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arXiv:cond-mat/9612027 · Physical review. B, Condensed matter

Bose-glass and Mott-insulator phase in the disordered boson Hubbard model

Jens Kisker, Heiko Rieger

Published May 1, 1997• 95 citations
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Abstract

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.

DOI
10.1103/physrevb.55.r11981

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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/\ensuremathχ2{\mathrm{\ensuremath{\chi}}}^{2}\ensuremathχ2 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.
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 review the physics of the Bose–Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.
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.
The phase diagram of the Bose-Hubbard model in the presence of off-diagonal disorder is determined using quantum Monte Carlo simulations. A sequence of quantum glass phases intervene at the interface between the Mott insulating and the superfluid phases of the clean system. In addition to the standard Bose glass phase, the coexistence of gapless and gapped regions close to the Mott insulating phase leads to a novel Mott glass regime which is incompressible yet gapless. Numerical evidence for the properties of these phases is given in terms of global (compressibility, superfluid stiffness) and local (compressibility, momentum distribution) observables.
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 prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove the compressibility of the system on the superfluid-insulator critical line and in its neighborhood. These conclusions follow from a general theorem of inclusions, which states that for any transition in a disordered system, one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: the critical disorder bound Delta(c) corresponding to the onset of disorder-induced superfluidity, satisfies the relation Delta(c)>Eg/2, with Eg/2 the half-width of the Mott gap in the pure system.