Field theory of charge sharpening in symmetric monitored quantum circuits

TL;DR

This paper develops a field theory for charge sharpening in monitored quantum circuits, revealing a critical phase and a Kosterlitz-Thouless transition between charge-fuzzy and charge-sharp phases, supported by numerical simulations.

Contribution

It introduces a controlled replica field theory for charge dynamics in monitored quantum circuits, identifying a novel critical phase and phase transition.

Findings

Charge fuzzy phase exhibits critical behavior with evolving exponents.

Transition to charge-sharp phase is a modified Kosterlitz-Thouless transition.

Numerical simulations confirm theoretical scaling predictions.

Abstract

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. By taking a continuous-time, weak-measurement limit, we construct a controlled replica field theory description of these phases and their intervening charge-sharpening transition in one spatial dimension. We find that the charge fuzzy phase is a critical phase with continuously evolving critical exponents that terminates in a modified Kosterlitz-Thouless transition to the short-range correlated charge-sharp phase. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations, and discuss generalizations to higher dimensions.