New publication appeared in the Annual Review of Condensed Matter Physics


Our publication on Diagonalizing Transfer Matrices and Matrix Product Operators: A Medley of Exact and Computational Methods appeared in the Annual Review of Condensed Matter Physics.

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.


Annual Review of Condensed Matter Physics Vol. 8: 355-406 (Volume publication date March 2017)
DOI: 10.1146/annurev-conmatphys-031016-025507