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arXiv:2506.18675 · SciPost Physics

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

Sergio Cerezo-Roquebrún, Simon Hands, A. Bermúdez

Published Apr 2, 2026• 0 citations
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Abstract

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.

DOI
10.21468/scipostphys.20.4.098

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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.
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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.
Symmetry-protected topology and deconfined solitons in a multi-link Z2\mathbb{Z}_2Z2​ gauge theory
With the advent of quantum simulators, exploring exotic collective phenomena in lattice models with local symmetries and unconventional geometries is at reach of near-term experiments. Motivated by recent progress in this direction, we study a Z2\mathbb{Z}_2Z2​ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell hosting the Z2\mathbb{Z}_2Z2​ gauge fields. Elementary Wilson loops along pairs of these bonds allow to identify a dynamical gauge-invariant flux, responsible for Aharonov-Bohm-like interference effects in the tunneling dynamics of charged matter residing on the vertices. Focusing on an odd number of links, we show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability. We find inhomogeneous phases in which an ordered pattern of the gauge fluxes spontaneously breaks translational invariance, and intertwines with a bond order wave for the gauge-invariant kinetic matter operators. Long-range order is shown to coexist with symmetry protected topological order, which survives the quantum fluctuations of the gauge flux induced by an external electric field. Doping the system above half filling leads to the formation of topological soliton/anti-soliton pairs interpolating between different inhomogeneous orderings of the gauge fluxes. By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization. Quasiparticles carrying fractional charge and bound at the soliton centers can be arbitrarily separated without feeling a confining force, in spite of the long-range attractive interactions set by the small electric field on the individual integer charges.
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Topological phases of matter can support fractionalized quasiparticles localized at topological defects. The current understanding of these exotic excitations, based on the celebrated bulk-defect correspondence, typically relies on crude approximations where such defects are replaced by a static classical background coupled to the matter sector. In this work, we explore the strongly correlated nature of symmetry-protected topological defects by focusing on situations where such defects arise spontaneously as dynamical solitons in intertwined topological phases, where symmetry breaking coexists with topological symmetry protection. In particular, we focus on the Z2{\mathbb{Z}}_{2}Z2​ Bose-Hubbard model, a one-dimensional chain of interacting bosons coupled to Z2{\mathbb{Z}}_{2}Z2​ fields, and show how solitons with Zn{\mathbb{Z}}_{n}Zn​ topological charges appear for particle/hole dopings about certain commensurate fillings, extending the results in D. Gonz\'alez-Cuadra et al. [Phys. Rev. Lett. 125, 265301 (2020)] beyond half filling. We show that these defects host fractionalized bosonic quasiparticles, forming bound states that travel through the system unless externally pinned, and repel each other giving rise to a fractional soliton lattice for sufficiently high densities. Moreover, we uncover the topological origin of these fractional bound excitations through a pumping mechanism, where the quantization of the intersoliton transport allows us to establish a generalized bulk-defect correspondence. This in-depth analysis of dynamical topological defects bound to fractionalized quasiparticles, together with the possibility of implementing our model in cold-atomic experiments, paves the way for further exploration of exotic topological phenomena in strongly correlated systems.
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