# Fidelity as a probe for a deconfined quantum critical point

## TL;DR

This paper demonstrates that fidelity susceptibility is an effective and simple tool for identifying and characterizing the continuous nature of deconfined quantum critical points in spin chains, supporting their second-order transition nature.

## Contribution

It introduces the use of fidelity susceptibility as a probe for deconfined quantum critical points and accurately determines the critical point and exponents through finite-size scaling.

## Key findings

- Fidelity susceptibility obeys conventional scaling at the critical point
- Supports the continuous (second-order) nature of the deconfined quantum phase transition
- Provides numerical estimates of the critical point and correlation length exponent

## Abstract

Deconfined quantum critical point was proposed as a second-order quantum phase transition between two broken symmetry phases beyond the Landau-Ginzburg-Wilson paradigm. However, numerical studies cannot completely rule out a weakly first-order transition because of strong violations of finite-size scaling. We demonstrate that the fidelity is a simple probe to study deconfined quantum critical point. We study the ground-state fidelity susceptibility close to the deconfined quantum critical point in a spin chain using the large-scale finite-size density matrix renormalization group method. We find that the finite-size scaling of the fidelity susceptibility obeys the conventional scaling behavior for continuous phase transitions, supporting the deconfined quantum phase transition is continuous. We numerically determine the deconfined quantum critical point and the associated correlation length critical exponent from the finite-size scaling theory of the fidelity susceptibility. Our results are consistent with recent results obtained directly from the matrix product states for infinite-size lattices using others observables. Our work provides a useful probe to study critical behaviors at deconfined quantum critical point from the concept of quantum information.