Entanglement transitions in structured and random nonunitary Gaussian circuits

TL;DR

This paper investigates measurement-induced phase transitions in nonunitary Gaussian quantum circuits, revealing volume-to-area law transitions, a critical phase with fractal properties, and robustness of these transitions in random circuit ensembles.

Contribution

It introduces a classical dynamical system mapping for nonunitary circuits, uncovers a critical phase with tunable properties, and demonstrates the robustness of phase transitions in random circuits.

Findings

Exact tractability of Floquet non-unitary evolution

Emergence of a critical phase with fractal origin

Robust volume-to-area law transition in random circuits

Abstract

We study measurement-induced phase transitions in quantum circuits consisting of kicked Ising models with postselected weak measurements, whose dynamics can be mapped onto a classical dynamical system. For a periodic (Floquet) non-unitary evolution, such circuits are exactly tractable and admit volume-to-area law transitions. We show that breaking time-translation symmetry down to a quasiperiodic (Fibonacci) time evolution leads to the emergence of a critical phase with tunable effective central charge and with a fractal origin. Furthermore, for some classes of random non-unitary circuits, we demonstrate the robustness of the volume-to-area law phase transition for arbitrary random realizations, thanks to the emergent compactness of the classical map encoding the circuit's dynamics.