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We construct parent Hamiltonians involving only local 2-body interactions for a broad class of Projected Entangled Pair States (PEPS).
J. R. Schrieffer and P. A. Wolff, “Relation between the Anderson and Kondo Hamiltonians,” Phys. Rev. 149
1966
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, “Valence bond ground states in isotropic quantum antiferromagnets,” Comm. Math. Phys. 115
1988
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Comm. Math. Phys. 144
1992
Earlier work this paper cites.
N. Datta, J. Frohlich, L. Rey-Bellet, and R. Fernandez, “Low-temperature phase diagrams of quantum lattice systems. II. Convergent perturbation expansions and stability in systems with infinite degeneracy,” Helvetica Physica Acta 69
1996
Earlier work this paper cites.
R. Raussendorf and H. J. Briegel, “A One-Way Quantum Computer,” Phys. Rev. Lett. 86
2001
Earlier work this paper cites.
G. Vidal, “Efficient Classical Simulation of Slightly Entangled Quantum Computations,” Phys. Rev. Lett. 91
2003
Earlier work this paper cites.
A. Y. Kitaev, “Fault-tolerant quantum computation by anyons,” Ann. Phys. 303
2003
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, “String-net condensation: A physical mechanism for topological phases,” Phys. Rev. B 71
2005
Earlier work this paper cites.
M. B. Hastings, “Solving gapped Hamiltonians locally,” Phys. Rev. B 73
2006
Earlier work this paper cites.
F. Verstraete, M. Wolf, D. Pérez-García, and J. I. Cirac, “Projected Entangled States: Properties and Applications,” Int. J. Mod. Phys. B 20
2006
Earlier work this paper cites.
J. Kempe, A. Kitaev, and O. Regev, “The Complexity of the Local Hamiltonian Problem,” SIAM J. Comput. 35
2006
Earlier work this paper cites.
S. D. Bartlett and T. Rudolph, “Simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation,” Phys. Rev. A 74
2006
Earlier work this paper cites.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. 321
2006
Earlier work this paper cites.
D. Pérez-García, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix Product State Representations,” Quant. Inf. Comp. 7
2007
Cited alongside, same era.
D. Pérez-García, F. Verstraete, J. I. Cirac, and M. M. Wolf, “PEPS as unique ground states of local Hamiltonians,” Quant. Inf. Comp. 8
2008
Cited alongside, same era.
R. Oliveira and B. M. Terhal, “The complexity of quantum spin systems on a two-dimensional square lattice,” Quant. Inf. Comp. 8
2008
Cited alongside, same era.
S. Bravyi, D. P. DiVincenzo, D. Loss, and B. M. Terhal, “Quantum Simulation of Many-Body Hamiltonians Using Perturbation Theory with Bounded-Strength Interactions,” Phy. Rev. Lett. 101
2008
Cited alongside, same era.
S. P. Jordan and E. Farhi, “Perturbative gadgets at arbitrary orders,” Phys. Rev. A 77
2008
Cited alongside, same era.
T.-C. Wei, I. Affleck, and R. Raussendorf, “Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource,” Phys. Rev. Lett. 106
2011
Later among the works it cites.
C. G. Brell, S. T. Flammia, S. D. Bartlett, and A. C. Doherty, “Toric codes and quantum doubles from two-body Hamiltonians,” New Journal of Physics 13
2011
Later among the works it cites.
S. Bravyi, D. P. DiVincenzo, and D. Loss, “Schrieffer-Wolff transformation for quantum many-body systems,” Annals of Physics 326
2011
Later among the works it cites.
S. Bravyi and M. B. Hastings, “A Short Proof of Stability of Topological Order under Local Perturbations,” Communications in Mathematical Physics 307
2011
Later among the works it cites.
N. Schuch, D. Pérez-García, and I. Cirac, “Classifying quantum phases using matrix product states and projected entangled pair states,” Phys. Rev. B 84
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M. Van den Nest, K. Luttmer, W. Dür, and H. J. Briegel, “Graph states as ground states of many-body spin- 1 / 2 1/2 Hamiltonians,” Phys. Rev. A 77
2008
Cited alongside, same era.
Z.-C. Gu, M. Levin, and X.-G. Wen, “Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions,” Phys. Rev. B 78
2008
Cited alongside, same era.
Z.-C. Gu, M. Levin, B. Swingle, and X.-G. Wen, “Tensor-product representations for string-net condensed states,” Phys. Rev. B 79
2009
Cited alongside, same era.
O. Buerschaper, M. Aguado, and G. Vidal, “Explicit tensor network representation for the ground states of string-net models,” Phys. Rev. B 79
2009
Cited alongside, same era.
A. Seidel, “Linear independence of nearest-neighbor valence-bond states on the kagome lattice and construction of S U ( 2 ) SU(2) -invariant spin- 1 2 \frac{1}{2} Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state,” Phys. Rev. B 80
2009
Cited alongside, same era.
S. Bravyi, M. B. Hastings, and S. Michalakis, “Topological quantum order: Stability under local perturbations,” Journal of Mathematical Physics 51
2010
Cited alongside, same era.
N. Schuch, I. Cirac, and D. Pérez-García, “PEPS as ground states: Degeneracy and topology,” Ann. Phys. 325
2010
Cited alongside, same era.
2011
Later among the works it cites.
A. S. Darmawan, G. K. Brennen, and S. D. Bartlett, “Measurement-based quantum computation in a two-dimensional phase of matter,” New Journal of Physics 14
2012
Later among the works it cites.
N. Schuch, D. Poilblanc, J. I. Cirac, and D. Pérez-García, “Resonating valence bond states in the PEPS formalism,” Phys. Rev. B 86
2012
Later among the works it cites.
O. Buerschaper, J. M. Mombelli, M. Christandl, and M. Aguado, “A hierarchy of topological tensor network states,” Journal of Mathematical Physics 54
2013
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S. Michalakis and J. P. Zwolak, “Stability of Frustration-Free Hamiltonians,” Communications in Mathematical Physics 322
2013
Later among the works it cites.
J. I. Cirac, S. Michalakis, D. Pérez-García, and N. Schuch, “Robustness in projected entangled pair states,” Phys. Rev. B 88
2013
Later among the works it cites.
O. Buerschaper, “Twisted Injectivity in PEPS and the Classification of Quantum Phases,” Annals of Physics 351
2014
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2014
Closest in time.