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arXiv:1503.02973 · Europhysics Letters (EPL)

Using entanglement to discern phases in the disordered one-dimensional Bose-Hubbard model

Andrew M. Goldsborough, Rudolf A. Römer

Published Jul 1, 2015• 13 citations
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Abstract

We perform a matrix-product-state–based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities , 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come for free when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when and 1/2 (without the Mott insulator) as found in previous studies. For the system we find a double-lobed superfluid phase with possible re-entrance.

DOI
10.1209/0295-5075/111/26004

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We perform a matrix-product-state–based density matrix renormalisation group analysis of the phases for the disordered one-dimensional Bose-Hubbard model. For particle densities , 1/2 and 2 we show that it is possible to obtain a full phase diagram using only the entanglement properties, which come for free when performing an update. We confirm the presence of Mott insulating, superfluid and Bose glass phases when and 1/2 (without the Mott insulator) as found in previous studies. For the system we find a double-lobed superfluid phase with possible re-entrance.
We calculate the zero-temperature phase diagram of the disordered Bose-Hubbard model in one dimension using the density matrix renormalization group. For integer filling the Mott insulator is always separated from the superfluid by a Bose glass phase. There is a re-entrance of the Bose glass both as a function of the repulsive interaction and of disorder. At half-filling where no Mott insulator exists, the superfluid density has a maximum where the kinetic and repulsive energies are about the same. Superfluidity is suppressed both for small and very strong repulsion but is always monotonic in disorder.
Introducing disorder into the Bose-Hubbard model at integer fillings leads to a Bose glass phase, along with the Mott insulator and superfluid phases. We suggest a new order parameter: the determinant of the one body density matrix, which is nonzero only within the Mott-insulator phase. Alongside the superfluid fraction, it is then possible to distinguish the three phases. The Bose glass phase is the only phase which has vanishing determinant and superfluid fraction. The vanishing of the determinant in the Bose glass phase occurs due to the partial fragmentation of the condensate into localized fragments, each with zero superfluid response, which implies the presence of unoccupied sites and hence the presence of lines of zeros in the one body density matrix. In the superfluid phase, the determinant vanish for another reason - due to the macroscopic occupation of a single particle state. Finally, we suggest the enhancement of the three body decay rate in the Bose glass phase, as an experimental indicator for the presence of localized fragments.
We study the one-dimensional Bose-Hubbard model using the density-matrix renormalization group. For the cases of on-site interactions and additional nearest-neighbor interactions the phase boundaries of the Mott insulators and charge-density wave phases are determined. We find a direct phase transition between the charge-density wave phase and the superfluid phase, and no supersolid or normal phases. In the presence of nearest-neighbor interaction the charge density wave phase is completely surrounded by a region in which the effective interactions in the superfluid phase are repulsive. In this region a single impurity causes the system to be insulating. An even bigger region of the superfluid phase is driven into a Bose-glass phase by any finite quenched disorder. We determine the boundaries of both regions in the phase diagram. The ac conductivity of the superfluid phase in the attractive and the repulsive region is calculated, and a big superfluid stiffness is found in the attractive as well as the repulsive region.
We use the density-matrix renormalization group to study the one-dimensional bosonic Hubbard model, with and without disorder. We obtain the gaps in all phases, certain correlation functions, and the superfluid density. A finite-size-scaling analysis enables us to obtain an accurate phase diagram and the $\ensuremath{\beta}$ function at the superfluid--Mott insulator transition and the Kosterlitz-Thouless essential singularity in the pure case. We also obtain coupling constants used in effective field theories for this system.
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 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.