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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 ofexact diagonalization, tensor network, and quantum Monte Carlo simulations, weshow how an intermediate incommensurate phase separates a crystalline and adisordered phase. We base our analysis on a variety of diagnostics, includingentanglement measures, fidelity susceptibility, correlation functions, andspectral properties. According to theoretical expectations, thedisordered-to-incommensurate-phase transition point is compatible withBerezinskii-Kosterlitz-Thouless universal behaviour. The second transition isinstead non-relativistic, with dynamical critical exponent $z > 1$. For thesake of comparison, we illustrate how some of the techniques applied here workat the Potts critical point present in the phase diagram of the model forfinite next-nearest-neighbor repulsion. This latter application also allows toquantitatively estimate which system sizes are needed to match the conformalfield theory spectra with experiments performing level spectroscopy.

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