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A. Jena, S. Genin, and M. Mosca, arXiv e-prints , arXiv:1907.07859 (2019), arXiv:1907.07859 [quant-ph]
Original
1907
Earlier work this paper cites.
P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, M. Martonosi, and F. T. Chong, arXiv e-prints , arXiv:1907.13623 (2019), arXiv:1907.13623 [quant-ph]
Original
1907
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A. Zhao, A. Tranter, W. M. Kirby, S. F. Ung, A. Miyake, and P. Love, arXiv e-prints , arXiv:1908.08067 (2019), arXiv:1908.08067 [quant-ph]
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1908
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O. Crawford, B. van Straaten, D. Wang, T. Parks, E. Campbell, and S. Brierley, arXiv e-prints , arXiv:1908.06942 (2019), arXiv:1908.06942 [quant-ph]
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I. Boettcher, P. Bienias, R. Belyansky, A. J. Kollár, and A. V. Gorshkov, arXiv e-prints , arXiv:1910.12318 (2019), arXiv:1910.12318 [quant-ph]
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2020

Characterization of solvable spin models via graph invariants

Chapman, Adrian, Flammia, Steven T.

Understand

Exactly solvable models are essential in physics.

For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph.
We provide a complete characterization of models which can be solved this way.
Specifically, we reduce the problem of recognizing such spin models to the graph-theoretic problem of recognizing line graphs, which has been solved optimally.

Built on

A. Jena, S. Genin, and M. Mosca, arXiv e-prints , arXiv:1907.07859 (2019), arXiv:1907.07859 [quant-ph]
Original
1907
Earlier work this paper cites.
P. Gokhale, O. Angiuli, Y. Ding, K. Gui, T. Tomesh, M. Suchara, M. Martonosi, and F. T. Chong, arXiv e-prints , arXiv:1907.13623 (2019), arXiv:1907.13623 [quant-ph]
Original
1907
Earlier work this paper cites.
A. Zhao, A. Tranter, W. M. Kirby, S. F. Ung, A. Miyake, and P. Love, arXiv e-prints , arXiv:1908.08067 (2019), arXiv:1908.08067 [quant-ph]
Original
1908
Earlier work this paper cites.
O. Crawford, B. van Straaten, D. Wang, T. Parks, E. Campbell, and S. Brierley, arXiv e-prints , arXiv:1908.06942 (2019), arXiv:1908.06942 [quant-ph]
Original
1908
Earlier work this paper cites.
X. Bonet-Monroig, R. Babbush, and T. E. O’Brien, arXiv e-prints , arXiv:1908.05628 (2019), arXiv:1908.05628 [quant-ph]
Original
1908
Earlier work this paper cites.
I. Boettcher, P. Bienias, R. Belyansky, A. J. Kollár, and A. V. Gorshkov, arXiv e-prints , arXiv:1910.12318 (2019), arXiv:1910.12318 [quant-ph]
Original
1910
Earlier work this paper cites.
Z. Jiang, A. Kalev, W. Mruczkiewicz, and H. Neven, arXiv e-prints , arXiv:1910.10746 (2019), arXiv:1910.10746 [quant-ph]
Original
1910
Earlier work this paper cites.
P. Jordan and E. Wigner, Zeitschrift für Physik 47
1928
Earlier work this paper cites.
H. Whitney, American Journal of Mathematics 54
1932
Earlier work this paper cites.
J. Krausz, Matematikai és Fizikai Lapok 50
1943
Earlier work this paper cites.
E. Lieb, T. Schultz, and D. Mattis, Annals of Physics 16
1961
Earlier work this paper cites.
P. Kasteleyn, Physica 27
1961
Earlier work this paper cites.
H. N. V. Temperley and M. E. Fisher, Philosophical Magazine 6
1961
Earlier work this paper cites.
P. Erdős, A. W. Goodman, and L. Pósa, Canadian Journal of Mathematics 18
1966
Earlier work this paper cites.
L. W. Beineke, Journal of Combinatorial Theory 9
1970
Earlier work this paper cites.
F. Harary, Graph Theory , Addison Wesley series in mathematics (Addison-Wesley, 1971)
1971
Earlier work this paper cites.
N. D. Roussopoulos, Information Processing Letters 2
1973
Earlier work this paper cites.
P. G. H. Lehot, J. ACM 21
1974
Earlier work this paper cites.
A. Bednarek, Discrete Mathematics 56
1985
Earlier work this paper cites.
E. Fradkin, Phys. Rev. Lett. 63
1989
Earlier work this paper cites.
Y. R. Wang, Phys. Rev. B 43
1991
Earlier work this paper cites.
L. Huerta and J. Zanelli, Phys. Rev. Lett. 71
1993
Earlier work this paper cites.
C. H. Papadimitriou, in Encyclopedia of Computer Science (John Wiley and Sons Ltd., Chichester, UK, 1994) pp. 260–265
1994
Earlier work this paper cites.
Ľ. Šoltés, Discrete Mathematics 132
1994
Earlier work this paper cites.

Similar

D. G. Degiorgi and K. Simon, in Graph-Theoretic Concepts in Computer Science (Springer Berlin Heidelberg, Berlin, Heidelberg, 1995) pp. 37–48
1995
Cited alongside, same era.
D. M. Goodmanson, American Journal of Physics 64
1996
Cited alongside, same era.
C. D. Batista and G. Ortiz, Phys. Rev. Lett. 86
2001
Cited alongside, same era.
E. Knill, ArXiv e-prints (2001), arXiv:quant-ph/0108033
2001
Cited alongside, same era.
A. Y. Kitaev, Physics-Uspekhi 44
2001
Cited alongside, same era.
N. Tantivasadakarn, arXiv e-prints , arXiv:2002.11345 (2020), arXiv:2002.11345 [cond-mat.str-el]
Original
2002
Cited alongside, same era.

Then

D. J. Brod and A. M. Childs, Quant. Info. Comput. 14
2014
Later among the works it cites.
H. Bombín, Phys. Rev. X 5
2015
Later among the works it cites.
A. Kubica and M. E. Beverland, Phys. Rev. A 91
2015
Later among the works it cites.
H. Bombín, New Journal of Physics 17
2015
Later among the works it cites.
D. J. Brod, Phys. Rev. A 93
2016
Later among the works it cites.
H. Bombín, New Journal of Physics 18
2016
Later among the works it cites.
B. J. Brown, N. H. Nickerson, and D. E. Browne, Nature Communications 7
2016
Later among the works it cites.

Beyond the bibliography

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