Numerical Studies of Correlated Lattice Systems in One and Two Dimensions
Creator
Tang, Baoming
Advisor
Rigol, Marcos
Abstract
We use numerical linked cluster expansions (NLCEs) to study correlated lattice systems in one and two dimensions. For fermions in the honeycomb lattice, we study its finite-temperature properties and short-range spin correlations using NLCEs and determinantal quantum Monte Carlo (DQMC) simulations. For the homogeneous system, we analyze a number of thermodynamic quantities, including the entropy, the specific heat, uniform and staggered spin susceptibilities, short-range spin correlations, and the double occupancy at and away from half filling. Employing a local density approximation (LDA), we examine the viability of adiabatic cooling by increasing the interaction strength for homogeneous as well as for trapped systems. We also use NLCEs to study thermodynamic properties of the two-dimensional spin-1/2 Ising, XY, and Heisenberg models with bimodal random-bond disorder on the square and honeycomb lattices. In all cases, the nearest-neighbor coupling between the spins takes values $\pm J$ with equal probability. We obtain the disorder averaged (over all disorder configurations) energy, entropy, specific heat, and uniform magnetic susceptibility in each case. These results are compared with the corresponding ones in the clean models. Analytic expressions are obtained for low orders in the expansion of these thermodynamic quantities in inverse temperature. For many-body localization in disordered isolated systems, we study quantum quenches in the thermodynamic limit. By a quantum quench it is meant that the initial state is stationary with respect to an initial Hamiltonian, which is suddenly changed to a new (time-independent) Hamiltonian. The latter then drives the (unitary) dynamics of the system. We are interested in the time average of observables after relaxation following the quench, which can be computed under the so-called diagonal ensemble.
Description
Ph.D.
Permanent Link
http://hdl.handle.net/10822/761508Date Published
2015Subject
Type
Publisher
Georgetown University
Extent
136 leaves
Collections
Metadata
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