Generic Hilbert Space Fragmentation in Kogut--Susskind Lattice Gauge Theories

TL;DR

The paper addresses how Hilbert-space fragmentation (HSF) can arise in Kogut–Susskind lattice gauge theories (LGTs) and what this implies for thermalization and continuum QCD. It develops a strong-coupling approach based on the Schrieffer–Wolff transformation to derive an effective Hamiltonian that freezes high-Casimir representations, yielding exponentially many Krylov subspaces and emergent, approximately conserved quantities. Numerical demonstrations in both U(1) and SU(2) LGTs corroborate the fragmentation scenario and show clear freezing behavior, both with and without dynamical matter. The work highlights the care needed when using truncated electric-basis LGTs to infer continuum QCD thermalization and points to potential benefits for quantum simulation of gauge theories.

Abstract

At the heart of quantum many-body physics lies the understanding of mechanisms that avoid quantum thermalization in an isolated system quenched far from equilibrium. A prominent example is Hilbert space fragmentation, which has recently emerged as an ergodicity-breaking mechanism in constrained spin models. Here, we show that Kogut--Susskind formulations of lattice gauge theories in $d+1$D ($d$ spatial and one temporal dimensions) give rise to Hilbert space fragmentation, and discuss possible implications for understanding continuum physics. Our findings not only prove that lattice gauge theories are a natural platform for Hilbert space fragmentation, they also serve as a guide to the conditions under which these models can be faithfully used to infer the thermalization properties of quantum chromodynamics.

Figures (3)

• Figure 1: Expectation and variance of $\hat{P}(s)$ and $\hat{D}(s)$ for eigenstates in the momentum zero sector of a $L=4$$\mathrm{U}(1)$ LGT. The upper plot shows the expectation of the operator and the lower plot shows the variance.
• Figure 2: The upper panel shows the half-chain entropy of the zero momentum energy eigenstates of a $\mathrm{U}(1)$$L=4$ plaquette chain with $g=0.6$. The red points show energy eigenstates that have $\abs{\bra{E_n}\ket{3,-2,3,-2}}^2>0.05$ and the states between the orange lines are in the microcanonical ensemble state $\ket{\psi_{MC}}$. The lower panel shows the expectation of $\sum_x\hat{E}^2_x$ as a function of time $t$ for the initial states $\ket{3,-2,3,-2}$ and $\ket{\psi_{MC}}$.
• Figure 3: Evolution of the electric energy as a function of time on a $6$ site lattice with open boundary conditions. The dark lines show the evolution of states with different numbers of quark pairs placed on top of the electric vacuum, and the light lines show the evolution of the corresponding microcanonical ensemble states.