Related papers: Compass model on a ladder and square clusters
We use exact symmetry properties of the two-dimensional quantum compass model to derive nonequivalent invariant subspaces in the energy spectra of $L\times L$ clusters up to L=6. The symmetry allows one to reduce the original $L\times L$…
We use high-temperature series expansions to obtain thermodynamic properties of the quantum compass model, and to investigate the phase transition on the square and simple cubic lattices. On the square lattice we obtain evidence for a phase…
It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial…
Thermodynamic properties of the four-dimensional cross-polytope model, the 16-cell model, which is an example of higher dimensional generalizations of the octahedron model, are studied on the square lattice. By means of the corner transfer…
We introduce a spin ladder with antiferromagnetic Ising ZZ interactions along the legs, and interactions on the rungs which interpolate between the Ising ladder and the quantum compass ladder. We show that the entire energy spectrum of the…
We prove some estimations of the correlation of two local observables in quantum spin systems (with Schr\"odinger equations) at large temperature. For that, we describe the heat kernel of the Hamiltonian for a finite subset of the lattice,…
A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…
We numerically compute the heat kernel on a square lattice torus equipped with the measure corresponding to Liouville quantum gravity (LQG). From the on-diagonal heat kernel we verify that the spectral dimension of LQG is 2. Furthermore,…
Heat capacity curves as functions of temperature for classical atomic clusters bound by pairwise Lennard-Jones potentials were calculated for aggregate sizes from 4 to 24 using Monte Carlo methods. J-walking (or jump-walking) was used to…
We present a brief overview of several approaches for calculating the local asymptotic expansion of the heat kernel for Laplace-type operators. The different methods developed in the papers of both authors some time ago are described in…
Quantum computers are predicted to outperform classical ones for solving partial differential equations, perhaps exponentially. Here we consider a prototypical PDE - the heat equation in a rectangular region - and compare in detail the…
We develop the heat kernel method in the context of finite temperature quantum field theory. We compute the heat kernel expansion in the presence of general gauge and scalar fields which may be non Abelian and non stationary. The Polyakov…
We investigate the thermal and magnetic properties of the integrable su(4) ladder model by means of the quantum transfer matrix method. The magnetic susceptibility, specific heat, magnetic entropy and high field magnetization are evaluated…
A simple two-qubit model showing Quantum Phase Transitions as a consequence of ground state level crossings is studied in detail. Using the Concurrence of the system as an entanglement measure and heat capacity as a marker of…
The specific heat of the $x-y$ model is studied on cubic lattices of sizes $L \times L \times L$ and on lattices $L \times L \times H$ with $L \gg H$ (i.e. on lattices representing a film geometry) using the Cluster Monte Carlo method.…
We study the directional-ordering transition in the two-dimensional classical and quantum compass models on the square lattice by means of Monte Carlo simulations. An improved algorithm is presented which builds on the Wolff cluster…
The kernel polynomial method allows to sample overall spectral properties of a quantum system, while sparse diagonalization provides accurate information about a few important states. We present a method combining these two approaches…
A new approximation hierarchy, called the LPSUB$m$ scheme, is described for the coupled cluster method (CCM). It is applicable to systems defined on a regular spatial lattice. We then apply it to two well-studied prototypical (spin-1/2…
Heat capacity curves as functions of temperature were calculated using Monte Carlo methods for the series of Ar_{13-n}Kr_n clusters (0 <= n <= 13). The clusters were modeled classically using pairwise additive Lennard-Jones potentials.…
Heat capacities of model systems with finite numbers of effective degrees of freedom are evaluated using canonical and microcanonical thermodynamics. Discrepancies between both approaches, which are observed even in the infinite-size limit,…