Generalized hydrodynamics of free fermions under extensive-charge monitoring

TL;DR

This paper develops a generalized hydrodynamics framework to analyze the transport of free fermions under extensive charge monitoring, revealing how measurement influences charge profiles and transport properties.

Contribution

It introduces a novel GHD-based approach to study monitored free fermion systems, including a hybrid numerical-analytic solution for hydrodynamic quench dynamics.

Findings

Monitoring causes discontinuities in charge profiles.

Increased monitoring rate enhances profile discontinuities.

Infinite monitoring rate (Zeno limit) suppresses transport.

Abstract

We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.