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Title: Tangent space to the manifold of critical classical Hamiltonians representable by tensor networks

Journal Article · · Physical Review E
 [1]
  1. Princeton Univ., NJ (United States)
+ Show Author Affiliations

We introduce a scheme to perform Monte Carlo renormalization group with the coupling constants of the system Hamiltonian encoded in a tensor network. Furthermore, with this scheme we compute the tangent space to the manifold of the critical Hamiltonians representable by a tensor network at the nearest-neighbor critical coupling for three models: the two- and three-dimensional Ising models and the two-dimensional three-state Potts model.

Research Organization:
Princeton Univ., NJ (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0017865
OSTI ID:
1612763
Alternate ID(s):
OSTI ID: 1558144
Journal Information:
Physical Review E, Vol. 100, Issue 2; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

References (16)

Renormalization Group by Monte Carlo Methods journal August 1976
Renormalization Group Flows of Hamiltonians Using Tensor Networks journal June 2017
Monte Carlo Renormalization Group journal April 1979
Gauge fixing, canonical forms, and optimal truncations in tensor networks with closed loops journal August 2018
The Potts model journal January 1982
Monte Carlo Calculation of Renormalized Coupling Parameters journal April 1984
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order journal October 2009
Renormalization of tensor networks using graph-independent local truncations journal January 2018
Monte Carlo renormalized hamiltonian journal November 1984
Loop Optimization for Tensor Network Renormalization journal March 2017
Renormalization Group and Critical Phenomena. I. Renormalization Group and the Kadanoff Scaling Picture journal November 1971
Variational Approach to Monte Carlo Renormalization Group journal November 2017
Tensor Network Renormalization journal October 2015
Algorithms for tensor network renormalization journal January 2017
Second Renormalization of Tensor-Network States journal October 2009
Renormalization-Group Approach to the Solution of General Ising Models journal December 1974

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
Monte Carlo methods
Tensor network renormalization