The quantum XY chain with boundary fields: finite-size gap and phase behavior
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914063864299520 |
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| author | Coraggio, Aldo Pelissetto, Andrea |
| author_facet | Coraggio, Aldo Pelissetto, Andrea |
| contents | We present a detailed study of the finite-size one-dimensional quantum XY chain in a transverse field in the presence of boundary fields coupled with the order-parameter spin operator. We consider fields located at the chain boundaries that have the same strength and that are oppositely aligned. We derive exact expressions for the gap $Δ$ as a function of the model parameters for large values of the chain length $L$. These results allow us to characterize the nature of the ordered phases of the model. We find a magnetic (M) phase ($Δ\sim e^{-aL}$), a magnetic-incommensurate (MI) phase ($Δ\sim e^{-aL} f_{MI}(L)$), a kink (K) phase ($Δ\sim L^{-2}$), and a kink-incommensurate (KI) phase ($Δ\sim L^{-2} f_{KI}(L)$); $f_{MI}(L)$ and $f_{KI}(L)$ are bounded oscillating functions of $L$. We also analyze the behavior along the phase boundaries. In particular, we characterize the universal crossover behavior across the K-KI phase boundary. On this boundary, the dynamic critical exponent is $z=4$, i.e., $Δ\sim L^{-4}$ for large values of $L$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22226 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The quantum XY chain with boundary fields: finite-size gap and phase behavior Coraggio, Aldo Pelissetto, Andrea Statistical Mechanics Quantum Physics We present a detailed study of the finite-size one-dimensional quantum XY chain in a transverse field in the presence of boundary fields coupled with the order-parameter spin operator. We consider fields located at the chain boundaries that have the same strength and that are oppositely aligned. We derive exact expressions for the gap $Δ$ as a function of the model parameters for large values of the chain length $L$. These results allow us to characterize the nature of the ordered phases of the model. We find a magnetic (M) phase ($Δ\sim e^{-aL}$), a magnetic-incommensurate (MI) phase ($Δ\sim e^{-aL} f_{MI}(L)$), a kink (K) phase ($Δ\sim L^{-2}$), and a kink-incommensurate (KI) phase ($Δ\sim L^{-2} f_{KI}(L)$); $f_{MI}(L)$ and $f_{KI}(L)$ are bounded oscillating functions of $L$. We also analyze the behavior along the phase boundaries. In particular, we characterize the universal crossover behavior across the K-KI phase boundary. On this boundary, the dynamic critical exponent is $z=4$, i.e., $Δ\sim L^{-4}$ for large values of $L$. |
| title | The quantum XY chain with boundary fields: finite-size gap and phase behavior |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2509.22226 |