Finite-size scalings in measurement-induced dynamical phase transition

TL;DR

This paper investigates measurement-induced phase transitions in an interacting fermionic system, analyzing finite-size effects and critical scaling using entanglement entropy and purity to understand the quantum Zeno transition.

Contribution

It introduces a finite-size scaling analysis for many-body quantum Zeno transitions, comparing different scaling ansatze with an unbiased numerical approach.

Findings

Finite-size scaling exponents are extracted for the quantum Zeno transition.

Measurement strength controls the phase transition between active and frozen dynamics.

The numerical strategy effectively compares various finite-size scaling hypotheses.

Abstract

Repetitive measurements can cause freezing of dynamics of a quantum state, which is known as quantum Zeno effect. We consider an interacting one-dimensional fermionic system and study the fate of the many-body quantum Zeno transition if the system is allowed to evolve repetitively under the unitary dynamics, followed by a measurement process. Measurement induced phase transitions can be accessed by tuning a suitably defined parameter representing measurement strength (frequency). We use different diagnostics, such as long-time evolved entanglement entropy, purity and their fluctuations in order to characterize the transition. We further perform a finite size scaling analysis in order to detect the transition points and evaluate associated scaling exponents via an unbiased numerical strategy of cost function minimization, which provides a platform to compare finite-size scaling ansatze proposed previously in context of many-body Zeno transition.