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arXiv:cond-mat/9502091 · Physical review. B, Condensed matter

Ground-state dynamical correlation functions: An approach using the density-matrix renormalization-group method

Hanbin Pang, H. Akhlaghpour, M. Jarrell

Published Mar 1, 1996• 14 citations
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Abstract

A numerical approach to ground-state dynamical correlation functions from the density-matrix renormalization group (DMRG) is developed. Using sum rules, moments of a dynamic correlation function can be calculated with DMRG, and with the moments the dynamical correlation function can be obtained by the maximum entropy method. We apply this method to a one-dimensional spinless fermion system, which can be converted to the spin-1/2 Heisenberg model in a special case. The dynamical density-density correlation function is obtained. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.53.5086

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A numerical approach to ground-state dynamical correlation functions from the density-matrix renormalization group (DMRG) is developed. Using sum rules, moments of a dynamic correlation function can be calculated with DMRG, and with the moments the dynamical correlation function can be obtained by the maximum entropy method. We apply this method to a one-dimensional spinless fermion system, which can be converted to the spin-1/2 Heisenberg model in a special case. The dynamical density-density correlation function is obtained. \textcopyright{} 1996 The American Physical Society.
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The density matrix renormalization group (DMRG) is a numerical method for studying low dimensional strongly correlated models. The study of these models is one of the most active areas of condensed matter physics today and has been spurred not only by the discovery of high temperature superconductivity but also by experiments on new compounds. In this thesis we study fundamentals of the density matrix renormalization group method as well as applications of the method to Heisenberg spin chains. The introductory text is meant as a brief overview of the DMRG as well as Heisenberg spin systems and provides an introduction to the papers. In papers I and II we investigate the density matrix renormalization group with the aim to better understand the underlying structure of the method. We find that if the renormalization converges to a fixed point in the thermodynamic limit, the resulting basis states can be written as a matrix product form. We also show an explicit relation of the DMRG to variational calculations using the fact that the matrix product states can be rederived through a variational ansatz without any reference to the DMRG calculation. It is then shown how the matrix product states can be used to define a set of Bloch waves for describing elementary excitations of the Heisenberg spin-1 chain. The low lying energy spectrum is calculated. In papers III and IV we investigate the thermodynamics of impurities in a spin-1/2 chain. For this purpose we have shown that a recently developed transfer matrix DMRG method can be used to calculate impurity properties. Both impurity corrections to thermodynamic properties and local properties at finite temperature can be obtained. The method gives quicker and more accurate results than quantum Monte Carlo. The numerical results show good agreement with field theory calculations for a number of impurity configurations and the cross-over function for the magnetic susceptibility from high- to low-temperature behavior shows the expected data collapse. Our results also give quantitative predictions for experiments on doped spin-1/2 chains.
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We present a numerical method for the evaluation of dynamical response functions at finite temperatures in one-dimensional strongly correlated systems. The approach is based on the density-matrix renormalization group method, combined with the finite-temperature Lanczos diagonalization. The feasibility of the method is tested on the example of dynamical spin correlations in the anisotropic Heisenberg chain, in particular, it yields nontrivial results for the critical behavior in the isotropic case.
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The density matrix renormalization group (DMRG) has become a powerful numerical method that can be applied to low-dimensional strongly correlated fermionic and bosonic systems. It allows for a very precise calculation of static, dynamic and thermodynamic properties. Its field of applicability has now extended beyond condensed matter, and is successfully used in quantum chemistry, statistical mechanics, quantum information theory, and nuclear and high-energy physics as well. In this article, we briefly review the main aspects of the method and present some of the most relevant applications so as to give an overview of the scope and possibilities of DMRG. We focus on the most important extensions of the method such as the calculation of dynamical properties, the application to classical systems, finite-temperature simulations, phonons and disorder, field theory, time-dependent properties and the ab initio calculation of electronic states in molecules. The recent quantum information interpretation, the development of highly accurate time-dependent algorithms and the possibility of using the DMRG as the impurity-solver of the dynamical mean field method (DMFT) give new insights into its present and potential uses. We review the numerous very recent applications of these techniques where the DMRG has shown to be one of the most reliable and versatile methods in modern computational physics.