entangled Pair States
• Non-Abelian optical lattices: Anomalous quantum Hall effect and Dirac Fermions
• Atomic quantum simulator for lattice gauge theories and ring exchange models
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Wilson Fermions and Axion Electrodynamics in Optical Lattices
• Cold atom simulation of interacting relativistic quantum field theories
• Finite-density lattice QCD and sign problem: current status and open problems
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Quantum Dynamics in Krylov Space: Methods and Applications
• Analogue of cosmological particle creation in an ion trap
• Inhomogeneous phases in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions
• Quantum Simulation of Chiral Phase Transitions
• Phase diagram of the large $N$ Gross-Neveu model in a finite periodic box
• Baryons in the Gross-Neveu model in 1+1 dimensions at finite number of flavors
• Renormalization group flows for Wilson-Hubbard matter and the topological Hamiltonian
• Quantum Simulation of the N flavor Gross-Neveu Model
• Large-$N$ Chern insulators: lattice field theory and quantum simulation approaches to correlation effects in the quantum anomalous Hall effect
• Bosonization of the interacting Su-Schrieffer-Heeger model
• Interaction-induced topological phase transition at finite temperature
• Topological chiral currents in the Gross-Neveu model extension
• Topological phases of the interacting Su-Schrieffer-Heeger model: An analytical study
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Anomalies and Persistent Order in the Chiral Gross-Neveu model
• Dense ${\text{QCD}}_2$ with matrix product states
• A higher-order topological twist on cold-atom SO(5) Dirac fields