Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions

Pirvu, B., Verstraete, F. and Vidal, G. (2011) Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions. Physical Review B: Condensed Matter and Materials Physics, 83 12: . doi:10.1103/PhysRevB.83.125104

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Author Pirvu, B.
Verstraete, F.
Vidal, G.
Title Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions
Journal name Physical Review B: Condensed Matter and Materials Physics   Check publisher's open access policy
ISSN 1098-0121
1550-235X
Publication date 2011-03-17
Sub-type Article (original research)
DOI 10.1103/PhysRevB.83.125104
Open Access Status File (Publisher version)
Volume 83
Issue 12
Total pages 14
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Formatted abstract
We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain with N sites and correlation length ξ, the computational cost formally scales as g(D,ξ/N)D3, where g(D,ξ/N) is a nontrivial function. For ξ<<N, this scaling reduces to D3, independent of the system size N, making our method N times faster than previous proposals. We apply the algorithm to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ
Additional Notes Article number 125104

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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