Scaling of entanglement support for matrix product states

Tagliacozzo, L., de Oliveira, Thiago. R., Iblisdir, S. and Latorre, J. I. (2008) Scaling of entanglement support for matrix product states. Physical Review B, 78 2: 024410-1-024410-14. doi:10.1103/PhysRevB.78.024410

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Author Tagliacozzo, L.
de Oliveira, Thiago. R.
Iblisdir, S.
Latorre, J. I.
Title Scaling of entanglement support for matrix product states
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
1550-235X
Publication date 2008-07-01
Sub-type Article (original research)
DOI 10.1103/PhysRevB.78.024410
Open Access Status File (Publisher version)
Volume 78
Issue 2
Start page 024410-1
End page 024410-14
Total pages 14
Place of publication New York, NY, U.S.A.
Publisher American Physical Society
Language eng
Subject 0101 Pure Mathematics
0105 Mathematical Physics
0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics
0206 Quantum Physics
0912 Materials Engineering
Formatted abstract
The power of matrix product states to describe infinite-size translational-invariant critical spin chains is investigated. At criticality, the accuracy with which they describe ground-state properties of a system is limited by the size χ of the matrices that form the approximation. This limitation is quantified in terms of the scaling of the half-chain entanglement entropy. In the case of the quantum Ising model, we find S∼⅙log χ with high precision. This result can be understood as the emergence of an effective finite correlation length ξχ ruling all the scaling properties in the system. We produce six extra pieces of evidence for this finite-χ scaling, namely, the scaling of the correlation length, the scaling of magnetization, the shift of the critical point, the scaling of the entanglement entropy for a finite block of spins, the existence of scaling functions, and the agreement with analogous classical results. All our computations are consistent with a scaling relation of the form ξχχκ, with κ=2 for the Ising model. In the case of the Heisenberg model, we find similar results with the value κ∼1.37. We also show how finite-χ scaling allows us to extract critical exponents. These results are obtained using the infinite time evolved block decimation algorithm which works in the thermodynamical limit and are verified to agree with density-matrix renormalization-group results and their classical analog obtained with the corner transfer-matrix renormalization group.
©2008 The American Physical Society
Keyword Quantum renormalization groups
Spin chains
Transverse field
Ising model
Systems
Entropy
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown

Document type: Journal Article
Sub-type: Article (original research)
Collections: Excellence in Research Australia (ERA) - Collection
School of Mathematics and Physics
 
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Created: Wed, 21 Apr 2010, 12:13:21 EST by Jon Swabey on behalf of Faculty of Science