Related papers: Fractal and Statistical Properties of Large Compac…
We investigate experimentally the distribution of configurations of a ring with an elementary topological constraint, a ``figure-8'' twist. Using vibrated granular chains, which permit controlled preparation and direct observation of such a…
Traditional Markov Chain Monte Carlo methods suffer from low acceptance rate, slow mixing and low efficiency in high dimensions. Hamiltonian Monte Carlo resolves this issue by avoiding the random walk. Hamiltonian Monte Carlo (HMC) is a…
We study quasi-Monte Carlo (QMC) methods for numerical integration of multivariate functions defined over the high-dimensional unit cube. Lattice rules and polynomial lattice rules, which are special classes of QMC methods, have been…
Conformal field theory has recently been applied to derive few-body Hamiltonians whose ground states are lattice versions of fractional quantum Hall states. The exact lattice models involve interactions over long distances, which is…
Here, we investigate the fractal-lattice Hubbard model using various numerical methods: exact diagonalization, the self-consistent diagonalization of a (mean-field) Hartree-Fock Hamiltonian and state-of-the-art Auxiliary-Field Quantum Monte…
We investigate the harmonic-trap control of size and shape of Mott regions in the Fermi Hubbard model on a square optical lattice. The use of Lanczos diagonalization on clusters with twisted boundary conditions, followed by an average over…
Potts spin systems play a fundamental role in statistical mechanics and quantum field theory, and can be studied within the spin, the Fortuin-Kasteleyn (FK) bond or the $q$-flow (loop) representation. We introduce a Loop-Cluster (LC) joint…
We discuss a model of protein conformations where the conformations are combinations of short fragments from some small set. For these fragments we consider a distribution of frequencies of occurrence of pairs (sequence of amino acids,…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Representing massless Dirac fermions on a spatial lattice poses a potential challenge known as the Fermion Doubling problem. Addition of a quadratic term to the Dirac Hamiltonian circumvents this problem. We show that the modified…
The topological susceptibility is one of the few physical quantities that directly measure the properties of the QCD vacuum. Chiral perturbation theory predicts that in the small quark mass limit the topological susceptibility depends…
The extended Hubbard Hamiltonian is a widely accepted model for uncovering the effects of strong correlations on the phase diagram of low-dimensional systems, and a variety of theoretical techniques have been applied to it. In this paper…
We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
We analyze time-discrete and continuous `fractional' random walks on undirected regular networks with special focus on cubic periodic lattices in $n=1,2,3,..$ dimensions. The fractional random walk dynamics is governed by a master equation…
We report grand canonical Monte Carlo simulations of the critical point properties of homopolymers within the Bond Fluctuation model. By employing Configurational Bias Monte Carlo methods, chain lengths of up to N=60 monomers could be…
We study a one-dimensional two-component Fermi gas in a harmonic trapping potential using finite temperature lattice quantum Monte Carlo methods. We are able to compute observables in the canonical ensemble via an efficient projective…
An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
In recent past, experiments and simulations have suggested that apart from the solvent friction, friction arising from the protein itself plays an important role in protein folding by affecting the intra-chain loop formation dynamics. This…