Symmetry and Topology of Monitored Quantum Dynamics

TL;DR

This paper classifies the symmetry and topology of monitored quantum dynamics, revealing how topological features influence measurement-induced phase transitions and dynamical properties in open quantum systems.

Contribution

It introduces a tenfold classification of symmetry and topology for monitored free fermions, linking topological invariants to dynamical phenomena and steady states.

Findings

Topological phases affect measurement-induced phase transitions.

Nontrivial topology leads to protected boundary states and zero modes.

Topologically protected slowdown of dynamical purification.

Abstract

The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.