ID: hep-lat/9304006

Computing Masses from Effective Transfer Matrices

April 13, 1993

View on ArXiv
M. Hasenbusch, K. Pinn, K. Rummukainen
High Energy Physics - Lattic...

We study the use of effective transfer matrices for the numerical computation of masses (or correlation lengths) in lattice spin models. The effective transfer matrix has a strongly reduced number of components. Its definition is motivated by a renormalization group transformation of the full model onto a 1-dimensional spin model. The matrix elements of the effective transfer matrix can be determined by Monte Carlo simulation. We show that the mass gap can be recovered exactly from the spectrum of the effective transfer matrix. As a first step towards application we performed a Monte Carlo study for the 2-dimensional Ising model. For the simulations in the broken phase we employed a multimagnetical demon algorithm. The results for the tunnelling correlation length are particularly encouraging.

Similar papers 1

Computing Masses and Surface Tension from Effective Transfer Matrices

December 20, 1993

91% Match
M. Hasenbusch, K. Rummukainen, K. Pinn
High Energy Physics - Lattic...

We propose an effective transfer-matrix method that allows a measurement of tunnelling correlation lengths that are orders of magnitude larger than the lattice extension. Combining this method with a particularly efficient implementation of the multimagnetical algorithm we were able to determine the interface tension of the 3D Ising model close to criticality with a relative error of less than 1 per cent.

Find SimilarView on arXiv

Polyakov loop and spin correlators on finite lattices A study beyond the mass gap

December 1, 1994

85% Match
J. ~Engels, V. K. ~Mitrjushkin, T. ~Neuhaus
High Energy Physics - Lattic...

We derive an analytic expression for point-to-point correlation functions of the Polyakov loop based on the transfer matrix formalism. For the $2d$ Ising model we show that the results deduced from point-point spin correlators are coinciding with those from zero momentum correlators. We investigate the contributions from eigenvalues of the transfer matrix beyond the mass gap and discuss the limitations and possibilities of such an analysis. The finite size behaviour of the ob...

Find SimilarView on arXiv

Effective One-Dimensional Models from Matrix Product States

March 9, 2015

85% Match
Frederik Keim, Götz S. Uhrig
Strongly Correlated Electron...

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of t...

Find SimilarView on arXiv

Transfer Matrix DMRG for Thermodynamics of One-Dimensional Quantum Systems

May 29, 1997

85% Match
Xiaoqun Institut Romand de Recherche Numérique en Physique des Materiaux, Lausanne, Switzerland Wang, Tao Interdisciplinary Research Centre in Superconductivity, The University of Cambridge, United Kindom Xiang
Condensed Matter

The transfer matrix DMRG method for one dimensional quantum lattice systems has been developed by considering the symmetry property of the transfer matrix and introducing the asymmetric reduced density matrix. We have evaluated a number of thermodynamic quantities of the anisotropic spin-1/2 Heisenberg model using this method and found that the results agree very accurately with the exact ones. The relative errors for the spin susceptibility are less than $10^{-3}$ down to $T...

Find SimilarView on arXiv

Critical amplitudes and mass spectrum of the 2D Ising model in a magnetic field

November 26, 1999

85% Match
M. Caselle, M. Hasenbusch
Statistical Mechanics

We compute the spectrum and several critical amplitudes of the two dimensional Ising model in a magnetic field with the transfer matrix method. The three lightest masses and their overlaps with the spin and the energy operators are computed on lattices of a width up to L=21. In extracting the continuum results we also take into account the corrections to scaling due to irrelevant operators. In contrast with previous Monte Carlo simulations our final results are in perfect agr...

Find SimilarView on arXiv

Density Matrix and Renormalization for Classical Lattice Models

October 14, 1996

85% Match
T. Nishino, K. Okunishi
Statistical Mechanics

We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state energy. The variational principle is applied to two-dimensional (2D) classical lattice models, where the density matrix is expressed as a product of corner transfer matrices. (CTMs) DMRG related fields and future directions of DMRG are brie...

Find SimilarView on arXiv

Amplitude ratios for the mass spectrum of the 2d Ising model in the high-T, H \neq 0 phase

August 30, 2004

85% Match
M. Caselle, P. Grinza, A. Rago
Statistical Mechanics

We study the behaviour of the 2d Ising model in the symmetric high temperature phase in presence of a small magnetic perturbation. We successfully compare the quantum field theory predictions for the shift in the mass spectrum of the theory with a set of high precision transfer matrix results. Our results rule out a prediction for the same quantity obtained some years ago with strong coupling methods.

Find SimilarView on arXiv

The analysis of Polyakov loop and spin correlators in finite volumes

November 29, 1993

84% Match
J. Engels, V. K. Mitrjushkin, T. Neuhaus
High Energy Physics - Lattic...

We derive an analytic expression for point to point correlation functions of the Polyakov loop based on the transfer matrix formalism. The contributions from the eigenvalues of the transfer matrix including and beyond the mass gap are investigated both for the $2d$ Ising model and in finite temperature $SU(2)$ gauge theory. We find that the leading matrix element shows similar scaling properties in both models. Just above the critical point we obtain for $SU(2)$ a Debye scree...

Find SimilarView on arXiv

Transfer-Matrix Monte Carlo Estimates of Critical Points in the Simple Cubic Ising, Planar and Heisenberg Models

February 15, 1996

84% Match
M. P. Department of Physics, University of Rhode Island, Kingston RI, USA Nightingale, H. W. J. Department of Applied Physics, Delft University of Technology, Delft, The Netherlands Bloete
Condensed Matter

The principle and the efficiency of the Monte Carlo transfer-matrix algorithm are discussed. Enhancements of this algorithm are illustrated by applications to several phase transitions in lattice spin models. We demonstrate how the statistical noise can be reduced considerably by a similarity transformation of the transfer matrix using a variational estimate of its leading eigenvector, in analogy with a common practice in various quantum Monte Carlo techniques. Here we take t...

Find SimilarView on arXiv

The density-matrix renormalization group applied to transfer matrices: Static and dynamical properties of one-dimensional quantum systems at finite temperature

October 25, 2006

84% Match
S. Glocke, A. Klümper, J. Sirker
Strongly Correlated Electron...

The density-matrix renormalization group (DMRG) applied to transfer matrices allows it to calculate static as well as dynamical properties of one-dimensional quantum systems at finite temperature in the thermodynamic limit. To this end the quantum system is mapped onto a two-dimensional classical system by a Trotter-Suzuki decomposition. Here we discuss two different mappings: The standard mapping onto a two-dimensional lattice with checkerboard structure as well as an altern...

Find SimilarView on arXiv