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We study the behavior of excitations in the tilted one-dimensional Bose-Hubbard model. In the phase with broken symmetry, fundamental excitations are domain-walls which show fractional statistics. Using perturbation theory, we derive an analytic model for the time evolution of these fractional excitations, and demonstrate the existence of a repulsively bound state above a critical center of mass momentum. The validity of the perturbative analysis is confirmed by the use of t- DMRG simulations...
We study the entanglement entropy scaling of the XXZ chain. While in the critical XY phase of the XXZ chain the entanglement entropy scales logarithmically with a coefficient that is determined by the associated conformal field theory, at the ferromagnetic point, however, the system is not conformally invariant yet the entanglement entropy still scales logarithmically albeit with a different coefficient. We investigate how such an nontrivial scaling at the ferromagnetic point influences the e...
Using numerical techniques, we study the miscible-immiscible quantum phase transition in a linearly coupled binary Bose-Hubbard model Hamiltonian that can describe low-energy properties of a two-component Bose-Einstein condensate in optical lattices. With the quantum many-body ground state obtained from density matrix renormalization group algorithm, we calculate the characteristic physical quantities of the phase transition controlled by the linear coupling between two components. Furthermor...
We study the sudden expansion of spin-imbalanced ultracold lattice fermions with attractive interactions in one dimension after turning off the longitudinal confining potential. We show that the momentum distribution functions of majority and minority fermions approach stationary values quickly due to a quantum distillation mechanism that results in a spatial separation of pairs and majority fermions. As a consequence, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) correlations are lost during the e...
We propose the use of a dynamical window to investigate the real-time evolution of quantum many-body systems in a one-dimensional lattice. In a recent paper [H. Phien et al, arxiv:????.????], we introduced infinite boundary conditions (IBC) in order to investigate real-time evolution of an infinite system under a local perturbation. This was accomplished by restricting the update of the tensors in the matrix product state to a finite window, with left and right boundaries held at fixed positi...
The representation theory of the Drinfeld doubles of dihedral groups is used to solve the Yang-Baxter equation. Use of the 2-dimensional representations recovers the six-vertex model solution. Solutions in arbitrary dimensions, which are viewed as descendants of the six-vertex model case, are then obtained using tensor product graph methods which were originally formulated for quantum algebras. Connections with the Fateev-Zamolodchikov model are discussed.
In an article in 2007, Mishra, Pai, and Das [Phys. Rev. A 76, 013604 (2007)] investigated the two-component Bose-Hubbard model using the numerical DMRG procedure. In the regime of inter-species repulsion $U^{ab}$ larger than the intra-species repulsion $U$, they found a transition from a uniform miscible phase to phase-separation occurring at a finite value of $U$ , e.g., at around $U = 1.3$ for $\Delta = U^{ab}/U = 1.05$ and $\rho_{a} = \rho_{b} = 1/2$. In this comment, we show that this res...
We perform a density-matrix renormalization group (DMRG) study of the S=1/2 Heisenberg antiferromagnet on the kagome lattice to identify the conjectured spin liquid ground state. Exploiting SU(2) spin symmetry, which allows us to keep up to 16,000 DMRG states, we consider cylinders with circumferences up to 17 lattice spacings and find a spin liquid ground state with an estimated per site energy of -0.4386(5), a spin gap of 0.13(1), very short-range decay in spin, dimer and chiral correlation...
We propose a formalism to study dynamical properties of a quantum many-body system in the thermodynamic limit by studying a finite system with infinite boundary conditions (IBC) where both finite size effects and boundary effects have been eliminated. For one-dimensional systems, infinite boundary conditions are obtained by attaching two boundary sites to a finite system, where each of these two sites effectively represents a semi-infinite extension of the system. One can then use standard fi...
We investigate the expansion of bosons and fermions in a homogeneous lattice after a sudden removal of the trapping potential using exact numerical methods. As a main result, we show that in one dimension, both bosonic and fermionic Mott insulators expand with the same velocity, irrespective of the interaction strength, provided the expansion starts from the ground state of the trapped gas. Furthermore, their density profiles become identical during the expansion: The asymptotic density dynam...
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