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Exploring the phase diagram for two-component Bose-Hubbard model in 2D: Mott Insulator to Superfluid transitions and exotic magnetic-like phases

Marco Guglielmino

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

In this dissertation I present results for Bose-Hubbard model in 2D obtained with quantum Monte Carlo simulations by the Worm algorithm and Mean Field techniques. First I study a uniform system and I describe how the Mottinsulator-to-superfluid transition for a majority component is affected by the presence of a minority superfluid one. Then I focus on magnetic-like ground states known as checkerboard phase which can be obtained in the strongly interacting regime. I am able to establish constraints on parameters relevant for experimental setups which allows the considered phase to manifest

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In this dissertation I present results for Bose-Hubbard model in 2D obtained with quantum Monte Carlo simulations by the Worm algorithm and Mean Field techniques. First I study a uniform system and I describe how the Mottinsulator-to-superfluid transition for a majority component is affected by the presence of a minority superfluid one. Then I focus on magnetic-like ground states known as checkerboard phase which can be obtained in the strongly interacting regime. I am able to establish constraints on parameters relevant for experimental setups which allows the considered phase to manifest
We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.
In my dissertation, I will discuss unconventional superfluid states of various bosonic systems and present benchmark calculations for phase diagrams. The method of study is based on quantum Monte Carlo simulations by the Worm algorithm. The two qualitatively different systems to be discussed in the thesis are: (i) superfluidity of lower dimensional objects, i.e dislocations and defects, embedded in solid structures both in optical lattices and in realistic systems such as 4He . (ii) the two-component Bose-Hubbard model. Besides the interesting phases and phase diagrams that they exhibit, bosonic optical lattice systems are also interesting for studies of quantum magnetism where under certain conditions they can be mapped onto various spin Hamiltonians. On the other hand, superfluid dislocations in 4He is an important and interesting subject for it's relevance to supersolid behavior observed in solid 4 He . I will also present technical details of the path integral Monte Carlo and the Worm algorithm and generalization of the algorithm to the two-component bosonic systems.
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.
The Bose-Hubbard model describes the physics of a system of bosonic ultracold atoms in an optical lattice, in which a phase transition is present between a superfluid phase and a Mott insulator one. \nThe exact solution of this Hamiltonian is only feasible to find the ground-state of small systems, while other techniques (as mean-field schemes or quantum Monte Carlo) are necessary to study systems of larger size. \n \nAs a first application, we study the trapped model - relevant for the comparison with current experiments - through an inhomogeneous mean-field scheme. We describe some signatures of the phase crossover between superfluid and Mott insulator. In particular, the visibility of the quasimomentum distribution shows some kinks as a function of the lattice depth; we describe these features and we link them with the ones observed in other works in the literature. \n \nAs a second application, we use quantum Monte Carlo techniques to study the one-dimensional Bose-Hubbard model with long-range interactions and we focus on the appearance of the Haldane insulating phase, distinguishable from the Mott one through the presence of non-local hidden order. \nNon-local correlation functions are also used to describe the difference between the superfluid phase and the Mott insulator one.
In this dissertation, I present my work on ground state entanglement in Bose-Hubbard-type models. Bose-Hubbard-type models form a wide class of bosonic lattice models and describe systems that can be realized by cold atoms or molecules trapped in optical lattices. By studying ground state entanglement, one can understand quantum phases and phase transitions among them from a microscopic point of view. I will first introduce the two-component Bose-Hubbard model describing Bose-Bose mixtures, and discuss the role played by the interspecies entanglement in the Mott-insulator-to-superfluid phase transition of one component in the presence of a second component. I will show that interspecies entanglement provides a new perspective to understand quantum phases in mixtures. Then I will discuss long-range spatial entanglement in single-species Bose-Hubbard-type models. Specifically, I will build a generic framework for understanding under which conditions these models harbor certain types of topological order. My results provide guidance for future numerical studies which can pave the way for searching experimentally realizable bosonic lattice models harboring nontrivial topological order.
We consider the Bose-Hubbard model on a two-leg ladder under an artificial magnetic field and investigate the superfluid--to--Mott insulator transition in this setting. Recently, this system has been experimentally realized [M. Atala et al., Nature Phys. 10, 588 (2014)], albeit in a parameter regime that is far from the Mott transition boundary. Depending on the strength of the magnetic field, the single-particle spectrum has either a single ground state or two degenerate ground states. The transition between these two phases is reflected in the many-particle properties. We first investigate these phases through the Bogoliubov approximation in the superfluid regime and calculate the transition boundary for weak interactions. For stronger interactions the system is expected to form a Mott insulator. We calculate the Mott transition boundary as a function of the magnetic field and interleg coupling with mean-field theory, strong-coupling expansion, and density matrix renormalization group (DMRG). Finally, using the DMRG, we investigate the particle-hole excitation gaps of this system at different filling factors and find peaks at simple fractions, indicating the possibility of correlated phases.