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Spectral gaps of frustration-free spin systems with boundary · Around

2018

Spectral gaps of frustration-free spin systems with boundary

Lemm, Marius, Mozgunov, Evgeny

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In quantum many-body systems, the existence of a spectral gap above the ground state has far-reaching consequences.

In this paper, we discuss "finite-size" criteria for having a spectral gap in frustration-free spin systems and their applications.
We extend a criterion that was originally developed for periodic systems by Knabe and Gosset-Mozgunov to systems with a boundary.
Our finite-size criterion says that if the spectral gaps at linear system size $n$ exceed an explicit threshold of order $n^{-3/2}$, then the whole system is gapped.

Built on

E. H. Lieb, T. Schultz, and D. Mattis,
1961
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,
1988
Earlier work this paper cites.
S. Knabe,
1988
Earlier work this paper cites.
M. Fannes, B. Nachtergaele and R.F. Werner,
1992
Earlier work this paper cites.
B. Nachtergaele,
1996
Earlier work this paper cites.
P. Di Francesco, P. Mathieu, and D. Sénéchal,
1997
Earlier work this paper cites.
M. B. Hastings,
2004
Earlier work this paper cites.
J. de Gier and F.H.L. Essler,
2006
Earlier work this paper cites.
M. Hastings, T. Koma,
2006
Earlier work this paper cites.

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