Quantum Potts chain in alternating field
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866913270887088128 |
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| author | Yehia, Péter Lajkó. Wedade Alaaeldin Ahmed Shafik Iglói, Ferenc |
| author_facet | Yehia, Péter Lajkó. Wedade Alaaeldin Ahmed Shafik Iglói, Ferenc |
| contents | The $q$-state Potts chain with ferromagnetic couplings, $J=1$, in the presence of a transverse field, $Γ$, has a quantum phase transition at $Γ/q=1$, which is continuous for $q \le 4$ and of first order for $q>4$. Here we introduce a $q$-periodic alternating longitudinal field of strength, $h$, and study the phase diagram and the critical properties of the model. For $h<q/(q-1)$ there is a ferromagnetic ordered phase, for $Γ<Γ_c(h)$ and at $h=q/(q-1)$ there is a classical endpoint at $Γ=0$, with finite entropy at $T=0$. We considered the $q=3$ model and using DMRG techniques we calculated the low-laying spectrum of the Hamiltonian, the transverse magnetisation and the spin-spin correlation function, all of which signalled a diverging correlation length at the transition point with the exponent of the three-state Potts model. In the vicinity of the classical endpoint the model is mapped to a quantum hard rod model, which belongs also to the universality class of the three-state Potts model. Also the spectrum of the critical Hamiltonian is found in agreement with conformal invariance. At the same time the correlation function shows a jump at the transition point, thus the transition is of mixed order for $h<q/(q-1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09127 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quantum Potts chain in alternating field Yehia, Péter Lajkó. Wedade Alaaeldin Ahmed Shafik Iglói, Ferenc Statistical Mechanics The $q$-state Potts chain with ferromagnetic couplings, $J=1$, in the presence of a transverse field, $Γ$, has a quantum phase transition at $Γ/q=1$, which is continuous for $q \le 4$ and of first order for $q>4$. Here we introduce a $q$-periodic alternating longitudinal field of strength, $h$, and study the phase diagram and the critical properties of the model. For $h<q/(q-1)$ there is a ferromagnetic ordered phase, for $Γ<Γ_c(h)$ and at $h=q/(q-1)$ there is a classical endpoint at $Γ=0$, with finite entropy at $T=0$. We considered the $q=3$ model and using DMRG techniques we calculated the low-laying spectrum of the Hamiltonian, the transverse magnetisation and the spin-spin correlation function, all of which signalled a diverging correlation length at the transition point with the exponent of the three-state Potts model. In the vicinity of the classical endpoint the model is mapped to a quantum hard rod model, which belongs also to the universality class of the three-state Potts model. Also the spectrum of the critical Hamiltonian is found in agreement with conformal invariance. At the same time the correlation function shows a jump at the transition point, thus the transition is of mixed order for $h<q/(q-1)$. |
| title | Quantum Potts chain in alternating field |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2306.09127 |