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

Autor(en)

Jutho Haegeman, Frank Verstraete

Abstrakt

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.

Organisation(en)

Quantenoptik, Quantennanophysik und Quanteninformation

Externe Organisation(en)

Ghent University

Band

8

Seiten

355-406

Anzahl der Seiten

52

DOI

https://doi.org/10.1146/annurev-conmatphys-031016-025507

Publikationsdatum

2017

Peer-reviewed

Ja

ÖFOS 2012

103015 Kondensierte Materie, 103019 Mathematische Physik

Schlagwörter

ASJC Scopus Sachgebiete

Condensed Matter Physics, Allgemeine Materialwissenschaften

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/a9ab5412-bdc2-4791-be6b-910ec05a7c24