skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Automatic contraction of unstructured tensor networks

Abstract

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

Authors:
 [1]
  1. Flatiron Institute
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1591698
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Published Article
Journal Name:
SciPost Physics Proceedings
Additional Journal Information:
Journal Name: SciPost Physics Proceedings Journal Volume: 8 Journal Issue: 1; Journal ID: ISSN 2542-4653
Publisher:
Stichting SciPost
Country of Publication:
Netherlands
Language:
English

Citation Formats

Jermyn, Adam. Automatic contraction of unstructured tensor networks. Netherlands: N. p., 2020. Web. doi:10.21468/SciPostPhys.8.1.005.
Jermyn, Adam. Automatic contraction of unstructured tensor networks. Netherlands. doi:10.21468/SciPostPhys.8.1.005.
Jermyn, Adam. Wed . "Automatic contraction of unstructured tensor networks". Netherlands. doi:10.21468/SciPostPhys.8.1.005.
@article{osti_1591698,
title = {Automatic contraction of unstructured tensor networks},
author = {Jermyn, Adam},
abstractNote = {The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.},
doi = {10.21468/SciPostPhys.8.1.005},
journal = {SciPost Physics Proceedings},
number = 1,
volume = 8,
place = {Netherlands},
year = {2020},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.21468/SciPostPhys.8.1.005

Save / Share:

Works referenced in this record:

Markov Chain Monte Carlo Convergence Diagnostics: A Comparative Review
journal, June 1996

  • Cowles, Mary Kathryn; Carlin, Bradley P.
  • Journal of the American Statistical Association, Vol. 91, Issue 434
  • DOI: 10.2307/2291683

Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
journal, January 2011

  • Halko, N.; Martinsson, P. G.; Tropp, J. A.
  • SIAM Review, Vol. 53, Issue 2
  • DOI: 10.1137/090771806

Nested Sampling
conference, January 2004

  • Skilling, John
  • BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING: 24th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, AIP Conference Proceedings
  • DOI: 10.1063/1.1835238

Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
journal, March 2012


Simulating Quantum Computation by Contracting Tensor Networks
journal, January 2008

  • Markov, Igor L.; Shi, Yaoyun
  • SIAM Journal on Computing, Vol. 38, Issue 3
  • DOI: 10.1137/050644756

Class of Quantum Many-Body States That Can Be Efficiently Simulated
journal, September 2008


Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
journal, April 2013

  • Nakatani, Naoki; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 138, Issue 13
  • DOI: 10.1063/1.4798639

Crystal Statistics. I. A Two-Dimensional Model with an Order-Disorder Transition
journal, February 1944


Phase diagrams for dilute spin glasses
journal, May 1985


Bayesian Computation Via Markov Chain Monte Carlo
journal, January 2014


The density-matrix renormalization group
journal, April 2005


An Application of Modular Equations in Analysis Situs
journal, January 1912

  • Veblen, Oswald
  • The Annals of Mathematics, Vol. 14, Issue 1/4
  • DOI: 10.2307/1967604

Tensor Network States and Geometry
journal, June 2011


Spin-glass theory for pedestrians
journal, May 2005


Grassmann tensor renormalization group approach to one-flavor lattice Schwinger model
journal, July 2014


Faster identification of optimal contraction sequences for tensor networks
journal, September 2014


Improving the efficiency of variational tensor network algorithms
journal, June 2014


Efficient tree decomposition of high-rank tensors
journal, January 2019


A New Scheme for the Tensor Representation
journal, October 2009


Tensor Networks and Hierarchical Tensors for the Solution of High-Dimensional Partial Differential Equations
journal, April 2016

  • Bachmayr, Markus; Schneider, Reinhold; Uschmajew, André
  • Foundations of Computational Mathematics, Vol. 16, Issue 6
  • DOI: 10.1007/s10208-016-9317-9

Renormalization Group Flows of Hamiltonians Using Tensor Networks
journal, June 2017


Efficient, Multiple-Range Random Walk Algorithm to Calculate the Density of States
journal, March 2001


Matplotlib: A 2D Graphics Environment
journal, January 2007


Phase diagram and exotic spin-spin correlations of anisotropic Ising model on the Sierpiński gasket
journal, February 2016


Loop Optimization for Tensor Network Renormalization
journal, March 2017


The NumPy Array: A Structure for Efficient Numerical Computation
journal, March 2011

  • van der Walt, Stéfan; Colbert, S. Chris; Varoquaux, Gaël
  • Computing in Science & Engineering, Vol. 13, Issue 2
  • DOI: 10.1109/MCSE.2011.37

Monte Carlo Sampling Methods Using Markov Chains and Their Applications
journal, April 1970


Lattice gauge tensor networks
journal, October 2014


Algorithms for tensor network renormalization
journal, January 2017


Second Renormalization of Tensor-Network States
journal, October 2009


Beitrag zur Theorie des Ferromagnetismus
journal, February 1925


Encoding universal computation in the ground states of Ising lattices
journal, July 2012


Tensor network method for reversible classical computation
journal, March 2018