Driven Non-Unitary Dynamics of Quantum Critical Systems

TL;DR

This paper explores how non-unitary, driven quantum dynamics influence entanglement and energy growth in (1+1)-D critical systems, revealing steady states and purification transitions through analytical and comparative methods.

Contribution

It introduces a coherent state approach to analyze non-unitary driven CFTs, uncovering steady states and purification phase transitions in quantum critical systems.

Findings

Analytical expressions for entanglement and energy growth.

Emergence of steady states under various drives.

Purification phase transitions in mixed states.

Abstract

We investigate the interplay between unitary and non-unitary driven many-body dynamics in (1+1)-dimensional quantum critical systems described by conformal field theory (CFT). By formulating a coherent state approach, we demonstrate that the growth of entanglement entropy and energy can be found analytically for a class of non-unitary driven CFTs, where the evolution alternates between real and imaginary time evolution, the latter corresponding to postselected weak measurements. We find that non-unitary evolution leads to the emergence of steady states at infinite times for the cases of periodic, quasiperiodic, and random drives. In a special class of drives, for mixed initial states, we uncover purification phase transitions that arise as a result of the competition between unitary evolution and weak measurements. We compare the CFT evolution with the corresponding non-unitary dynamics of critical lattice models, finding remarkable agreement.