Fetching the paper…

Reading the bibliography…

Gaplessness is not generic for translation-invariant spin chains · Around

2019

Gaplessness is not generic for translation-invariant spin chains

Lemm, Marius

Original
PDF
Post on X

Understand

The existence of a spectral gap above the ground state has far-reaching consequences for the low-energy physics of a quantum many-body system.

A recent work of Movassagh [R.
Movassagh, PRL 119 (2017), 220504] shows that a spatially random local quantum Hamiltonian is generically gapless.
Here we observe that a gap is more common for translation-invariant quantum spin chains, more specifically, that these are gapped with a positive probability if the interaction is of small rank.

Built on

H. Abdul-Rahman, M. Lemm, A. Lucia, B. Nachtergaele, and A. Young,
Original
1901
Earlier work this paper cites.
M. Lemm,
Original
1902
Earlier work this paper cites.
J. von Neumann,
1950
Earlier work this paper cites.
F.D.M. Haldane,
1983
Earlier work this paper cites.
F.D.M. Haldane,
1983
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,
1987
Earlier work this paper cites.
I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,
1988
Earlier work this paper cites.
S. Knabe,
1988
Earlier work this paper cites.

Similar

M. Fannes, B. Nachtergaele, R.F. Werner,
1992
Cited alongside, same era.
M. Hastings,
2004
Cited alongside, same era.
M. Hastings, T. Koma,
2006
Cited alongside, same era.
B. Nachtergaele, and R. Sims,
2006
Cited alongside, same era.
M. B. Hastings,
2007
Cited alongside, same era.
S. Bravyi, M. Hastings, S. Michalakis,
2010
Cited alongside, same era.
R. Movassagh, E. Farhi, J. Goldstone, D. Nagaj, T.J. Osborne, and P.W. Shor
2010
Cited alongside, same era.

Then

S. Bachmann, S. Michalakis, B. Nachtergaele, and R. Sims,
2012
Later among the works it cites.
S. Bravyi and D. Gosset,
2015
Later among the works it cites.
T.S. Cubitt, D. Perez-Garcia, and M.M. Wolf,
2015
Later among the works it cites.
Z. Landau, U. Vazirani and T. Vidick,
2015
Later among the works it cites.
D. Gosset and E. Mozgunov,
2016
Later among the works it cites.
R. Movassagh,
2017
Later among the works it cites.
I. Arad, Z. Landau, U. Vazirani and T. Vidick,
2018
Later among the works it cites.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark,

2010

Cited alongside, same era.

I. Arad, A. Kitaev, Z. Landau, and U. Vazirani,

Cited in the paper.

J. Bausch, T. Cubitt, A. Lucia, D. Perez-Garcia,

Cited in the paper.

M. Coudron and R. Movassagh,

Cited in the paper.

M. Lemm and B. Nachtergaele,

Cited in the paper.

M. Lemm and E. Mozgunov,

2019

Closest in time.