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The AKLT model on a hexagonal chain is gapped · Around

2019

The AKLT model on a hexagonal chain is gapped

Lemm, Marius, Sandvik, Anders, Yang, Sibin

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In 1987, Affleck, Kennedy, Lieb, and Tasaki introduced the AKLT spin chain and proved that it has a spectral gap above the ground state.

Their concurrent conjecture that the two-dimensional AKLT model on the hexagonal lattice is also gapped remains open.
In this paper, we show that the AKLT Hamiltonian restricted to an arbitrarily long chain of hexagons is gapped.
The argument is based on explicitly verifying a finite-size criterion which is tailor-made for the system at hand.

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.
M. Lemm and B. Nachtergaele,
Original
1902
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.

Similar

I. Affleck, T. Kennedy, E. H. Lieb, and H. Tasaki,
1988
Cited alongside, same era.
T. Kennedy, E.H. Lieb, and H. Tasaki,
1988
Cited alongside, same era.
S. Knabe,
1988
Cited alongside, same era.
M. Fannes, B. Nachtergaele, R.F. Werner,
1992
Cited alongside, same era.
A.W. Sandvik, AIP Conf. Proc
2010
Cited alongside, same era.
M. Lemm and E. Mozgunov,
Original
Cited in the paper.

Then

A. Miyake,
2011
Later among the works it cites.
T-C. Wei, I. Affleck, and R. Raussendorf,
2011
Later among the works it cites.
A. Garcia-Saez, V. Murg, and T.-C. Wei,
2013
Later among the works it cites.
T-C. Wei, P. Haghnegahdar, and R. Raussendorf,
2014
Later among the works it cites.
D. Gosset and E. Mozgunov,
2016
Later among the works it cites.

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