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arXiv:cond-mat/0511579 · Physical Review B

Quasiparticle gap in a disordered boson Hubbard model in two dimensions

Ji-Woo Lee, Min-Chul Cha

Published Dec 30, 2005• 5 citations
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Abstract

We investigate the behavior of the quasiparticle energy gap near quantum phase transitions in a two-dimensional disordered boson Hubbard model at a commensurate filling. Via Monte Carlo simulations of ensembles with fixed numbers of particles, we observe the behavior of the gap as a function of the tuning parameter for various strengths of diagonal disorder. For weak disorder, we find that gapped Mott insulating phase is sustained up to the transition point and disappears only in a superfluid, strongly supporting a direct Mott-insulator-to-superfluid transition. Bose glass behavior, insulating with vanishing gap, appears only when the strength of disorder is bigger than a critical value.

DOI
10.1103/physrevb.72.212515

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We investigate the behavior of the quasiparticle energy gap near quantum phase transitions in a two-dimensional disordered boson Hubbard model at a commensurate filling. Via Monte Carlo simulations of ensembles with fixed numbers of particles, we observe the behavior of the gap as a function of the tuning parameter for various strengths of diagonal disorder. For weak disorder, we find that gapped Mott insulating phase is sustained up to the transition point and disappears only in a superfluid, strongly supporting a direct Mott-insulator-to-superfluid transition. Bose glass behavior, insulating with vanishing gap, appears only when the strength of disorder is bigger than a critical value.
We investigate the Bose glass phase and the insulator-to-superfluid transition in the two-dimensional disordered Boson Hubbard model in the Villain representation via Monte Carlo simulations. In the Bose glass phase the probability distribution of the local susceptibility is found to have a 1χ2 tail and the imaginary time Green's function decays algebraically C(τ) ≈ τ−1 giving rise to a divergent global susceptibility. By considering the participation ratio it is shown that the excitations in the Bose glass phase are fully localized and a scaling law is established. For commensurate Boson densities we find direct Mott insulator to superfluid transition without an intervening Bose glass phase for weak disorder. For this transition we obtain the critical exponents z = 1, v = 0.7 ± 0.1 and η = 0.1 ± 0.1, which agree with those for the classical three-dimensional XY model without disorder. This indicates that disorder is irrelevant at the tip of the Mott-lobes and that here the inequality v⩾2d is violated.
We study the zero-temperature phase transitions of a two-dimensional disordered boson Hubbard model at incommensurate boson densities. Via matrix diagonalization and quantum Monte Carlo simulations, we construct the phase diagram and evaluate the correlation length exponent $\ensuremath{\nu}.$ In the presence of weak disorder, we obtain $\ensuremath{\nu}=0.5\ifmmode\pm\else\textpm\fi{}0.1,$ the same value as that in the pure model, near the tip of a Mott insulator lobe, using the dynamical critical exponent z=2.z=2.z=2. As the strength of disorder is increased beyond a certain value, however, the value of $\ensuremath{\nu}$ is found to change to $0.9\ifmmode\pm\else\textpm\fi{}0.1.$ This result strongly suggests that there exist direct Mott insulator-to-superfluid transitions around the tip of a Mott insulator lobe in the weak disorder regime.
We establish the full ground state phase diagram of the disordered Bose-Hubbard model in two dimensions at a unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions persisting up to extremely large values of disorder and interaction strength which, however, have small superfluid fractions and thus low transition temperatures. In the vicinity of the superfluid-insulator transition of the pure system, we observe an unexpectedly weak--almost not resolvable--sensitivity of the critical interaction to the strength of (weak) disorder.
We use renormalization-group theory to examine the quantum phase transitions upon exiting the insulating phase of a disordered, strongly interacting boson system. For weak disorder we find a direct transition from this Mott insulator to the superfluid phase. In d>4d>4d>4 a finite region around the particle-hole symmetric point supports this direct transition, whereas for 2< d<42<~d<42< d<4 perturbative arguments suggest that the direct transition survives only precisely at commensurate filling. For strong disorder the renormalization trajectories pass next to two fixed points, describing a pair of distinct transitions; first from the Mott insulator to the Bose glass, and then from the Bose glass to the superfluid. The latter fixed point possesses statistical particle-hole symmetry and a dynamical exponent zzz, equal to the dimension ddd.
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 two-dimensional disordered boson Hubbard model via quantum Monte Carlo simulations. It is shown that the probability distribution of the local susceptibility has a 1/${\mathrm{\ensuremath{\chi}}}^{2}$ tail in the Bose-glass phase. This gives rise to a divergence although particles are completely localized here as we prove with the help of the participation ratio. We demonstrate the presence of an incompressible Mott lobe within the Bose-glass phase and show that a direct Mott-insulator-to-superfluid transition happens at the tip of the lobe. Here we find critical exponents z=1, \ensuremath{\nu}\ensuremath{\sim}0.7 and \ensuremath{\eta}\ensuremath{\sim}0.1, which agree with those of the pure three-dimensional classical XY model.