The spin-one Motzkin chain is gapped for any area weight $t<1$
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866911711363072000 |
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| author | Andrei, Radu Lemm, Marius Movassagh, Ramis |
| author_facet | Andrei, Radu Lemm, Marius Movassagh, Ramis |
| contents | We consider the spin-one Motzkin chain with area weight $t>0$. We resolve three questions from the literature about this model. We prove (i) existence of a uniform spectral gap for all $t<1$ as conjectured by Zhang--Ahmadein--Klich \cite{zhang2017novel} (ii) an explicit formula for the long-distance limit of the string order parameter, which implies it is non-vanishing at small $t$, confirming a conjecture by Barbiero et al. \cite{barbiero2017haldane}, and (iii) that gaplessness for $t>1$ is robust and extends to hard boundary conditions, answering a question of Zhang--Klich \cite{zhang2017entropy}. These conclusions rest on an effective approximate description of the ground states of finite open Motzkin chains in terms of height-controlled imbalanced Motzkin walks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_04517 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The spin-one Motzkin chain is gapped for any area weight $t<1$ Andrei, Radu Lemm, Marius Movassagh, Ramis Quantum Physics Statistical Mechanics Mathematical Physics We consider the spin-one Motzkin chain with area weight $t>0$. We resolve three questions from the literature about this model. We prove (i) existence of a uniform spectral gap for all $t<1$ as conjectured by Zhang--Ahmadein--Klich \cite{zhang2017novel} (ii) an explicit formula for the long-distance limit of the string order parameter, which implies it is non-vanishing at small $t$, confirming a conjecture by Barbiero et al. \cite{barbiero2017haldane}, and (iii) that gaplessness for $t>1$ is robust and extends to hard boundary conditions, answering a question of Zhang--Klich \cite{zhang2017entropy}. These conclusions rest on an effective approximate description of the ground states of finite open Motzkin chains in terms of height-controlled imbalanced Motzkin walks. |
| title | The spin-one Motzkin chain is gapped for any area weight $t<1$ |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2204.04517 |