Complete boundary phase diagram of the spin- XXZ chain with boundary fields in the antiferromagnetic gapped regime
Phys. Rev. B 113, 054424 – Published 12 February, 2026
DOI: https://doi.org/10.1103/5j68-1pqh
Abstract
We consider the spin- XXZ chain with diagonal boundary fields and solve it exactly using the Bethe ansatz in the gapped antiferromagnetic regime, and we obtain the complete phase boundary diagram. Depending on the values of the boundary fields, the system exhibits several phases that can be categorized based on the ground state exhibited by the system and also on the number of bound states localized at the boundaries. We show that the Hilbert space is comprised of a certain number of towers, depending on the number of boundary bound states exhibited by the system. The system undergoes boundary phase transitions when boundary fields are varied across certain critical values. There are two types of phase transitions. In the first type, the ground state of the system undergoes a change. In the second type, named the “eigenstate phase transition,” the number of towers of the Hilbert space changes, which is again associated with the change in the number of boundary bound states exhibited by the system. We use the density matrix renormalization group and exact diagonalization techniques to probe the signature of the eigenstate phase transition and the ground-state phase transition by analyzing the spin profiles in each eigenstate.
