Density-matrix renormalization group for transfer matrices: Static and dynamical properties of 1D quantum systems at finite temperature

Abstract

The density-matrix renormalization group (DMRG) applied to transfer matrices allows it to calculate static as well as dynamical properties of one-dimensional (1D) quantum systems at finite temperature in the thermodynamic limit. To this end the quantum system is mapped onto a 2D classical system by a Trotter-Suzuki decomposition. Here we discuss two different mappings: The standard mapping onto a 2D lattice with checkerboard structure as well as an alternative mapping introduced by two of us. For the classical system an appropriate quantum transfer matrix is defined which is then treated using a DMRG scheme. As applications, the calculation of thermodynamic properties for a spin-1/2 Heisenberg chain in a staggered magnetic field and the calculation of boundary contributions for open spin chains are discussed. Finally, we show how to obtain real-time dynamics from a classical system with complex Boltzmann weights and present results for the autocorrelation function of the XXZ-chain. © Springer-Verlag Berlin Heidelberg 2008.