# Diagnosing Potts criticality and two-stage melting in one-dimensional hard-boson models

## TL;DR

This paper studies a one-dimensional hard-boson model revealing a two-stage melting process with an intermediate incommensurate phase, using advanced numerical methods to analyze phase transitions and critical behavior.

## Contribution

It provides a comprehensive numerical analysis of phase transitions in a 1D hard-boson model, identifying the nature of the incommensurate phase and critical points, including Berezinskii-Kosterlitz-Thouless behavior.

## Key findings

- Identification of an intermediate incommensurate phase separating crystalline and disordered phases.
- Confirmation of Berezinskii-Kosterlitz-Thouless universality at the disordered-to-incommensurate transition.
- Observation of a non-relativistic second transition with dynamical critical exponent z > 1.

## Abstract

We investigate a model of hard-core bosons with infinitely repulsive nearest- and next-nearest-neighbor interactions in one dimension, introduced by Fendley, Sengupta and Sachdev in Phys. Rev. B 69, 075106 (2004). Using a combination of exact diagonalization, tensor network, and quantum Monte Carlo simulations, we show how an intermediate incommensurate phase separates a crystalline and a disordered phase. We base our analysis on a variety of diagnostics, including entanglement measures, fidelity susceptibility, correlation functions, and spectral properties. According to theoretical expectations, the disordered-to-incommensurate-phase transition point is compatible with Berezinskii-Kosterlitz-Thouless universal behaviour. The second transition is instead non-relativistic, with dynamical critical exponent $z > 1$. For the sake of comparison, we illustrate how some of the techniques applied here work at the Potts critical point present in the phase diagram of the model for finite next-nearest-neighbor repulsion. This latter application also allows to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy.