Boundary One-Point Functions in the Open XXZ Spin Chain with Generic Integrable Boundaries

Abstract

We consider the problem of computing observables beyond the spectrum in the open XXZ spin chain with the most generic integrable boundary conditions. For such boundaries, the residual u(1) symmetry is broken and the familiar Baxter TQ equation describing the spectrum becomes inhomogeneous, placing the model outside the realm of existing approaches to correlation functions and form factors. We show that the Functional Separation of Variables method, so far developed mainly for rational, (quasi-)periodic spin chains, is largely insensitive to these modifications, and works equally well for diagonal and generic boundaries. Using this method, we compute exact determinant expressions for a prototypical example of form factors in open-boundary systems, namely the longitudinal and transverse boundary-spin one-point functions in arbitrary Hamiltonian eigenstates at finite system size. No constraint relating the two boundary configurations and no reference state are required. We verify the resulting formulae against direct finite-volume diagonalisation.

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BibTeX RIS

BibTeX

@misc{bargheer2026boundary,
  title = {{Boundary One-Point Functions in the Open XXZ Spin Chain with Generic Integrable Boundaries}},
  author = {Till Bargheer and Tengis Batmunkh and Paul Ryan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27062},
  eprint = {2610.27062},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27062},
}

RIS

TY  - UNPB
TI  - Boundary One-Point Functions in the Open XXZ Spin Chain with Generic Integrable Boundaries
AU  - Till Bargheer
AU  - Tengis Batmunkh
AU  - Paul Ryan
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.27062
UR  - https://arxiv.org/abs/2610.27062
AB  - We consider the problem of computing observables beyond the spectrum in the open XXZ spin chain with the most generic integrable boundary conditions. For such boundaries, the residual u(1) symmetry is broken and the familiar Baxter TQ equation describing the spectrum becomes inhomogeneous, placing the model outside the realm of existing approaches to correlation functions and form factors. We show that the Functional Separation of Variables method, so far developed mainly for rational, (quasi-)periodic spin chains, is largely insensitive to these modifications, and works equally well for diagonal and generic boundaries. Using this method, we compute exact determinant expressions for a prototypical example of form factors in open-boundary systems, namely the longitudinal and transverse boundary-spin one-point functions in arbitrary Hamiltonian eigenstates at finite system size. No constraint relating the two boundary configurations and no reference state are required. We verify the resulting formulae against direct finite-volume diagonalisation.
ER  -

Abstract

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