# Single-shot determination of quantum phases via continuous measurements

## TL;DR

This paper introduces a method using continuous weak measurements to identify quantum phases in many-body systems, successfully detecting phase transitions through measurement records alone, even in highly excited states.

## Contribution

It demonstrates a novel phase detection criterion based on continuous measurements, applicable to complex quantum systems, aligning well with known phase transition points.

## Key findings

- Phase transition points are identified accurately via measurement records.
- The method works in highly excited states, not just ground states.
- High measurement strength induces a Zeno regime suppressing state transitions.

## Abstract

We propose that weak continuous probing may be exploited to determine and define quantum phases of complex many-body systems based on the measurement record alone. We test the resulting phase criterion in numerical simulations of measurements on the Bose-Hubbard model and the quantum Ising chain. This yields a phase transition point in reasonable agreement with the quantum phase transition in the ground state of the closed system in the thermodynamic limit, despite the system being highly excited through the measurement dynamics. At high measurement strengths, the system's response enters a Zeno regime suppressing transitions between eigenstates of the measurement operator.