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arXiv:1608.06862 · Journal of Physics Conference Series

Superuid-Mott glass quantum multicritical point on a percolating lattice

Martin Puschmann, Thomas Vojta

Published Oct 1, 2017• 2 citations
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Abstract

We employ large-scale Monte Carlo simulations to study a particle-hole symmetric site-diluted quantum rotor model in two dimensions. The ground state phase diagram of this system features two distinct quantum phase transitions between the superuid and the insulating (Mott glass) phases. They are separated by a multicritical point. The generic transition for dilutions below the lattice percolation threshold is driven by quantum uctuations while thetransition across the percolation threshold is due to the geometric uctuations of the lattice. We determine the location of the multicritical point between these two transitions and find its critical behavior. The multicritical exponents read z = 1:72(2), β / ν = 0:41(2), and γ/ν = 2:90(5). We compare our results to other quantum phase transitions in disordered systems, and we discuss experiments.

DOI
10.1088/1742-6596/905/1/012038

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We employ large-scale Monte Carlo simulations to study a particle-hole symmetric site-diluted quantum rotor model in two dimensions. The ground state phase diagram of this system features two distinct quantum phase transitions between the superuid and the insulating (Mott glass) phases. They are separated by a multicritical point. The generic transition for dilutions below the lattice percolation threshold is driven by quantum uctuations while thetransition across the percolation threshold is due to the geometric uctuations of the lattice. We determine the location of the multicritical point between these two transitions and find its critical behavior. The multicritical exponents read z = 1:72(2), β / ν = 0:41(2), and γ/ν = 2:90(5). We compare our results to other quantum phase transitions in disordered systems, and we discuss experiments.
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 $z=1.52(3), \ensuremath{\nu}=1.16(5), \ensuremath{\beta}/\ensuremath{\nu}=0.48(2), \ensuremath{\gamma}/\ensuremath{\nu}=2.52(4)$, 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.
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.
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We study the zero-temperature phase transition of a two-dimensional disordered boson Hubbard model. The phase diagram is constructed in terms of the disorder strength and the chemical potential. Via Monte Carlo simulations, we find a multicritical line separating the weak-disorder regime, where the Mott-insulator-to-superfluid transition occurs, from the strong-disorder regime, where the Bose-glass-to-superfluid transition occurs. On the multicritical line, the insulator-to-superfluid transition has the dynamical critical exponent $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.35\ifmmode\pm\else\textpm\fi{}0.05$ and the correlation length critical exponent $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.67\ifmmode\pm\else\textpm\fi{}0.03$. We suggest that the proliferation of the particle-hole pairs screens out the weak-disorder effects.
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.
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.