The study of the disordered Bose-Hubbard model is key to understanding the interplay of disorder and interactions. Despite many studies with uniform diagonal disorder, few have inquired into experimental realizations with an additional correlated off-diagonal disorder. The presence of a trap and finite temperature effects in experiments lead to multiple do- mains of the Superfluid, Mott-Insulator/normal and the Bose-Glass phase. Previous studies using approximate theories produced results that are not in accordance with experiments. Stochastic Series Expansion is a finite temperature technique that can solve Bosonic lattice Hamiltonians exactly for large systems. Here, studies are performed for an extensive range of parameters using disorder distributions that are similar to experiments. Insights are first acquired by studying trap-free situations. Constant density calculations show that, although the qualitative features of the phase diagram remain robust between speckle disorder and uniform box disorder, there are quantitative differences. Studies of the Bose-glass phase ex- plicitly show that it is composed of superfluid puddles that are stable to finite temperature effects for large temperature ranges. Finite temperature behavior of a strongly correlated sys- tem reveals that at unit filling, the transition temperature of the superfluid is increased due to the addition of disorder. Inquires are then extended to discern the properties of trapped systems. Extensive calculations show that domain-like structures that develop can be rig- orously demarcated using the single-particle eigenstates extracted from the single-particle density matrix. Observables are calculated for the system at the single-site and global scales, showing that intermediate length scales provide the correct description of the physics of the domains in these systems. These techniques are used to conclusively show the possibility of the re-entrant superfluid that should be accessible to experiments. The temperature de- pendence of the re-entrant domain is explicitly calculated to be within experimental limits provided interactions are not too large. Comparisons with the local density approximation show reasonable agreement at low disorder strengths. At large disorder strengths there can be quantitative errors and can also result in qualitative errors. The phase diagram due to speckle disorder is presented for a range of values that are readily accessible to experiments. It is quantitatively shown that the effects of off-diagonal disorder are minimal. The superfluid remains unaffected despite large disorder in the tunneling term. Full scale ab initio calcu- lations of the largest trapped disordered systems to date are performed in order to identify the superfluid-Bose-glass phase boundary in collaboration with experiments. Results show remarkable agreement, but there are open questions with regards to the possibility of glassy dynamics.
The study of the disordered Bose-Hubbard model is key to understanding the interplay of disorder and interactions. Despite many studies with uniform diagonal disorder, few have inquired into experimental realizations with an additional correlated off-diagonal disorder. The presence of a trap and finite temperature effects in experiments lead to multiple do- mains of the Superfluid, Mott-Insulator/normal and the Bose-Glass phase. Previous studies using approximate theories produced results that are not in accordance with experiments. Stochastic Series Expansion is a finite temperature technique that can solve Bosonic lattice Hamiltonians exactly for large systems. Here, studies are performed for an extensive range of parameters using disorder distributions that are similar to experiments. Insights are first acquired by studying trap-free situations. Constant density calculations show that, although the qualitative features of the phase diagram remain robust between speckle disorder and uniform box disorder, there are quantitative differences. Studies of the Bose-glass phase ex- plicitly show that it is composed of superfluid puddles that are stable to finite temperature effects for large temperature ranges. Finite temperature behavior of a strongly correlated sys- tem reveals that at unit filling, the transition temperature of the superfluid is increased due to the addition of disorder. Inquires are then extended to discern the properties of trapped systems. Extensive calculations show that domain-like structures that develop can be rig- orously demarcated using the single-particle eigenstates extracted from the single-particle density matrix. Observables are calculated for the system at the single-site and global scales, showing that intermediate length scales provide the correct description of the physics of the domains in these systems. These techniques are used to conclusively show the possibility of the re-entrant superfluid that should be accessible to experiments. The temperature de- pendence of the re-entrant domain is explicitly calculated to be within experimental limits provided interactions are not too large. Comparisons with the local density approximation show reasonable agreement at low disorder strengths. At large disorder strengths there can be quantitative errors and can also result in qualitative errors. The phase diagram due to speckle disorder is presented for a range of values that are readily accessible to experiments. It is quantitatively shown that the effects of off-diagonal disorder are minimal. The superfluid remains unaffected despite large disorder in the tunneling term. Full scale ab initio calcu- lations of the largest trapped disordered systems to date are performed in order to identify the superfluid-Bose-glass phase boundary in collaboration with experiments. Results show remarkable agreement, but there are open questions with regards to the possibility of glassy dynamics.
We investigate the properties of the superfluid phase in the three-dimensional disordered Bose-Hubbard model using quantum Monte Carlo simulations. The phase diagram is generated using Gaussian disorder on the on-site potential. Comparisons with box and speckle disorder show qualitative similarities leading to the reentrant behavior of the superfluid. Quantitative differences that arise are controlled by the specific shape of the disorder. Statistics pertaining to disorder distributions are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. Despite this, both the superfluid fraction and compressibility remain self-averaging throughout the superfluid phase. Close to the superfluid--Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. Our results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not possible.
