# Thermodynamic limit and boundary energy of the spin-1 Heisenberg chain with non-diagonal boundary fields

### Submission summary

 As Contributors: Xiaotian Xu Preprint link: scipost_202106_00001v4 Date accepted: 2022-01-13 Date submitted: 2021-11-17 10:28 Submitted by: Xu, Xiaotian Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Mathematical Physics Approach: Theoretical

### Abstract

The thermodynamic limit and boundary energy of the isotropic spin-1 Heisenberg chain with non-diagonal boundary fields are studied. The finite size scaling properties of the inhomogeneous term in the $T-Q$ relation at the ground state are calculated by the density matrix renormalization group. Based on our findings, the boundary energy of the system in the thermodynamic limit can be obtained from Bethe ansatz equations of a related model with parallel boundary fields. These results can be generalized to the $SU(2)$ symmetric high spin Heisenberg model directly.

###### Current status:
Publication decision taken: accept

Editorial decision: For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)

Dear editor,

We are extremely pleased that now all three referees are so strongly supportive of our manuscript (Ref. No. scipost_202106_00001v3). Please pass our great thanks to the referees for their appreciations of our work and also for valuable suggestions which help us to further improve our presentation.

We have given some minor revisions for our manuscript according to the referees' suggestions as follows:

1) We have added the sentences lines 66-79 in P. 2 and 3 to explain the terminology "reduced BAEs".

2) We have added new references [25], [29], [36]-[49] and [51]-[53] (which includes all the references pointed by one of the referees), and given their citations in corresponding positions of the paper.

3) In lines 233-234 of P.10, we have rewritten the sentences as "The O(N^1) bulk term and the O(N^0) boundary term for the ground state energy do not depend on the orientations of the boundary fields".

4) We also give some corrections for the typos.

We are resubmitting our paper for publication in SciPost Physics.

Many thanks for your kind helps and with the best regards!

Sincerely Yours,

Xiaotian Xu