Efficient evaluation of partition functions of frustrated and inhomogeneous spin systems

Abstract

We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate the algorithm by calculating the finite--temperature properties of bosonic particles in 1--D optical lattices, as realized in current experiments.

arXiv comment5 pages, 3 figures

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• Unifying Projected Entangled Pair States contractions
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• The Algebraic Bethe Ansatz and Tensor Networks
• Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz
• Quantum algorithms for spin models and simulable gate sets for quantum computation
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• Ultracold atomic Bose and Fermi spinor gases in optical lattices
• Completeness of classical spin models and universal quantum computation
• Partial long-range order in antiferromagnetic Potts models
• Product Wave Function Renormalization Group: construction from the matrix product point of view
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• Entanglement and Majorana edge states in the Kitaev model
• An algorithmic proof for the completeness of two-dimensional Ising model
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• New method for the quantum ground states in one dimension
• Classical spin systems and the quantum stabilizer formalism: general mappings and applications
• Phase boundary location with information-theoretic entropy in tensor renormalization group flows
• Variational Neural and Tensor Network Approximations of Thermal States
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