Energy transport in Z3 chiral clock model
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914947435331584 |
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| author | Nishad, Naveen Sreejith, G J |
| author_facet | Nishad, Naveen Sreejith, G J |
| contents | We characterize the energy transport in a one dimensional $\mathbb{Z}_3$ chiral clock model. The model generalizes the $\mathbb{Z}_2$ symmetric transverse field Ising model (TFIM). The model is parametrized by a chirality parameter $θ$, in addition to $f$ and $J$ which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, does not transform to a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of sizes up to $48$. We present the estimated NESS current and its scaling exponent $γ$ as a function of $θ$ at different $f/J$. The estimated $γ(f/J,θ)$ point to a ballistic energy transport along a line of integrable points $f=J\cos{3θ}$ in the parameter space; all other points deviate from ballistic transport. Analysis of finite size effects within the available system sizes suggest a diffusive behavior away from the integrable points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_11230 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Energy transport in Z3 chiral clock model Nishad, Naveen Sreejith, G J Statistical Mechanics Disordered Systems and Neural Networks We characterize the energy transport in a one dimensional $\mathbb{Z}_3$ chiral clock model. The model generalizes the $\mathbb{Z}_2$ symmetric transverse field Ising model (TFIM). The model is parametrized by a chirality parameter $θ$, in addition to $f$ and $J$ which are analogous to the transverse field and the nearest neighbour spin coupling in the TFIM. Unlike the well studied TFIM and XYZ models, does not transform to a fermionic system. We use a matrix product states implementation of the Lindblad master equation to obtain the non-equilibrium steady state (NESS) in systems of sizes up to $48$. We present the estimated NESS current and its scaling exponent $γ$ as a function of $θ$ at different $f/J$. The estimated $γ(f/J,θ)$ point to a ballistic energy transport along a line of integrable points $f=J\cos{3θ}$ in the parameter space; all other points deviate from ballistic transport. Analysis of finite size effects within the available system sizes suggest a diffusive behavior away from the integrable points. |
| title | Energy transport in Z3 chiral clock model |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2109.11230 |