相关论文: Complexity in parametric Bose-Hubbard Hamiltonians…
We study quantum vortex states of strongly interacting bosons in a two-dimensional rotating optical lattice. The system is modeled by Bose-Hubbard Hamiltonian with rotation. We consider lattices of different geometries, such as square,…
We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected…
The Bose-Hubbard Hamiltonian can be simplified to have only two lattice sites, in which case the system being described is referred to as a dimer. Due to its structure, the hopping term of the dimer Hamiltonian enjoys invariance in a family…
We examine ground state correlations for repulsive, quasi one-dimensional bosons in a harmonic trap. In particular, we focus on the few particle limit N=2,3,4,..., where exact numerical solutions of the many particle Schroedinger equation…
We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain…
Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body…
Quantum Hamiltonian complexity studies computational complexity aspects of local Hamiltonians and ground states; these questions can be viewed as generalizations of classical computational complexity problems related to local constraint…
We analyze the self-thermalization dynamics of the $M$-site Bose-Hubbard model in terms of the single-particle density matrix that is calculated by using the pseudoclassical approach. It is shown that a weak inter-particle interaction,…
A set of coupled complex Ginzburg-landau type amplitude equations which operates near a Hopf-Turing instability boundary is analytically investigated to show localized oscillatory patterns. The spatial structure of those patterns are the…
We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to…
Local unitary invariants allow one to test whether multipartite states are equivalent up to local basis changes. Equivalently, they specify the geometry of the "orbit space" obtained by factoring out local unitary action from the state…
An interacting quantum system can transition from an ergodic to a many-body localized (MBL) phase under the presence of sufficiently large disorder. Both phases are radically different in their dynamical properties, which are characterized…
In most realistic models for quantum chaotic systems, the Hamiltonian matrices in unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such systems and derive explicit expressions for some of the correlation…
Strongly interacting systems are characterized by heavily dressed entities with internal degrees of freedom, which, on a local level, can be described in terms of coherent quantum states. We examine the modification of these local coherent…
Isolated quantum many-body systems are often well-described by the eigenstate thermalization hypothesis. There are, however, mechanisms that cause different behavior: many-body localization and quantum many-body scars. Here, we show how one…
We explore the influence of external perturbations on the energy levels of a Hamiltonian drawn at random from the Gaussian unitary distribution of Hermitian matrices. By deriving the joint distribution function of eigenvalues, we obtain the…
We investigate eigenstate localization in the phase space of the Bunimovich mushroom billiard, a paradigmatic mixed-phase-space system whose piecewise-$C^{1}$ boundary yields a single clean separatrix between one regular and one chaotic…
We study a quantum particle in a tilted honeycomb lattice in the tight-binding approximation. First we discuss the particle eigenstates, i.e., the stationary Wannier-Stark states. These states are proved to be extended states for the…
Quantum chaotic dynamics is obtained for a tight-binding model in which the energies of the atomic levels at the boundary sites are chosen at random. Results for the square lattice indicate that the energy spectrum shows a complex behavior…
Experimental realizations of disorder in optical lattices generate a distribution of the Bose-Hubbard (BH) parameters, like on-site potentials, hopping strengths, and interaction energies. We analyze this distribution for bosons in a…