Measurement-induced transitions for interacting fermions

TL;DR

This paper develops a theoretical framework to study measurement-induced phase transitions in interacting fermionic systems, revealing how interactions influence entanglement and charge fluctuations, and identifying a new phase with stabilized volume-law entanglement.

Contribution

The authors introduce a Keldysh field-theoretical approach and a replicated NLSM to analyze measurement effects in interacting fermions, uncovering phenomena like information-charge separation and interaction-stabilized phases.

Findings

Interaction stabilizes volume-law entanglement phase.

Charge cumulants exhibit logarithmic growth in 1D.

Measurement transitions occur in all dimensions with interactions.

Abstract

Effect of measurements on interacting fermionic systems with particle-number conservation, whose dynamics is governed by a time-independent Hamiltonian, is studied. We develop Keldysh field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM), which incorporates boundary conditions specifically designed to produce generating functions for charge cumulants and entanglement entropies directly in the NLSM language. By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables. Crucially, the interaction-induced terms in the NLSM action reduce its symmetry, which affects the physics of the problem in a dramatic way. First, this leads to the "information-charge separation": charge cumulants get decoupled from entanglement entropies. Second, the interaction stabilizes the volume-law phase for the entanglement. Third, for spatial dimensionality $d=1$, the interaction stabilizes the phase with logarithmic growth of charge cumulants (in the thermodynamic limit). Thus, in the presence of interaction, there are measurement transitions in any $d$, at variance with free fermions, for which a $d=1$ system is always in the area-law phase. Analytical results are supported by numerical simulations using time-dependent variational principles for matrix product states, which, in particular, confirm the separation of information and charge as a hallmark of the delocalized phase.