Renormalization and tensor product states in spin chains and lattices

J. Ignacio Cirac; Frank Verstraete

doi:10.1088/1751-8113/42/50/504004

Renormalization and tensor product states in spin chains and lattices

J. Ignacio Cirac (Corresponding author), Frank Verstraete (Corresponding author)

Quantum Optics, Quantum Nanophysics and Quantum Information

Publications: Contribution to journal › Review › Peer Reviewed

Abstract

We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.

Original language	English
Article number	504004
Number of pages	34
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	42
Issue number	50
DOIs	https://doi.org/10.1088/1751-8113/42/50/504004
Publication status	Published - 18 Dec 2009

Austrian Fields of Science 2012

103025 Quantum mechanics

Keywords

DENSITY-MATRIX RENORMALIZATION
3D CLASSICAL-MODELS
BOND GROUND-STATES
QUANTUM ANTIFERROMAGNETS
CAYLEY TREES
SYSTEMS
FORMULATION
ALGORITHM
ENTROPY

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10.1088/1751-8113/42/50/504004

http://arxiv.org/abs/0910.1130

Cite this

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title = "Renormalization and tensor product states in spin chains and lattices",

abstract = "We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.",

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AU - Cirac, J. Ignacio

AU - Verstraete, Frank

PY - 2009/12/18

Y1 - 2009/12/18

N2 - We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.

AB - We review different descriptions of many-body quantum systems in terms of tensor product states. We introduce several families of such states in terms of the known renormalization procedures, and show that they naturally arise in that context. We concentrate on matrix product states, tree tensor states, multiscale entanglement renormalization ansatz and projected entangled pair states. We highlight some of their properties, and show how they can be used to describe a variety of systems.

KW - DENSITY-MATRIX RENORMALIZATION

KW - 3D CLASSICAL-MODELS

KW - BOND GROUND-STATES

KW - QUANTUM ANTIFERROMAGNETS

KW - CAYLEY TREES

KW - SYSTEMS

KW - FORMULATION

KW - ALGORITHM

KW - ENTROPY

U2 - 10.1088/1751-8113/42/50/504004

DO - 10.1088/1751-8113/42/50/504004

M3 - Review

SN - 1751-8113

VL - 42

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 50

M1 - 504004

ER -

Renormalization and tensor product states in spin chains and lattices

Abstract

Austrian Fields of Science 2012

Keywords

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