Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
arxiv(2024)
摘要
Symmetry in mixed quantum states can manifest in two distinct forms: strong
symmetry, where each individual pure state in the quantum ensemble is symmetric
with the same charge, and weak symmetry, which applies only to the entire
ensemble. This paper explores a novel type of spontaneous symmetry breaking
(SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak
symmetry is measured by the long-ranged two-point correlation function
Tr(O_xO^†_yρ), the strong-to-weak SSB (SW-SSB) is
measured by the fidelity F(ρ, O_xO^†_yρ O_yO^†_x),
dubbed the fidelity correlator. We prove that SW-SSB is a universal property of
mixed-state quantum phases, in the sense that the phenomenon of SW-SSB is
robust against symmetric low-depth local quantum channels. We argue that a
thermal state at a nonzero temperature in the canonical ensemble (with fixed
symmetry charge) should have spontaneously broken strong symmetry.
Additionally, we study non-thermal scenarios where decoherence induces SW-SSB,
leading to phase transitions described by classical statistical models with
bond randomness. In particular, the SW-SSB transition of a decohered Ising
model can be viewed as the "ungauged" version of the celebrated toric code
decodability transition. We confirm that, in the decohered Ising model, the
SW-SSB transition defined by the fidelity correlator is the only physical
transition in terms of channel recoverability. We also comment on other
(inequivalent) definitions of SW-SSB, through correlation functions with higher
Rényi indices.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要