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arXiv:1901.10850 · Physical review. B./Physical review. B

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

Giuliano Giudici, Adriano Angelone, Giuseppe Magnifico, Zhongda Zeng, Giacomo Giudice, Tiago Mendes-Santos, Marcello Dalmonte

Published Mar 22, 2019• 27 citations

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 [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 nonrelativistic, 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.

DOI: 10.1103/physrevb.99.094434

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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 [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 nonrelativistic, with dynamical critical exponent

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. 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.

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The disorder-induced quantum phase transition between superfluid and nonsuperfluid states of bosonic particles in one dimension is generally expected to be of the Berezinskii-Kosterlitz-Thouless (BKT) type. Here, we show that hard-core lattice bosons with power-law hopping decaying with distance as $1/{r}^{\ensuremath{\alpha}}$ with a finite integral over space---corresponding in spin language to an

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model with power-law couplings---undergo a non-BKT continuous phase transition instead. We use exact quantum Monte Carlo methods to determine the phase diagram for different values of the exponent $\ensuremath{\alpha}$, focusing on the regime $\ensuremath{\alpha}>2$. We find that the scaling of the superfluid stiffness with the system size is scale invariant at the transition point for any $\ensuremath{\alpha}\ensuremath{\le}3$---a behavior incompatible with the BKT scenario and typical of continuous phase transitions in higher dimension. By a scaling analysis near the transition point, we find that our data are consistent with a correlation length exponent satisfying the Harris bound $\ensuremath{\nu}\ensuremath{\ge}2$ and demonstrate a universal behavior of disordered bosons in one dimension. For $\ensuremath{\alpha}>3$ our data are consistent with a BKT scenario where the liquid is pinned by infinitesimal disorder.

We use quantum Monte Carlo simulations to study the effect of disorder, in the form of a disordered chemical potential, on the phase diagram of the hard-core Bosonic Hubbard model in two dimensions. We find numerical evidence that in two dimensions, no matter how weak the disorder, it will always destroy the long-range density wave order (checkerboard solid) present at half filling and strong nearest-neighbor repulsion and replace it with a bose glass phase. We study the properties of this glassy phase including the superfluid density, energy gaps, and the full Green's function. We also study the possibility of other localized phases at weak nearest-neighbor repulsion, i.e., Anderson localization. We find that such a phase does not truly exist: The disorder must exceed a threshold before the bosons (at weak nearest-neighbor repulsion) are localized. The phase diagram for hard-core bosons with disorder cannot be obtained easily from the soft-core phase diagram discussed in the literature.

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The entanglement entropy and quantum fidelity in a hard-core-boson model with nearest- and next-nearest-neighbor interactions are studied numerically. By using exact diagonalization and the density-matrix renormalization group, the effects of interactions on the entanglement entropy and fidelity susceptibility in the model are investigated. We focus our attention on looking for three quantum phase transitions. It is found that the first derivative of the entanglement entropy can indicate all three phase transitions, while the fidelity susceptibility cannot predict the transition from superfluid to bond order in a finite-size system.