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

TL;DR

This paper investigates the phase diagram of the Gross-Neveu-Wilson model at finite density, revealing inhomogeneous phases like topological crystals and soliton lattices through matrix product state simulations.

Contribution

It uncovers novel inhomogeneous ground states, including topological crystals and chiral spirals, in a lattice field theory model using non-perturbative numerical methods.

Findings

Identification of topological crystal phases with localized charges at defects.

Observation of a transition to a parity-broken phase with modulated pseudoscalar condensate.

Evidence of chiral spirals characterized by a wavevector proportional to density.

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.