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arXiv:1607.01860 · Physical review. B./Physical review. B

Quantum critical behavior of the superfluid-Mott glass transition

Thomas Vojta, Jack Crewse, Martin Puschmann, Daniel P. Arovas, Yury Kiselev

Published Oct 3, 2016• 28 citations
arXivHTMLPDF

Abstract

We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical $(2+1)$-dimensional $XY$ model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents $z=1.52(3), \ensuremath{\nu}=1.16(5), \ensuremath{\beta}/\ensuremath{\nu}=0.48(2), \ensuremath{\gamma}/\ensuremath{\nu}=2.52(4)$, and $\ensuremath{\eta}=\ensuremath{-}0.52(4)$. These values agree with and improve upon earlier Monte Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments.

DOI
10.1103/physrevb.94.134501

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We investigate the zero-temperature superfluid to insulator transitions in a diluted two-dimensional quantum rotor model with particle-hole symmetry. We map the Hamiltonian onto a classical (2+1)(2+1)(2+1)-dimensional XYXYXY model with columnar disorder which we analyze by means of large-scale Monte Carlo simulations. For dilutions below the lattice percolation threshold, the system undergoes a generic superfluid-Mott glass transition. In contrast to other quantum phase transitions in disordered systems, its critical behavior is of conventional power-law type with universal (dilution-independent) critical exponents z=1.52(3),\ensuremathν=1.16(5),\ensuremathβ/\ensuremathν=0.48(2),\ensuremathγ/\ensuremathν=2.52(4)z=1.52(3), \ensuremath{\nu}=1.16(5), \ensuremath{\beta}/\ensuremath{\nu}=0.48(2), \ensuremath{\gamma}/\ensuremath{\nu}=2.52(4)z=1.52(3),\ensuremathν=1.16(5),\ensuremathβ/\ensuremathν=0.48(2),\ensuremathγ/\ensuremathν=2.52(4), and \ensuremathη=\ensuremath−0.52(4)\ensuremath{\eta}=\ensuremath{-}0.52(4)\ensuremathη=\ensuremath−0.52(4). These values agree with and improve upon earlier Monte Carlo results [Phys. Rev. Lett. 92, 015703 (2004)] while (partially) excluding other findings in the literature. As a further test of universality, we also consider a soft-spin version of the classical Hamiltonian. In addition, we study the percolation quantum phase transition across the lattice percolation threshold; its critical behavior is governed by the lattice percolation exponents in agreement with recent theoretical predictions. We relate our results to a general classification of phase transitions in disordered systems, and we briefly discuss experiments.
The superfluid to insulator quantum phase transition of a three-dimensional particle-hole symmetric system of disordered bosons is studied. To this end, a site-diluted quantum rotor Hamiltonian is mapped onto a classical (3+1)-dimensional XYXYXY model with columnar disorder and analyzed by means of large-scale Monte Carlo simulations. The superfluid-Mott insulator transition of the clean, undiluted system is in the four-dimensional XYXYXY universality class and shows mean-field critical behavior with logarithmic corrections. The clean correlation length exponent $\ensuremath{\nu}=1/2$ violates the Harris criterion, indicating that disorder must be a relevant perturbation. For nonzero dilutions below the lattice percolation threshold of pc=0.688392{p}_{c}=0.688\phantom{\rule{0.16em}{0ex}}392pc​=0.688392, our simulations yield conventional power-law critical behavior with dilution-independent critical exponents z=1.67(6)z=1.67(6)z=1.67(6), $\ensuremath{\nu}=0.90(5)$, $\ensuremath{\beta}/\ensuremath{\nu}=1.09(3)$, and $\ensuremath{\gamma}/\ensuremath{\nu}=2.50(3)$. The critical behavior of the transition across the lattice percolation threshold is controlled by the classical percolation exponents. Our results are discussed in the context of a classification of disordered quantum phase transitions, as well as experiments in superfluids, superconductors, and magnetic systems.
We study the zero-temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by a percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.