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two-dimensional(2D) optical lattice. The scale-invariant, finite temperature state diagram is presented for the Bose-Hubbard model in terms of experimental parameters -- the particle number, confining potential and interaction strength. To distinguish the nature of the spatially separated superfluid, Mott insulator, and normal Bose liquid phases, we examine the local density, compressibility, superfluid density, and Green's function. In the annular superfluid rings, as the width of the ring decreases, the long-range superfluid correlations start to deviate from an equivalent homogeneous 2D system. At zero temperature, the correlation decay is intermediate between one-dimension and two-dimensions, while at a finite temperature, the decay is similar to that in one-dimension at a much lower temperature. The calculations reveal shortcomings of the local density approximation in describing superfluid properties of trapped bosons. We also present the finite-temperature phase diagram for the homogeneous two dimensional Bose-Hubbard model. We compare our state diagram with the results of a recent experiment at NIST on a harmonically trapped 2D lattice [Phys. Rev. Lett. 105, 110401 (2010)], and identify a finite-temperature effect in the experiment.
We discuss the stochastic mean-field theory (SMFT) method, which is a new approach for describing disordered Bose systems in the thermodynamic limit including localization and dimensional effects. We explicate the method in detail and apply it to the disordered Bose-Hubbard model at finite temperature, with on-site box disorder, as well as experimentally relevant unbounded speckle disorder. We find that disorder-induced condensation and re-entrant behavior at constant filling are only possible at low temperatures, beyond the reach of current experiments [M. Pasienski, D. McKay, M. White, and B. DeMarco, e-print arXiv:0908.1182]. Including off-diagonal hopping disorder as well, we investigate its effect on the phase diagram in addition to pure on-site disorder. To make connection to present experiments on a quantitative level, we also combine SMFT with an LDA approach and obtain the condensate fraction in the presence of an external trapping potential.
Abstract We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose–Hubbard model. The criteria for identifying the superfluid, the Mott-insulator, and the Bose-glass phases at finite temperatures are discussed for small values of the kinetic energy associated with the tunnelling of particles between potential wells. Field theoretical considerations are applied in order to construct a diagrammatic hopping expansion to the finite-temperature Green’s function. By performing a summation of subsets of diagrams we are able to find the condition to the long-range correlations which leads to the phase boundary between superfluid and insulating phases. The perturbative expression to the local correlations allows us to calculate an approximation to the single-particle density of states of low-energy excitations in the presence of small hopping, which characterizes unambiguously the distinction between the Mott-insulator and the Bose-glass phases. We obtain the phase diagram for bounded on-site disorder. It is demonstrated that our analysis is capable of going beyond the mean-field theory results for the classification of these different ground states.
The question of how the low-energy properties of disordered quantum systems may be connected to exotic localization phenomena at high energy is a key open question in the context of quantum glasses and many-body localization. In the preceding Letter [L. Villa, S. J. Thomson, and L. Sanchez-Palencia, preceding Letter, Phys. Rev. A 104, L021301 (2021)] we have shown that key features of the excitation spectrum of a disordered system can be efficiently probed from out-of-equilibrium dynamics following a quantum quench, providing distinctive signatures of the various phases. Here we extend this work by providing a more-in-depth study of the behavior of the quench spectral functions associated with different observables and investigating an extended parameter regime. We provide a detailed introduction to quench spectroscopy for disordered systems and show how spectral properties can be probed using both local operators and two-point correlation functions. We benchmark the technique using the one-dimensional Bose-Hubbard model in the presence of a random external potential, focusing on the low-lying excitations, and demonstrate that quench spectroscopy can distinguish the Mott insulator, superfluid, and Bose glass phases. We then explicitly reconstruct the zero-temperature phase diagram of the disordered Bose-Hubbard at fixed filling using two independent methods, experimentally accessible via both time-of-flight imaging and quantum gas microscopy, respectively, and demonstrate that quench spectroscopy can give valuable insights into the distribution of rare regions within disordered systems.
Ultracold atoms in optical lattices offer an important tool for studying dynamics in many-body interacting systems in a pristine environment. This thesis focuses on three theoretical works motivated by recent optical lattice experiments. In the first, we theoretically study the center of mass dynamics of states derived from the disordered Bose-Hubbard model in a trapping potential. We find that the edge states in the trap allow center of mass motion even with insulating states in the center. We identify short and long-time mechanisms for edge state transport in insulating phases. We also argue that the center of mass velocity can aid in identifying a Bose-glass phase. Our zero temperature results offer important insights into mechanisms of transport of atoms in trapped optical lattices while putting bounds on center of mass dynamics expected at non-zero temperature. In the second work, we study the domain wall expansion dynamics of strongly interacting bosons in 2D optical lattices with disorder in a recent experiment {[}J.-y. Choi et al., Science 352, 1547 (2016)]. We show that Gutzwiller mean-field theory (GMFT) captures the main experimental observations, which are a result of the competition between disorder and interactions. Our findings highlight the difficulty in distinguishing glassy dynamics, which can be captured by GMFT, and many-body localization, which cannot be captured by GMFT, and indicate the need for further experimental studies of this system. The last work features our study of phase diagrams of the 2D Bose-Hubbard model in an optical lattice with synthetic spin-orbit coupling. We investigate the transitions between superfluids with different phase patterns, which may be detected by measuring the spin-dependent momentum distribution.