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arXiv:2408.04241 · Physical review. B./Physical review. B

Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits

Yoshihito Kuno, Takahiro Orito, Ikuo Ichinose

Published Sep 19, 2024• 21 citations
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Abstract

Discovering mixed state quantum orders is an ongoing issue. Recently, it has been recognized that there are (at least) two kinds of symmetries in the mixed state: strong and weak symmetries. Under symmetry-respective decoherence, spontaneous strong-to-weak symmetry breaking (SSSB) can occur. This paper provides a scheme to describe SSSB and other decoherence phenomena in the mixed state by employing the stabilizer formalism and the efficient numerical algorithm of Clifford circuits. We present two systematic numerical studies. In a two-dimensional circuit with a stochastic Ising type decoherence, an SSSB phase transition is clearly observed and its criticality is elucidated by the numerical methods. In particular, we calculate R\'enyi-2 correlations and estimate critical exponents of the SSSB transition. For the second system, we introduce an idea of subgroup SSSB. As an example, we study a system with symmetry-protected-topological order provided by both one-form and zero-form symmetries, and observe how the system evolves under decoherence. After displaying numerical results, we show that viewpoint of percolation is quite useful to understand the SSSB transition, which is applicable for a wide range of decohered states. Finally, we comment on SSSB of one-form-symmetry exemplifying toric code.

DOI
10.1103/physrevb.110.094106

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Decoherence on quantum many-body systems induces nontrivial mixed states with specific properties that have no counterparts in pure states. The authors clarify here the emergence of ``intrinsic mixed state topological order'' in a toric code state under decoherence, which accompanies exotic anyon proliferation. Furthermore, the authors find that the decoherence-induced phase transition in the stabilizer formalism is described by a percolation picture in two dimensions. The viewpoint of one-form symmetry and its spontaneous symmetry breaking plays an important role in this study.