Variational Monte Carlo with the multiscale entanglement renormalization ansatz

Ferris, Andrew J. and Vidal, Guifre (2012) Variational Monte Carlo with the multiscale entanglement renormalization ansatz. Physical Review B, 85 16: 165147-1-165147-10.


Author Ferris, Andrew J.
Vidal, Guifre
Title Variational Monte Carlo with the multiscale entanglement renormalization ansatz
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
1550-235X
Publication date 2012-04
Sub-type Article (original research)
DOI 10.1103/PhysRevB.85.165147
Volume 85
Issue 16
Start page 165147-1
End page 165147-10
Total pages 10
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2013
Language eng
Abstract Monte Carlo sampling techniques have been proposed as a strategy to reduce the computational cost of contractions in tensor network approaches to solving many-body systems. Here, we put forward a variational Monte Carlo approach for the multiscale entanglement renormalization ansatz (MERA), which is a unitary tensor network. Two major adjustments are required compared to previous proposals with nonunitary tensor networks. First, instead of sampling over configurations of the original lattice, made of L sites, we sample over configurations of an effective lattice, which is made of just ln(L) sites. Second, the optimization of unitary tensors must account for their unitary character while being robust to statistical noise, which we accomplish with a modified steepest descent method within the set of unitary tensors. We demonstrate the performance of the variational Monte Carlo MERA approach in the relatively simple context of a finite quantum spin chain at criticality, and discuss future, more challenging applications, including two-dimensional systems.
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published 30 April 2012. Article number 165147

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2013 Collection
 
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