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Annual Review of Condensed Matter Physics

Volume 8, 2017

Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods

Abstract

Transfer matrices and matrix product operators play a ubiquitous role in the field of many-body physics. This review gives an idiosyncratic overview of applications, exact results, and computational aspects of diagonalizing transfer matrices and matrix product operators. The results in this paper are a mixture of classic results, presented from the point of view of tensor networks, and new results. Topics discussed are exact solutions of transfer matrices in equilibrium and nonequilibrium statistical physics, tensor network states, matrix product operator algebras, and numerical matrix product state methods for finding extremal eigenvectors of matrix product operators.

Keyword(s): Bethe ansatz, entanglement, equilibrium and nonequilibrium statistical physics, fusion tensor categories, many-body physics, quantum spin chains, tensor networks
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2017-03-31
2024-07-03
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Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods
Annual Review of Condensed Matter Physics 8, 355 (2017); https://doi.org/10.1146/annurev-conmatphys-031016-025507
/content/journals/10.1146/annurev-conmatphys-031016-025507
/content/journals/10.1146/annurev-conmatphys-031016-025507
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