Spacetime duality between localization transitions and measurement-induced transitions

TL;DR

This paper explores the deep connection between localization transitions and measurement-induced entanglement transitions by employing space-time rotation of quantum circuits, revealing new types of entanglement phase transitions.

Contribution

It introduces a novel approach of space-time rotating unitary circuits to relate localization phenomena with measurement-induced entanglement transitions, including new models exhibiting rich entanglement behavior.

Findings

Demonstrates a non-unitary circuit for 1d free fermions with an entanglement transition from logarithmic to volume-law scaling.

Constructs a 2d Clifford circuit showing a transition from area to volume-law entanglement.

Proposes an unconventional correlator that signals localization transitions in non-unitary circuits.

Abstract

Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via spatial disorder, or subjecting the system to non-unitary evolution, e.g., via projective measurements. Here we employ the idea of space-time rotation of a circuit to explore the relation between systems that fall into these two classes. In particular, by space-time rotating unitary Floquet circuits that display a localization transition, we construct non-unitary circuits that display a rich variety of entanglement scaling and phase transitions. One outcome of our approach is a non-unitary circuit for free fermions in 1d that exhibits an entanglement transition from logarithmic scaling to volume-law scaling. This transition is accompanied by a 'purification transition' analogous to that seen in hybrid projective-unitary circuits. We follow a similar strategy to construct a non-unitary 2d Clifford circuit that shows a transition from area to volume-law entanglement scaling. Similarly, we space-time rotate a 1d spin chain that hosts many-body localization to obtain a non-unitary circuit that exhibits an entanglement transition. Finally, we introduce an unconventional correlator and argue that if a unitary circuit hosts a many-body localization transition, then the correlator is expected to be singular in its non-unitary counterpart as well.