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

Abstract

We investigate a model of hard-core bosons with infinitely repulsive nearest-and next-nearestneighbor 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 behavior. 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 us to quantitatively estimate which system sizes are needed to match the conformal field theory spectra with experiments performing level spectroscopy. arXiv:1901.10850v2 [cond-mat.quant-gas]

Geometry of quantum phase transitions

“…We will review the main results on the spectral properties of the quadratic Fermionic Liouvillian (191). Note that the real matrix X defined in (211) has no general structure apart from the fact that X + X T = 8ReM ≥ 0, where M is the bath matrix defined in (213), whose positive semi-definiteness implies ReM ≥ 0. We will drop here the assumption made in Section 15, about the diagonalisability of X , and will show that the qualitative aspects of the results derived in Section 16 still hold.…”

“…Various methods have been developed to evaluate the fidelity, such as exact diagonalisation, density matrix renormalisation group [160,204,205], quantum Monte Carlo methods [195,206,207], tensor network algorithms [208,209]. This provides the means to venture into the study of models where analytical solutions are not available [160,204,205,207,210,211].…”

“…The fidelity approach has been employed in the investigation of first order phase transitions [212], in higherthan-second order QPTs [213], in finite temperature phase transitions [51,164,165,193,214] and non-equilibrium phase transitions [177,178,[215][216][217]. The efficacy of this approach in signalling QPTs that elude the Landau-Ginzburg-Wilson paradigm has been tested against Berezinskii-Kosterlitz-Thouless phase transitions [218][219][220][221][222], topological phase transitions [167,[223][224][225], and in strongly correlated models whose critical features are yet to be understood [210,211,226,227]. The universal scaling properties of quantities related to the fidelity approach, such as the fidelity susceptibility [195,228,229], the quantum geometric tensor [42,160] and the Fisher information matrix [230], have been investigated and exploited in numerous scenarios.…”

Microscopic characterization of Ising conformal field theory in Rydberg chains

“…It was further explored via large-scale numerics in Refs. [14,[26][27][28] (see also Refs. [13,15,24]).…”

“…The broader phase diagram features additional phases (not shown) including a threefold-degenerate charge density wave and incommensurate order; see Refs. [11,14,[26][27][28].…”