Identifying Entanglement Phases with Bipartite Projected Ensembles

TL;DR

This paper introduces bipartite projected ensembles (BPEs) and their average entanglement (EAE) as tools to identify and analyze entanglement phases and phase transitions in quantum many-body systems, including measurement-induced transitions.

Contribution

The paper presents a novel method using BPEs and EAE to diagnose entanglement phases and transitions, applicable to quantum simulators and measured circuits.

Findings

EAE converges to a nonzero value in volume-law states.

EAE exhibits power-law decay at criticality.

EAE decays exponentially in area-law states.

Abstract

We introduce bipartite projected ensembles (BPEs) for quantum many-body wave functions, which consist of pure states supported on two local subsystems, with each state associated with the outcome of a projective measurement of the complementary subsystem in a fixed local basis. We demonstrate that the corresponding ensemble-averaged entanglements (EAEs) between two subsystems can effectively identify entanglement phases. In volume-law entangled states, EAE converges to a nonzero value with increasing distance between subsystems. For critical systems, EAE exhibits power-law decay, and it decays exponentially for area-law systems. Thus, entanglement phase transitions can be viewed as a disordered-ordered phase transition. We also apply BPE and EAE to measured random Clifford circuits to probe measurement-induced phase transitions. We show that EAE serves not only as a witness to phase transitions, but also unveils additional critical phenomena properties, including dynamical scaling and surface critical exponents. Our findings provide an alternative approach to diagnosing entanglement laws, thus enhancing the understanding of entanglement phase transitions. Moreover, given the accessibility of measuring EAE in quantum simulators, our results hold promise for impacting quantum simulations.