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

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.

18 pages, 14 figures

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• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice
• Tunable quantum criticality in multicomponent Rydberg arrays
• Gauge theory description of Rydberg atom arrays with a tunable blockade radius
• Eight-vertex criticality in the interacting Kitaev chain
• Resolving chiral transitions in Rydberg arrays with quantum Kibble-Zurek mechanism and finite-time scaling
• Numerical investigation of quantum phases and phase transitions in a two-leg ladder of Rydberg atoms
• Quantum criticality of a ${\mathbb{Z}}_3$ symmetric spin chain with long-range interactions
• Critical properties of the quantum Ashkin-Teller chain with chiral perturbations
• Emergence of non-Abelian SU(2) invariance in Abelian frustrated fermionic ladders
• Lee-Yang zeros in the Rydberg atoms
• From Kosterlitz-Thouless to Pokrovsky-Talapov transitions in spinless fermions and spin chains with next-nearest neighbour interactions
• Variational manifolds for ground states and scarred dynamics of blockade-constrained spin models on two and three dimensional lattices
• ${\mathbb{Z}}_4$ transitions in quantum loop models on a zig-zag ladder
• Engineering a Josephson junction chain for the simulation of the clock model
• Topological floating phase of dipolar bosons in an optical ladder
• Emergent U(1) symmetry in non-particle-conserving one-dimensional models