Explicit Boundary-Entropy Deficits in the XX Spin Chain with arbitrary boundary fields
Abstract
The exact thermodynamics of the XX spin-1/2 chain with arbitrary Hermitian boundary fields is constructed via fusion techniques. The rigorous result shows that (1) each end with a nonzero transverse field contributes +1/2Tln2 to the low-temperature free energy, whereas strictly diagonal and free ends contribute no such linear term; (2) each nondiagonal end has a characteristic temperature TB, which scales as TB∝ h⊥2/J in the weak-field regime. For T≪min{J,TB}, the boundary entropy approaches a deficit of 1/2ln2 relative to a diagonal end. As the transverse field tends to zero, the boundary crossover scale vanishes and the low-temperature expansion becomes nonuniform. The present result provides a clear benchmark not only for the boundary thermodynamics of open boundary quantum integrable systems, but also for dot defects in quantum critical systems.
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BibTeX
@misc{qiao2026explicit,
title = {{Explicit Boundary-Entropy Deficits in the XX Spin Chain with arbitrary boundary fields}},
author = {Yi Qiao and Pei Sun and Junpeng Cao and Wen-Li Yang and Yupeng Wang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00946},
eprint = {2611.00946},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00946},
}
RIS
TY - UNPB
TI - Explicit Boundary-Entropy Deficits in the XX Spin Chain with arbitrary boundary fields
AU - Yi Qiao
AU - Pei Sun
AU - Junpeng Cao
AU - Wen-Li Yang
AU - Yupeng Wang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00946
UR - https://arxiv.org/abs/2611.00946
AB - The exact thermodynamics of the XX spin-1/2 chain with arbitrary Hermitian boundary fields is constructed via fusion techniques. The rigorous result shows that (1) each end with a nonzero transverse field contributes +1/2Tln2 to the low-temperature free energy, whereas strictly diagonal and free ends contribute no such linear term; (2) each nondiagonal end has a characteristic temperature T_B, which scales as T_B∝ h_⊥^2/J in the weak-field regime. For T≪min{J,T_B}, the boundary entropy approaches a deficit of 1/2ln2 relative to a diagonal end. As the transverse field tends to zero, the boundary crossover scale vanishes and the low-temperature expansion becomes nonuniform. The present result provides a clear benchmark not only for the boundary thermodynamics of open boundary quantum integrable systems, but also for dot defects in quantum critical systems.
ER -