Efficient Evaluation of Partition Functions of Inhomogeneous Many-Body Spin Systems

We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2D classical spin systems and 1D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite-temperature properties of bosonic particles in 1D optical lattices, as realized in current experiments

Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.Comment: Review from 200

Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks

We present a tree-tensor-network-based method to study strongly correlated systems with nonlocal interactions in higher dimensions. Although the momentum-space and quantum-chemistry versions of the density matrix renormalization group (DMRG) method have long been applied to such systems, the spatial topology of DMRG-based methods allows efficient optimizations to be carried out with respect to one spatial dimension only. Extending the matrix-product-state picture, we formulate a more general approach by allowing the local sites to be coupled to more than two neighboring auxiliary subspaces. Following Shi. et. al. [Phys. Rev. A, 74, 022320 (2006)], we treat a tree-like network ansatz with arbitrary coordination number z, where the z=2 case corresponds to the one-dimensional scheme. For this ansatz, the long-range correlation deviates from the mean-field value polynomially with distance, in contrast to the matrix-product ansatz, which deviates exponentially. The computational cost of the tree-tensor-network method is significantly smaller than that of previous DMRG-based attempts, which renormalize several blocks into a single block. In addition, we investigate the effect of unitary transformations on the local basis states and present a method for optimizing such transformations. For the 1-d interacting spinless fermion model, the optimized transformation interpolates smoothly between real space and momentum space. Calculations carried out on small quantum chemical systems support our approach

COMPARISON OF A SIERPINSKI GASKET MONOPOLE ANTENNA TO BOW-TIE ANTENNAS BASED OFF THE FRACTAL ITERATIVE SHAPES

Antennas are an integral part of mobile devices. Recently, the demand for smaller phones has increased requiring smaller components within the device. This leads to problems with performance and limitations of RF systems within mobile devices including antennas which have been affected by the size thus affected frequency output. In this thesis, fractal theory will be utilized to compare the performance of the Sierpinski Gasket Monopole antenna to single band antennas to see if this is a viable substitute in mobile applications. By utilizing simulations and physical antennas, the performance will be observed at each frequency band and compared

Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)

We have studied the system of hard-core bosons on a 2-D optical lattice using a variational algorithm based on projected entangled-pair states (PEPS). We have investigated the ground state properties of the system as well as the responses of the system to sudden changes in the parameters. We have compared our results to mean field results based on a Gutzwiller ansatz.Comment: 9 pages, 9 figure