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Bulletin of the American Physical Society

Ground state properties of one- and two-component Bose-Hubbard model

Barbara Capogrosso-Sansone, Şebnem Güneş Söyler, Nikolay V. Prokof'ev, Boris V. Svistunov

Published Mar 12, 2008• 0 citations
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•Jan 1, 2017•0 citations
We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state of the two-component Bose-Hubbard model are compared to those of the effective spin model as the interspecies interaction approaches the intraspecies one. A numerical study of the entanglement properties of the two-component Bose-Hubbard model is supplemented with analytical expressions derived from the effective spin Hamiltonian. When the pure ferromagnetic Heisenberg chain is considered, the entanglement properties of the effective Hamiltonian are not properly predicted by the quantum simulator.
We study the degeneracy of the ground-state energy E of the two-component Bose-Hubbard model and of the perturbative correction E(1). We show that the degeneracy properties of E and E(1) are closely related to the connectivity properties of the lattice. We determine general conditions under which E is nondegenerate. This analysis is then extended to investigate the degeneracy of E(1). In this case, in addition to the lattice structure, the degeneracy also depends on the number of particles present in the system. After identifying the cases in which E(1) is degenerate and observing that the standard (degenerate) perturbation theory is not applicable, we develop a method to determine the zeroth-order correction to the ground state by exploiting the symmetry properties of the lattice. This method is used to implement the perturbative approach to the two-component Bose-Hubbard model in the case of degenerate E(1) and is expected to be a valid tool to perturbatively study the asymmetric character of the Mott insulator to superfluid transition between the particle and hole side.
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.