1301.2246 (Thomas Barthel)

Precise evaluation of thermal response functions by optimized density
matrix renormalization group schemes    [PDF]

Thomas Barthel

This paper provides a study and discussion of earlier as well as novel schemes for the precise evaluation of finite-temperature response functions of strongly correlated quantum systems in the framework of the time-dependent density matrix renormalization group (tDMRG). The computational costs as functions of time and temperature are examined at the example of the XXZ Heisenberg chain in the critical XY phase and the gapped N\'eel phase. The matrix product state purifications occurring in the algorithms are in one-to-one relation with corresponding matrix product operators. This notational simplification elucidates implications of quasi-locality on the computation costs. Based on the observation that there is considerable freedom in designing efficient tDMRG schemes for the calculation of dynamical correlators at finite temperatures, a new class of optimizable schemes, as recently suggested in arXiv:1212.3570, is explained and analyzed numerically. A specific novel near-optimal scheme that requires no additional optimization reaches maximum times that are typically increased by a factor of two, when compared against earlier approaches. These increased reachable times make many more physical applications accessible. For each of the described tDMRG schemes, one can devise a corresponding transfer matrix renormalization group (TMRG) variant.

View original: http://arxiv.org/abs/1301.2246