Two-dimensional transverse-field $XY$ model with the in-plane anisotropy and Dzyaloshinskii-Moriya interaction: Anisotropy-driven transition
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866929744162848768 |
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| author | Nishiyama, Yoshihiro |
| author_facet | Nishiyama, Yoshihiro |
| contents | The two-dimensional (2D) quantum spin-$S=1/2$ $XY$ model with the transverse-field $H$, in-plane-anisotropy $γ$, and Dzyaloshinskii-Moriya (DM) $D$ interactions was investigated by means of the exact diagonalization method, which enables us to treat the $D$-mediated complex-valued Hermitian matrix elements. According to the preceding real-space renormalization group analysis at $H=0$, the $γ$-driven phase transition occurs generically for $D\ne 0$ in contrast to the 1D $XY$ model where both $γ$- and $D$-induced phases are realized for $γ>D$ and $ γ<D$, respectively. In this paper, we evaluated the $β$ function $β(γ)$, namely, the differential of $γ$ with respect to the concerned energy scale, and from its behavior in proximity to $γ=0$, we observed an evidence of the $γ$-driven phase transition; additionally, $γ$'s scaling dimension is estimated from $β(γ)$'s slope. It was also determined how the value of the DM interaction influences the order-disorder phase boundary $H_c(γ)$ around the multi-critical point, $γ\to 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00679 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-dimensional transverse-field $XY$ model with the in-plane anisotropy and Dzyaloshinskii-Moriya interaction: Anisotropy-driven transition Nishiyama, Yoshihiro Statistical Mechanics The two-dimensional (2D) quantum spin-$S=1/2$ $XY$ model with the transverse-field $H$, in-plane-anisotropy $γ$, and Dzyaloshinskii-Moriya (DM) $D$ interactions was investigated by means of the exact diagonalization method, which enables us to treat the $D$-mediated complex-valued Hermitian matrix elements. According to the preceding real-space renormalization group analysis at $H=0$, the $γ$-driven phase transition occurs generically for $D\ne 0$ in contrast to the 1D $XY$ model where both $γ$- and $D$-induced phases are realized for $γ>D$ and $ γ<D$, respectively. In this paper, we evaluated the $β$ function $β(γ)$, namely, the differential of $γ$ with respect to the concerned energy scale, and from its behavior in proximity to $γ=0$, we observed an evidence of the $γ$-driven phase transition; additionally, $γ$'s scaling dimension is estimated from $β(γ)$'s slope. It was also determined how the value of the DM interaction influences the order-disorder phase boundary $H_c(γ)$ around the multi-critical point, $γ\to 0$. |
| title | Two-dimensional transverse-field $XY$ model with the in-plane anisotropy and Dzyaloshinskii-Moriya interaction: Anisotropy-driven transition |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2503.00679 |