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

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

2006-10-25

arxiv.org/abs/cond-mat/0610689v1

Lecture Notes in Physics, Vol. 739: Computational Many-Particle Physics (Springer, Berlin, 2008)

Physics

Condensed Matter

Strongly Correlated Electrons

14 pages, 9 figures, Lecture notes WE-Heraeus summerschool 'Computational Many-Particle Physics', Greifswald 2006

Scientific paper

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 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.

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