Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

On the closedness and geometry of tensor network state sets

Journal Article · · Letters in Mathematical Physics

Not provided.

Research Organization:
Duke Univ., Durham, NC (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
DOE Contract Number:
SC0019449
OSTI ID:
1976698
Journal Information:
Letters in Mathematical Physics, Vol. 112, Issue 4; ISSN 0377-9017
Publisher:
Springer
Country of Publication:
United States
Language:
English

References (66)

A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal October 2014
Optimizing the density-matrix renormalization group method using quantum information entropy journal November 2003
Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group journal March 2002
Measuring orbital interaction using quantum information theory journal April 2006
Fermionic Orbital Optimization in Tensor Network States journal November 2016
Density matrix formulation for quantum renormalization groups journal November 1992
Density-matrix algorithms for quantum renormalization groups journal October 1993
The density-matrix renormalization group journal April 2005
Matrix product states represent ground states faithfully journal March 2006
A polynomial time algorithm for the ground state of one-dimensional gapped local Hamiltonians journal June 2015
Sign problem in the numerical simulation of many-electron systems journal May 1990
Meron-Cluster Solution of Fermion Sign Problems journal October 1999
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations journal May 2005
Contraction of fermionic operator circuits and the simulation of strongly correlated fermions journal October 2009
Fermionic multiscale entanglement renormalization ansatz journal October 2009
Unitary circuits for strongly correlated fermions journal May 2010
Fermionic projected entangled pair states journal May 2010
Simulation of interacting fermions with entanglement renormalization journal January 2010
Dimers on a Rectangular Lattice journal April 1968
Topics in quantum probability journal November 1981
Finitely correlated states on quantum spin chains journal March 1992
Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group journal January 1997
The density-matrix renormalization group in the age of matrix product states journal January 2011
Classical simulation of quantum many-body systems with a tree tensor network journal August 2006
Simulating strongly correlated quantum systems with tree tensor networks journal November 2010
Entanglement Renormalization journal November 2007
Class of Quantum Many-Body States That Can Be Efficiently Simulated journal September 2008
Quantum phase transition in spin-3/2 systems on the hexagonal lattice — optimum ground state approach journal January 1997
Self-consistent tensor product variational approximation for 3D classical models journal June 2000
Stripe ansätze from exactly solved models journal July 2001
Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States journal June 2006
Tensor-Train Decomposition journal January 2011
A New Scheme for the Tensor Representation journal October 2009
Hierarchical Singular Value Decomposition of Tensors journal January 2010
Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension journal February 2007
Infinite time-evolving block decimation algorithm beyond unitary evolution journal October 2008
Variational optimization algorithms for uniform matrix product states journal January 2018
Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions journal December 2008
Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction journal September 2009
Algorithms for entanglement renormalization journal April 2009
Critical exponents with a multiscale entanglement renormalization Ansatz channel journal September 2009
Projected Entangled Pair States: Fundamental Analytical and Numerical Limitations journal November 2020
On manifolds of tensors of fixed TT-rank journal September 2011
Tensor Spaces and Numerical Tensor Calculus book February 2012
Scaling laws for ising models near T c journal June 1966
Kondo Lattice: Real-Space Renormalization-Group Approach journal June 1977
Quantum field theories on a lattice: Variational methods for arbitrary coupling strengths and the Ising model in a transverse magnetic field journal September 1977
Real-Space Renormalization Yields Finite Correlations journal July 2010
Colloquium : Area laws for the entanglement entropy journal February 2010
A short review on entanglement in quantum spin systems journal December 2009
Quantum entanglement in condensed matter systems journal August 2016
Three qubits can be entangled in two inequivalent ways journal November 2000
O(n2.7799) complexity for n × n approximate matrix multiplication journal June 1979
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem journal January 2008
A Quantum Version of Wielandt's Inequality journal September 2010
Quantum Version of Wielandt’s Inequality Revisited journal August 2019
Normal projected entangled pair states generating the same state journal November 2018
Valence bond ground states in isotropic quantum antiferromagnets journal September 1988
Spin nematics correlations in bilinear-biquadratic S = 1 spin chains journal October 2006
Low-energy physics of isotropic spin-1 chains in the critical and Haldane phases journal July 2020
Rigorous results on valence-bond ground states in antiferromagnets journal August 1987
The Expression of a Tensor or a Polyadic as a Sum of Products journal April 1927
Analysis of individual differences in multidimensional scaling via an n-way generalization of “Eckart-Young” decomposition journal September 1970
Construction and analysis of degenerate PARAFAC models journal January 2000
Low-Rank Approximation of Generic $p \timesq \times2$ Arrays and Diverging Components in the Candecomp/Parafac Model journal January 2008
Optimization at the boundary of the tensor network variety journal May 2021

Cited By (1)

Two-electron wavefunctions are matrix product states with bond dimension three journal September 2022

Similar Records

Related Subjects