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arXiv:1902.10006 · Journal of Magnetism and Magnetic Materials

Thermal density matrix renormalization group for highly frustrated quantum spin chains: A user perspective

Robin Heveling, Johannes Richter, Jürgen Schnack

Published May 20, 2019• 1 citation
arXivHTMLPDF
DOI
10.1016/j.jmmm.2019.165327

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We apply the transfer-matrix density matrix renormalization group (DMRG) approach to frustrated quantum spin chains, down to T=0.025KT\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.025\mathrm{K}T=0.025K in the thermodynamic limit. The incommensurability problem of exact diagonalization and the negative sign problem of quantum Monte Carlo vanish completely. For illustration, we give results for chains with next-nearest-neighbor frustration and for the delta chain, which has been a testbed for many thermodynamic methods. The DMRG approach proves to be an extremely powerful method for the old problem of the thermodynamics of frustrated systems.
Density matrix renormalization group methods or tensor network methods in general can not only be used to determine ground states but also to evaluate thermal equilibrium properties. Although convergence is superior for one-dimensional quantum spin systems with nearest neighbor exchange and open boundary conditions, the hope is that these methods can as well be employed to approximate magnetic observables of magnetic molecules with more complex interaction patterns. Here, we assume the position of a user and study the accuracy that can realistically be achieved for several archetypical quasi one-dimensional structures using the TenPy suite. In our study, we aim at systems that are too large for exact diagonalization or Krylov space methods.