Measurement-Induced Phase Transition in a Quantum Spin System

TL;DR

This paper investigates a measurement-induced phase transition in a quantum spin system, revealing a non-analytic response linked to Hamiltonian parameters and measurement intervals, distinct from traditional ground-state phase transitions.

Contribution

It analytically demonstrates a new type of phase transition driven by measurement dynamics in an interacting quantum spin system, not related to ground state properties.

Findings

Non-analytic response as a function of Hamiltonian parameters and measurement interval.

Identification of a measurement-induced phase transition distinct from quantum ground state transitions.

Analysis of different measurement types and their effects on the system.

Abstract

Suppose a quantum system starts to evolve under a Hamiltonian from some initial state. When for the first time, will an observable attain a preassigned value? To answer this question, one method often adopted is to make instantaneous measurements periodically and note down the serial number for which the desired result is obtained for the first time. We apply this protocol to an interacting spin system at zero temperature and show analytically that the response of this system shows a non-analyticity as a function of the parameter of the Hamiltonian and the time interval of measurement. In contrast to quantum phase transitions, this new type of phase transition is not a property of the ground state and arises from the Hamiltonian dynamics and quantum mechanical nature of the measurement. The specific system studied is transverse Ising chain and the measurement performed is, whether the total transverse magnetic moment (per site) is not equal to 1. The results for some other types of measurement is also discussed.