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We present a conjugate-gradient method for the ground-state optimization of projected entangled-pair states (PEPS) in the thermodynamic limit, as a direct implementation of the variational principle within the PEPS manifold.
R. Fletcher and C. Reeves, “Function minimization by conjugate gradients,” Comput. J. 7
1964
Earlier work this paper cites.
R. J. Baxter, “Dimers on a Rectangular Lattice,” Journal of Mathematical Physics 9
1968
Earlier work this paper cites.
R. J. Baxter, “Corner transfer matrices,” Physica A 106
1981
Earlier work this paper cites.
E. Manousakis, “The spin-1/2 Heisenberg antiferromagnet on a square lattice and its application to the cuprous oxides,” Reviews of Modern Physics 63
1991
Earlier work this paper cites.
T. Nishino and K. Okunishi, “Corner Transfer Matrix Renormalization Group Method,” Journal of the Physical Society of Japan 65
1996
Earlier work this paper cites.
T. Nishino and K. Okunishi, “Corner Transfer Matrix Algorithm for Classical Renormalization Group,” Journal of the Physical Society of Japan 66
1997
Earlier work this paper cites.
A. W. Sandvik, “Finite-size scaling of the ground-state parameters of the two-dimensional Heisenberg model,” Physical Review B 56
1997
Earlier work this paper cites.
A. W. Sandvik and C. J. Hamer, “Ground-state parameters, finite-size scaling, and low-temperature properties of the two-dimensional S = 1/2 XY model,” Physical Review B 60
1999
Earlier work this paper cites.
S. Sorella, “Generalized Lanczos algorithm for variational quantum Monte Carlo,” Physical Review B 64
2001
Earlier work this paper cites.
H. W. J. Blöte and Y. Deng, “Cluster Monte Carlo simulation of the transverse Ising model,” Physical Review E 66
2002
Earlier work this paper cites.
F. Verstraete and J. I. Cirac, “Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions,” (2004) , arXiv:0407066
2004
Earlier work this paper cites.
S. Sorella, “Wave function optimization in the variational Monte Carlo method,” Physical Review B 71
2005
Earlier work this paper cites.
W. Zheng, J. Oitmaa, and C. J. Hamer, “Series studies of the spin-1/2 Heisenberg antiferromagnet at T=0 : Magnon dispersion and structure factors,” Physical Review B 71
2005
Earlier work this paper cites.
J. F. Bonnans, J. C. Gilbert, C. Lemaréchal, and C. A. Sagastizábal, Numerical Optimization (Springer-Verlag Berlin Heidelberg, 2006)
2006
Earlier work this paper cites.
J. Nocedal and S. Wright, Numerical optimization (Springer, New York, 2006)
2006
Earlier work this paper cites.
W. W. Hager and H. Zhang, “A survey of nonlinear conjugate gradient methods,” Pacific journal of Optimization 2
2006
Earlier work this paper cites.
G. Vidal, “Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension,” Physical Review Letters 98
2007
Earlier work this paper cites.
V. Murg, Frank Verstraete, and J. I. Cirac, “Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states,” Physical Review A 75
2007
Earlier work this paper cites.
J. Jordan, R. Orús, G. Vidal, F. Verstraete, and J. I. Cirac, “Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions,” Physical Review Letters 101
2008
Earlier work this paper cites.
H. Jiang, Z. Weng, and T. Xiang, “Accurate Determination of Tensor Network State of Quantum Lattice Models in Two Dimensions,” Physical Review Letters 101
2008
Earlier work this paper cites.
2008
Earlier work this paper cites.
R. Orús and G. Vidal, “Infinite time-evolving block decimation algorithm beyond unitary evolution,” Physical Review B 78
2008
Earlier work this paper cites.
P.-A. Absil, R. Mahony, and R. Sepulchre, Optimization algorithms on matrix manifolds (Princeton University Press, 2008)
2008
Cited alongside, same era.
R. Orús and G. Vidal, “Simulation of two-dimensional quantum systems on an infinite lattice revisited: Corner transfer matrix for tensor contraction,” Physical Review B 80
2009
Cited alongside, same era.
B. Bauer, G. Vidal, and M. Troyer, “Assessing the accuracy of projected entangled-pair states on infinite lattices,” Journal of Statistical Mechanics: Theory and Experiment 2009
2009
Cited alongside, same era.
A. Lüscher and A. M. Läuchli, “Exact diagonalization study of the antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field,” Physical Review B 79
2009
Cited alongside, same era.
V. Murg, F. Verstraete, and J. I. Cirac, “Exploring frustrated spin systems using projected entangled pair states,” Phys. Rev. B 79
T. Wahl, H.-H. Tu, N. Schuch, and J. I. Cirac, “Projected Entangled-Pair States Can Describe Chiral Topological States,” Physical Review Letters 111
2013
Later among the works it cites.
