Exact phase diagram of the XXZ Heisenberg chain in a staggered magnetic field
Abstract
We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.
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BibTeX
@misc{zhang2026exact,
title = {{Exact phase diagram of the XXZ Heisenberg chain in a staggered magnetic field}},
author = {H. P. Zhang and Z. Song},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29728},
eprint = {2609.29728},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29728},
}
RIS
TY - UNPB
TI - Exact phase diagram of the XXZ Heisenberg chain in a staggered magnetic field
AU - H. P. Zhang
AU - Z. Song
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29728
UR - https://arxiv.org/abs/2609.29728
AB - We study the phase diagram of the spin-1/2 XXZ Heisenberg chain in a staggered magnetic field. An exact solution is obtained along the phase boundary, where the exchange anisotropy and the staggered-field strength satisfy an exact analytical relation, yielding a highly degenerate manifold of ground states with off-diagonal long-range order. We demonstrate that these exact ground states lie on the boundary between the ferromagnetic phase and a gapless Luttinger liquid phase. Upon further decreasing the anisotropy, the gapless phase eventually gives way to a gapped quantum-disordered phase. Large-scale density-matrix renormalization group calculations confirm this phase structure and indicate that the transition across the exact boundary is of first order. Our results provide an exact benchmark for understanding quantum phase transitions driven by staggered magnetic fields in one-dimensional quantum spin systems.
ER -