The spin-one Motzkin chain is gapped for any area weight $t<1
We prove a conjecture by Zhang, Ahmadain, and Klich that the spin-$1$ Motzkin chain is gapped for any area weight $t<1$. Existence of a finite spectral gap is necessary for the Motzkin Hamiltonian to belong to the Haldane phase, which has been argued to potentially be the case in recent work of B...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
09.04.2022
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| Online Access | Get full text |
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| Abstract | We prove a conjecture by Zhang, Ahmadain, and Klich that the spin-$1$ Motzkin
chain is gapped for any area weight $t<1$. Existence of a finite spectral gap
is necessary for the Motzkin Hamiltonian to belong to the Haldane phase, which
has been argued to potentially be the case in recent work of Barbiero,
Dell'Anna, Trombettoni, and Korepin. Our proof rests on the combinatorial
structure of the ground space and the analytical verification of a finite-size
criterion. |
|---|---|
| AbstractList | We prove a conjecture by Zhang, Ahmadain, and Klich that the spin-$1$ Motzkin
chain is gapped for any area weight $t<1$. Existence of a finite spectral gap
is necessary for the Motzkin Hamiltonian to belong to the Haldane phase, which
has been argued to potentially be the case in recent work of Barbiero,
Dell'Anna, Trombettoni, and Korepin. Our proof rests on the combinatorial
structure of the ground space and the analytical verification of a finite-size
criterion. |
| Author | Movassagh, Ramis Lemm, Marius Andrei, Radu |
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| BackLink | https://doi.org/10.48550/arXiv.2204.04517$$DView paper in arXiv |
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| Snippet | We prove a conjecture by Zhang, Ahmadain, and Klich that the spin-$1$ Motzkin
chain is gapped for any area weight $t<1$. Existence of a finite spectral gap
is... |
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| SubjectTerms | Mathematics - Mathematical Physics Physics - Mathematical Physics Physics - Quantum Physics Physics - Statistical Mechanics |
| Title | The spin-one Motzkin chain is gapped for any area weight $t<1 |
| URI | https://arxiv.org/abs/2204.04517 |
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