N. Schuch, D. Poilblanc, J. I. Cirac, and D. Pérez-García, “Topological Order in the Projected Entangled-Pair States Formalism: Transfer Operator and Boundary Hamiltonians,” Physical Review Letters 111
2013
Later among the works it cites.
Z.-C. Gu, H.-C. Jiang, D. N. Sheng, H. Yao, L. Balents, and X.-G. Wen, “Time-reversal symmetry breaking superconducting ground state in the doped Mott insulator on the honeycomb lattice,” Physical Review B 88
2013
Later among the works it cites.
P. Corboz and F. Mila, “Tensor network study of the Shastry-Sutherland model in zero magnetic field,” Physical Review B 87
2013
Later among the works it cites.
J. Haegeman, T. J. Osborne, and F. Verstraete, “Post-Matrix Product State Methods: To tangent space and beyond,” Physical Review B 88
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2009
Cited alongside, same era.
L. Balents, “Spin liquids in frustrated magnets,” Nature 464
2010
Cited alongside, same era.
J. Eisert, M. Cramer, and M. B. Plenio, “Colloquium: Area laws for the entanglement entropy,” Reviews of Modern Physics 82
2010
Cited alongside, same era.
N. Schuch, J. I. Cirac, and D. Pérez-García, “PEPS as ground states: Degeneracy and topology,” Annals of Physics 325
2010
Cited alongside, same era.
A. W. Sandvik, A. Avella, and F. Mancini, “Computational Studies of Quantum Spin Systems,” in AIP Conf. Proc. (2010) pp. 135–338
2010
Cited alongside, same era.
Iztok Pižorn and Frank Verstraete, “Fermionic implementation of projected entangled pair states algorithm,” Phys. Rev. B 81
2010
Cited alongside, same era.
S. Yan, D. A. Huse, and S. R. White, “Spin-Liquid Ground State of the S = 1/2 Kagome Heisenberg Antiferromagnet,” Science 332
2011
Cited alongside, same era.
J. I. Cirac, D. Poilblanc, N. Schuch, and F. Verstraete, “Entanglement spectrum and boundary theories with projected entangled-pair states,” Physical Review B 83
2011
Cited alongside, same era.
2013
Later among the works it cites.
A. Milsted, J. Haegeman, and T. J. Osborne, “Matrix product states and variational methods applied to critical quantum field theory,” Physical Review D 88
2013
Later among the works it cites.
D. Poilblanc, N. Schuch, and J. I. Cirac, “Field-induced superfluids and Bose liquids in projected entangled pair states,” Physical Review B 88
2013
Later among the works it cites.
R. Orús, “A practical introduction to tensor networks: Matrix product states and projected entangled pair states,” Annals of Physics 349
2014
Later among the works it cites.
2014
Later among the works it cites.
O. Buerschaper, “Twisted injectivity in projected entangled pair states and the classification of quantum phases,” Annals of Physics 351
2014
Later among the works it cites.
S. Yang, L. Lehman, D. Poilblanc, K. Van Acoleyen, F. Verstraete, J. I. Cirac, and N. Schuch, “Edge Theories in Projected Entangled Pair State Models,” Physical Review Letters 112
2014
Later among the works it cites.
J. O. Iregui, P. Corboz, and M. Troyer, “Probing the stability of the spin-liquid phases in the Kitaev-Heisenberg model using tensor network algorithms,” Physical Review B 90
2014
Later among the works it cites.
P. Corboz and F. Mila, “Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model,” Physical Review Letters 112
2014
Later among the works it cites.
P. Corboz, T. M. Rice, and M. Troyer, “Competing States in the t-J Model: Uniform d-Wave State versus Stripe State,” Physical Review Letters 113
2014
Later among the works it cites.
M. Lubasch, J. I. Cirac, and M.-C. Bañuls, “Algorithms for finite projected entangled pair states,” Physical Review B 90
2014
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2015
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2015
Later among the works it cites.
H. N. Phien, J. A. Bengua, H. D. Tuan, P. Corboz, and R. Orús, “Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing,” Physical Review B 92
2015
Later among the works it cites.
T. Picot and D. Poilblanc, “Nematic and supernematic phases in kagome quantum antiferromagnets under the influence of a magnetic field,” Physical Review B 91
2015
Later among the works it cites.
Shenghan Jiang and Ying Ran, “Symmetric tensor networks and practical simulation algorithms to sharply identify classes of quantum phases distinguishable by short-range physics,” Phys. Rev. B 92
2015
Later among the works it cites.
T. Picot, M. Ziegler, R. Orús, and D. Poilblanc, “Spin-S kagome quantum antiferromagnets in a field with tensor networks,” Physical Review B 93
2016
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Pierre Nataf, Miklós Lajkó, Philippe Corboz, Andreas M. Läuchli, Karlo Penc, and Frédéric Mila, “Plaquette order in the SU(6) Heisenberg model on the honeycomb lattice,” Physical Review B 93
2016
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