We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find a ``two negatives make a positive'' effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.
We propose an exactly solvable model to reveal the physics of the interplay between interaction and disorder in bosonic systems. Considering interacting bosons in a double-well potential, in which disorder is mimicked by taking the energy level mismatch between the two wells to be randomly distributed, we find a ``two negatives make a positive'' effect. While disorder or interaction by itself suppresses the phase coherence between the two wells, both together enhance the phase coherence. This model captures several striking features of the disordered Bose-Hubbard model found in recent numerical simulations. Results at finite temperatures may help explain why a recent experiment did not find any evidence for the enhancement of phase coherence in a disordered bosonic system.
We theoretically and numerically investigate the coherence of disordered bosonic gas with effective two- and three-body interactions within a two-site Bose–Hubbard model. By properly adjusting the two- and three-body interactions and the disorder, the coherence of the system exhibits new and interesting phenomena, including the resonance character of coherence against the disorder in the purely two- or three-body interactions system. More interestingly, the disorder and three-body interactions together can suppress the coherence of the purely three-body interactions system, which is different from the case in which the disorder and two-body interactions together can enhance the coherence in certain values of two-body interaction. Furthermore, when two- or three-body interactions are attractive or repulsive, the phase coherence exhibits completely different phenomena. In particular, if two- or three-body interactions are attractive, the coherence of the system can be significantly enhanced in certain regions. Correspondingly, the phase coherence of the system is strongly related to the effective interaction energy. The results provide a possible way for studying the coherence of bosonic gas with multi-atoms' interactions in the presence of the disorder.
We study the interplay of disorder localization and strong local interactions within the Anderson-Hubbard model. Taking into account local Mott-Hubbard physics and static screening of the disorder potential, the system is mapped onto an effective single-particle Anderson model, which is studied within the self-consistent theory of electron localization. For fermions, we find rich nonmonotonic behavior of the localization length ξ, particularly in two-dimensional systems, including an interaction-induced exponential enhancement of ξ for small and intermediate disorders and a strong reduction of ξ due to hopping suppression by strong interactions. In three dimensions, we identify for half filling a Mott-Hubbard-assisted Anderson localized phase existing between the metallic and the Mott-Hubbardgapped phases. For small U there is re-entrant behavior from the Anderson localized phase to the metallic phase. For bosons, the unrestricted particle occupation number per lattice site yields a monotonic enhancement of ξ as a function of decreasing interaction, which we assume to persist until the superfluid Bose- Einstein condensate phase is entered. Besides, we study cold atomic gases expanding, by a diffusion process, in a weak random potential. We show that the density-density correlation function of the expanding gas is strongly affected by disorder and we estimate the typical size of a speckle spot, i.e., a region of enhanced or depleted density. Both a Fermi gas and a Bose-Einstein condensate (in a mean-field approach) are considered.
We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling which has been controversial for many years. The theorem of inclusions, proven by Pollet et al. [Phys. Rev. Lett. 103, 140402 (2009)] states that the Bose-glass phase always intervenes between the Mott insulating and superfluid phases. Here, we note that assumptions on which the theorem is based exclude phase transitions between gapped (Mott insulator) and gapless phases (Bose glass). The apparent paradox is resolved through a unique mechanism: such transitions have to be of the Griffiths type when the vanishing of the gap at the critical point is due to a zero concentration of rare regions where extreme fluctuations of disorder mimic a regular gapless system. An exactly solvable random transverse field Ising model in one dimension is used to illustrate the point. A highly nontrivial overall shape of the phase diagram is revealed with the worm algorithm. The phase diagram features a long superfluid finger at strong disorder and on-site interaction. Moreover, bosonic superfluidity is extremely robust against disorder in a broad range of interaction parameters; it persists in random potentials nearly 50 (!) times larger than the particle half-bandwidth. Finally, we comment on the feasibility of obtaining this phase diagram in cold-atom experiments, which work with trapped systems at finite temperature.
The consequences of disorder on interacting bosons trapped in one-dimensional optical lattices are investigated by quantum Monte Carlo simulations. A numerical analysis of the momentum distribution function, the stiffness and the compressibility reveals a unique response to small to moderate strengths of potential disorder. If there is a Mott plateau at the centre of the trap in the clean limit, phase coherence increases as a result of disorder. The localization effects due to correlation and disorder compete against each other, resulting in a partial delocalization of the particles in the Mott region, which in turn leads to increased phase coherence. In the absence of a Mott plateau, this effect is absent. A detailed analysis of the uniform system without a trap shows that the disordered states participate in a Bose glass phase.
