Decoherence-induced self-dual criticality in topological states of matter

TL;DR

This paper explores how measurement-induced phase transitions in quantum many-body systems can be understood as decoherence-driven critical states, emphasizing the role of self-dual symmetry and topological order in such phenomena.

Contribution

It introduces a framework linking measurement-induced phase transitions to decoherence-induced critical mixed states with self-dual symmetry, advancing the understanding of criticality in topological quantum states.

Findings

Measurement-induced phase transitions can be viewed as decoherence-driven critical states.

Self-dual symmetry plays a crucial role in protecting critical mixed states.

The critical bulk is described by a specific non-linear sigma model with topological features.

Abstract

Quantum measurements performed on a subsystem of a quantum many-body state can generate entanglement for its remaining constituents. The whole system including the measurement record is described by a hybrid mixed state, which can exhibit exotic phase transitions and critical phenomena. We demonstrate that generic measurement-induced phase transitions (MIPTs) can be cast as decoherence-induced critical mixed states in one higher dimension, by constructing a projected entangled pair state (PEPS) prior to decoherence or measurement. In this context, a deeper conceptual understanding of such mixed-state criticality is called for, particularly with regard to algebraic symmetry as an advanced organizing principle for such entangled states of matter. Integrating these connections we investigate the role of self-dual symmetry -- a fundamental notion in theoretical physics -- in mixed states, showing that the decoherence of electric (e) and magnetic (m) vortices from the 2D bulk of the toric code, or equivalently, a 2D cluster state with symmetry-protected topological order, can leave a (1+1)D quantum critical mixed state protected by a weak Kramers-Wannier self-dual symmetry. The corresponding self-dual critical bulk is described by the N->1 limit of the 2D Non-linear Sigma Model in symmetry class D with target space SO(2N)/U(N) at $\Theta$-angle $\pi$, and represents a "measurement-version" of the Cho-Fisher network model subjected to Born-rule randomness...