The phase diagrams and phase transitions of bosons with short-ranged repulsive interactions moving in periodic and/or random external potentials at zero temperature are investigated with emphasis on the superfluid-insulator transition induced by varying a parameter such as the density. Bosons in periodic potentials (e.g., on a lattice) at T=0 exhibit two types of phases: a superfluid phase and Mott insulating phases characterized by integer (or commensurate) boson densities, by the existence of a gap for particle-hole excitations, and by zero compressibility. Generically, the superfluid onset transition in d dimensions from a Mott insulator to superfluidity is ``ideal,'' or mean field in character, but at special multicritical points with particle-hole symmetry it is in the universality class of the (d+1)-dimensional XY model. In the presence of disorder, a third, ``Bose glass'' phase exists. This phase is insulating because of the localization effects of the randomness and analogous to the Fermi glass phase of interacting fermions in a strongly disordered potential.The Bose glass phase is characterized by a finite compressibility, no gap, but an infinite superfluid susceptibility. In the presence of disorder the transition to superfluidity is argued to occur only from the Bose glass phase, and never directly from the Mott insulator. This zero-temperature superfluid-insulator transition is studied via generalizations of the Josephson scaling relation for the superfluid density at the ordinary \ensuremath{\lambda} transition, highlighting the crucial role of quantum fluctuations. The transition is found to have a dynamic critical exponent z exactly equal to d and correlation length and order-parameter correlation exponents \ensuremath{\nu} and \ensuremath{\eta} which satisfy the bounds \ensuremath{\nu}\ensuremath{\ge}2/d and \ensuremath{\eta}\ensuremath{\le}2-d, respectively. It is argued that the superfluid-insulator transition in the presence of disorder may have an upper critical dimension dc{d}_{c}dc​ which is infinite, but a perturbative renormalization-group calculation wherein the critical exponents have mean-field values for weak disorder above d=4 is also discussed. Many of these conclusions are verified by explicit calculations on a model of one-dimensional bosons in the presence of both random and periodic potentials. The general results are applied to experiments on 4He^{4}\mathrm{He}4He absorbed in porous media such as Vycor. Some measurable properties of the superfluid onset are predicted exactly [e.g., the exponent x relating the \ensuremath{\lambda} transition temperature to the zero-temperature superfluid density is found to be d/2(d-1)], while stringent bounds are placed on others. Analysis of preliminary data is consistent with these predictions.
We study the phase diagram and the quantum phase transitions of a site-diluted two-dimensional O(3) quantum rotor model by means of large-scale Monte Carlo simulations. This system has two quantum phase transitions: a generic one for small dilutions and a percolation transition across the lattice percolation threshold. We determine the critical behavior for both transitions and for the multicritical point that separates them. In contrast to the exotic scaling scenarios found in other random quantum systems, all these transitions are characterized by finite-disorder fixed points with power-law scaling. We relate our findings to a recent classification of phase transitions with quenched disorder according to the rare region dimensionality, and we discuss experiments in disordered quantum magnets.
We use quantum Monte Carlo simulations to study a dimer-diluted S = 1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J 1 and interlayer interaction J 2 . Below the classical percolation threshold p c , the system has three phases reachable by tuning the interaction ratio g = J 2 / J 1 : a Néel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g . The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T > 0; χ u exp(- b / T α ) with α < 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O (3) universality class in 2+1 dimensions.
The amplitude (Higgs) mode near the two-dimensional superfluid--Mott glass quantum phase transition is studied. We map the Bose-Hubbard Hamiltonian of disordered interacting bosons onto an equivalent classical XY\mathit{XY}XY model in (2+12+12+1) dimensions and compute the scalar susceptibility of the order parameter amplitude via Monte Carlo simulation. Analytic continuation of the scalar susceptibilities from imaginary to real frequency to obtain the spectral densities is performed by a modified maximum entropy technique. Our results show that the introduction of disorder into the system leads to unconventional dynamical behavior of the Higgs mode that violates naive scaling, despite the underlying thermodynamics of the transition being of the conventional power-law type. The computed spectral densities exhibit a broad, noncritical response for all energies, and a momentum-independent dispersion for long wavelengths, indicating strong evidence for the localization of the Higgs mode for all dilutions.