We investigate the coherence of correlated dipolar gas in the presence of disorder within a three-site Bose–Hubbard model. We show that the interplay between the on-site interaction, the inter-site dipole–dipole interactions (DDI) and the disorder exhibits new and interesting coherence characters that cannot take place in a non-dipolar system. The ratio between the on-site interaction and DDI plays a dominant role in the phase coherence. The resonance character of the coherence against both disorder and interactions emerges. DDI can enhance the coherence at certain values of the disorder and on-site interaction. In the coherence region, the enhancement of the coherence by disorder in a dipolar system is more significant than that in a non-dipolar system. In particular, the on-site interaction and DDI together can enhance the coherence even in the clean dipolar system (i.e. a dipolar system without disorder). However, without the on-site interaction, disorder, DDI or both together suppress the coherence. Furthermore, the relationship between the coherence and the energy gap and the compressibility of the system is also discussed.
Bosonic excitations within long-range ordered, but strongly inhomogeneous phases have been studied in quite some detail. My thesis focuses instead on understanding the insulating, localized phase of disordered bosonic systems. In particular I study localization properties of strongly interacting bosons and spin systems in a disorder potential at zero temperature. I focus on simple, prototypical spin models (Ising model and XY model) in random fields on a Cayley tree with large connectivity. Regarding the nature of the quantum phase transition in strong disorder I find the following results: i) With a uniformly distributed disorder non-extensive excitations in the disordered phase are all localized. ii)Moreover, I find that the order arises due to a collective condensation, which is qualitatively distinct from a Bose Einstein condensation of single particle excitations into a delocalized state. In particular, in non-frustrated Bose glasses, I do not find evidence for a boson mobility edge in the Bose glass. These results are qualitatively different from claims in the recent literatures . Considering that (many body) localization of bosons is a kind of quantum glass transition, it is an interesting question to ask what phenomena occur, if the ingredients for more conventional (classical) glassy physics are added to a disordered bosons system, namely: random, frustrated interactions between the bosons. One can still think about such a system as bosons in a disordered potential, where the disordered potential is, at least partly, self-generated by random frustrated interactions between the bosons. This question takes us to the study of another type of disordered systems: glassy systems. Those are typically characterized by low temperature phases with an inhomogeneous density or magnetization pattern, which is extremely long-lived due to the occurrence of non-trivial ergodicity breaking. I study a solvable model of hard core bosons (pseudospins) subject to disorder and frustrating interactions. This solvable model provides insight into the possibility of coexistence of super uidity and glassy density order, as well as into the nature of the coexistence phase (the superglass). In particular, for the considered mean field model I prove the existence of a superglass phase. This complements the numerical evidence for such phases provided by quantum Monte Carlo investigations in finite dimensions and on random graphs. Those were, however, limited to finite temperature, and could thus not fully elucidate the structure of the phases at T = 0. In contrast, my analytical approach allows one to understand the quantum phase transition between glassy superfluid and insulator, and the non-trivial role played by glassy correlations. When the frustrated interactions are strong enough, the superfluid order may be destroyed. As I will show in a mean field model, this happens within the glass phase of the system, where a disorder induced superfluid-insulator phase transition takes place to give way to a frustrated Bose glass. The glassy background on top of which this happens leads to many interesting phenomena which seem not to have been noticed before. To understand the nature of the glassy superfluid-insulator quantum phase transition at zero temperature and the transport properties on the insulating, Bose glass side of the transition is the goal of the third part of my thesis. To address the above questions, I studied an exactly solvable model of a glassy superfluid-insulator quantum phase transition on a Bethe lattice geometry with high connectivity. My main results can be summarized as follows: i) I found that the superfluid-insulator transition is shifted to stronger hopping. This is a result of the pseudo gap in the density of states of the glass state, which tends to strongly disfavor the onset of superfluidity. ii) In the glassy insulator, the discrete local energy levels become broadened due to the quantum fluctuations.The level-broadening process appears as a phase transition which has strong similarities with an Anderson localization transition, and has implications on many body localization. By using the locator expansion for bosons I found that, the glassy insulator has a finite mobility edge for the bosonic excitations, which, however, does not close upon approaching the SI quantum phase transition point. This finding helps to understand the nature of the superfluid-to-frustrated Bose glass transition: the superfluid emerges as a collective phase ordering phenomenon at zero temperature, and not as a condensation in to a single particle delocalized state, in contrast to opposite predictions in the recent literatures. The existence of a mobility edge in the insulator suggests the possibility of phononless, activated transport in the bosonic insulator, which might be a candidate explanation for the experimentally seen activated transport, which has remained a mystery for a long time.