Quantum Breakdown Condensate as a Disorder-Free Quantum Glass

TL;DR

This paper introduces a novel disorder-free quantum glass phase called the quantum breakdown condensate, characterized by exponential symmetry breaking, a bulk gap violating Goldstone's theorem, and a large degeneracy of ground states.

Contribution

The study reveals a new quantum glass phase with exponential U(1) symmetry breaking, finite entropy density, and unique edge modes, expanding the classification of quantum phases.

Findings

Exhibits exponential U(1) SSB phase with 2^L ground states

Displays a bulk gap violating Goldstone's theorem

Behaves as a disorder-free quantum glass with non-decaying autocorrelations

Abstract

We study the phase diagram of a one-dimensional spin quantum breakdown model, which has an exponential $U(1)$ symmetry with charge unit decaying as $2^{-j}$ with site position $j$. By exact diagonalization (ED), we show that the model with spin $S\ge2$ exhibits an exponential $U(1)$ spontaneous symmetry breaking (SSB) phase dubbed a quantum breakdown condensate. It exhibits a bulk gap violating the Goldstone theorem, and an edge mode only on the left edge if in open boundary condition. In a length $L$ lattice, the condensate has $\mathcal{O}(2^L)$ number of SSB ground states originating from the $\mathcal{O}(2^L)$ number of exponential $U(1)$ charge sectors, leading to a finite entropy density $\ln 2$. This enforces a first order SSB phase transition into this phase, as observed in ED and verified in the large $S$ limit on an exactly solvable Rokhsar-Kivelson line. The condensate has an SSB order parameter being the local in-plane spin, which points in angles related by the chaotic Bernoulli (dyadic) map and thus is effectively random. Moreover, we show the condensate exhibits non-decaying local autocorrelations, and does not have an off-diagonal long-range order. The quantum breakdown condensate thus behaves as a disorder-free quantum glass and is beyond the existing classifications of phases of matter.