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The European Physical Journal B

Quantum-statistical mechanics of non-linear excitations in the one-dimensional antiferromagnet

Antonio S. T. Pires, Sérgio Luiz Talim

Published Jun 1, 1987• 5 citations
Publisher
DOI
10.1007/bf01307286

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arXiv:2003.01142•Quantum•Sep 21, 2020•24 citations
RRcent theoretical and experimental results on non-linear excitations in one dimensional classical antiferromagnetic chains are reviewed with a particular emphasis on dynamic properties. The main investigated substance is TMMC which can be regarded as a quasi-onedimensional antiferromagnet with easy plane anisotropy. A discussion of Haldane's conjecture that there is an excitation gap for integer, but not half-integer spin is given. The open questions and possible investigation for the future are discussed.
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state. Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the description of such complex many-body systems, close to optimal variational principles based on such states are less obvious to come by. In this work, we generalize a recently proposed variational uniform matrix product state algorithm for capturing one-dimensional quantum lattices in the thermodynamic limit, to the study of regular two-dimensional tensor networks with a non-trivial unit cell. A key property of the algorithm is a computational effort that scales linearly rather than exponentially in the size of the unit cell. We demonstrate the performance of our approach on the computation of the classical partition functions of the antiferromagnetic Ising model and interacting dimers on the square lattice, as well as of a quantum doped resonating valence bond state.