Gibbs-state phases beyond microscopic symmetry breaking: A phase invariant for the 3D toric code
Year: 2026
Type: preprint
Abstract: Do phases of Gibbs states admit a classification beyond symmetry breaking? We study the three-dimensional toric code with transverse and longitudinal fields that explicitly break both microscopic higher-form symmetries. We introduce the connected correlation $f_W$ of two locally decoded winding Wilson loops. Nonzero asymptotic $f_W$ rules out shallow local preparation from product states. An asymptotic optimization over the observables and physical recovery channels defines an invariant $\mathcal{F}$, which we prove constant within phases defined by two-way local channels with product ancillas and sublinear causal radius. The invariant equals one for the canonical zero-temperature state of the field-free toric code. Quantum Monte Carlo tests the conjectured thermodynamic values $f_W=1$ at weak fields and low temperature and $f_W=0$ elsewhere. The fixed-decoder correlation provides a lower bound on $\mathcal{F}$, so the results suggest an extended region with $\mathcal{F}=1$. Product states, including the infinite-temperature state and fully polarized infinite-field limits, have $\mathcal{F}=0$ exactly and therefore lie in a different phase from states with $\mathcal{F}=1$.
Source: arXiv (Cornell University)
Author: Watanabe, Haruki
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167073268