Measurement-Induced Quantum Phase Transitions

Abstract

There has been a recent increase in interest towards a nonequilibrium phenomenon called the measurement-induced quantum phase. These phases occur in "hybrid" systems where unitary evolution is interspersed with projective measurements. We look at two such systems. First we investigate a bosonic system of qudits. This is a one-dimensional chain with a d-dimensional local Hilbert space at each site. We forward a generalization of the stabilizer formalism to simulate hybrid dynamics on the system for certain prime numbers d and find evidence of both a measurement-induced entanglement transition and a measurement-induced purification transition. We find critical exponents ν=1.3 for all studied cases, consistent with known results for d=2. We then investigate a fermionic system. Viewing the system as populated with Majorana fermions, we show a connection to a previously studied statistical mechanics model. We then generalize this model by leveraging the Gaussian state formalism. We simulate the hybrid dynamics of this generalized system under free fermion unitary evolution and measurement of local occupation number. We find evidence of a measurement-induced purification transition, and find the corresponding phase diagram. These models advance what is known about these classes of models and demonstrate the robustness of their corresponding measurement-induced quantum phases.