Fetching the paper…
Reading the bibliography…
Hastings established exponential decay of correlations for ground states of gapped quantum many-body systems.
P. Pfeuty, “The one-dimensional Ising model with a transverse field,” Annals of Physics 57
1970
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki, “Rigorous results on valence-bond ground states in antiferromagnets,” Physical Review Letters 59
1987
Earlier work this paper cites.
D. S. Rokhsar and S. A. Kivelson, “Superconductivity and the quantum hard-core dimer gas,” Physical Review Letters 61
1988
Earlier work this paper cites.
M. Fannes, B. Nachtergaele, and R. F. Werner, “Finitely correlated states on quantum spin chains,” Communications in Mathematical Physics 144
1992
Earlier work this paper cites.
M. A. Continentino, “Quantum scaling in many-body systems,” Physics Reports 239
1994
Earlier work this paper cites.
F. C. Alcaraz, S. R. Salinas, and W. F. Wreszinski, “Anisotropic ferromagnetic quantum domains,” Physical Review Letters 75
1995
Earlier work this paper cites.
T. Koma and B. Nachtergaele, “The spectral gap of the ferromagnetic X X Z XXZ -chain,” Letters in Mathematical Physics 40
1997
Earlier work this paper cites.
A. Y. Kitaev, A. H. Shen, and M. N. Vyalyi, Classical and Quantum Computation , Graduate Studies in Mathematics, Vol. 47 (American Mathematical Society, Providence, 2002)
2002
Earlier work this paper cites.
A. Y. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics 303
2003
Earlier work this paper cites.
M. A. Levin and X.-G. Wen, “String-net condensation: A physical mechanism for topological phases,” Physical Review B 71
2005
Cited alongside, same era.
B. Nachtergaele and R. Sims, “Lieb-Robinson bounds and the exponential clustering theorem,” Communications in Mathematical Physics 265
2006
Cited alongside, same era.
M. B. Hastings and T. Koma, “Spectral gap and exponential decay of correlations,” Communications in Mathematical Physics 265
2006
Cited alongside, same era.
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “Matrix product state representations,” Quantum Information and Computation 7
2007
Cited alongside, same era.
M. B. Hastings, “An area law for one-dimensional quantum systems,” Journal of Statistical Mechanics: Theory and Experiment 2007
2007
Cited alongside, same era.
A. Ambainis, J. Kempe, and O. Sattath, “A quantum Lovász local lemma,” Journal of the ACM 59
2012
Later among the works it cites.
S. Bravyi, L. Caha, R. Movassagh, D. Nagaj, and P. W. Shor, “Criticality without frustration for quantum spin-1 chains,” Physical Review Letters 109
2012
Later among the works it cites.
T. J. Osborne, “Hamiltonian complexity,” Reports on Progress in Physics 75
2012
Later among the works it cites.
I. Arad, Z. Landau, and U. Vazirani, “Improved one-dimensional area law for frustration-free systems,” Physical Review B 85
2012
Later among the works it cites.
D. Gosset and D. Nagaj, “Quantum 3-SAT is QMA 1 -complete,” in Proceedings of the 54th Annual IEEE Symposium on Foundations of Computer Science (IEEE Computer Society, Los Alamitos, 2013) pp. 756–765
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
D. Perez-Garcia, F. Verstraete, M. M. Wolf, and J. I. Cirac, “PEPS as unique ground states of local Hamiltonians,” Quantum Information and Computation 8
2008
Cited alongside, same era.
S. Bravyi, C. Moore, and A. Russell, “Bounds on the quantum satisfiability threshold,” in Proceedings of the 1st Symposium on Innovations in Computer Science (Tsinghua University Press, Beijing, 2010) pp. 482–489
2010
Cited alongside, same era.
S. Bravyi, “Efficient algorithm for a quantum analogue of 2-SAT,” in Cross Disciplinary Advances in Quantum Computing , Contemporary Mathematics, Vol. 536 (American Mathematical Society, Providence, 2011) pp. 33–48
2011
Cited alongside, same era.
D. Aharonov, I. Arad, U. Vazirani, and Z. Landau, “The detectability lemma and its applications to quantum Hamiltonian complexity,” New Journal of Physics 13
2011
Cited alongside, same era.
M. B. Hastings, “Lieb-Schultz-Mattis in higher dimensions,” Physical Review B 69
Cited in the paper.
M. B. Hastings, “Locality in quantum and Markov dynamics on lattices and networks,” Physical Review Letters 93
Cited in the paper.
M. B. Hastings, “Locality in quantum systems,” ArXiv:1008.5137
Cited in the paper.
F. G. S. L. Brandao and M. Horodecki, “An area law for entanglement from exponential decay of correlations,” Nature Physics 9
2013
Later among the works it cites.
S. Bravyi and D. Gosset, “Gapped and gapless phases of frustration-free spin- 1 2 \frac{1}{2} chains,” Journal of Mathematical Physics 56
2015
Closest in time.
S. Gharibian, Y. Huang, Z. Landau, and S. W. Shin, “Quantum Hamiltonian complexity,” Foundations and Trends in Theoretical Computer Science 10
2015
Closest in time.