Establishing Mixed-State Phase Equivalence beyond Renormalization Fixed Points

TL;DR

This paper develops a framework to analyze mixed-state quantum phase equivalence beyond renormalization fixed points, using low-depth circuits and Lindbladian constructions to connect states within phases.

Contribution

It introduces a novel approach to establish phase equivalence of nontrivial mixed states beyond fixed points via explicit circuit constructions and Lindbladian methods.

Findings

Constructed low-depth, quasi-local channel circuits within each phase.

Established phase equivalence analytically for mixed states.

Generalized the framework to a broad class of nontrivial phases.

Abstract

Understanding mixed-state quantum phases is a central challenge in the era of quantum simulation, where many existing studies focus on renormalization fixed points. In this work, we move beyond the renormalization fixed-point paradigm by constructing a quantum phase transition connecting two distinct one-dimensional fixed points, both exhibiting finite conditional mutual information and one of which is intrinsically nontrivial. We analytically establish phase equivalence within each of the two phases by explicitly constructing low-depth, quasi-local channel circuits that connect states within each phase. Crucially, our approach leverages the parent Lindbladian construction to generate the desired channel circuits. We further demonstrate that this framework generalizes naturally to a broad class of intrinsically nontrivial mixed-state quantum phases. Our method establishes a framework for rigorously analyzing phase equivalence of intrinsically non-trivial mixed states beyond the renormalization fixed points.