Mutual information across the commensurate--incommensurate crossover and near the Kosterlitz--Thouless point of the spin-1/2 J₁--J₂ Heisenberg chain

@misc{pankeaw2026mutual,
  title = {{Mutual information across the commensurate--incommensurate crossover and near the Kosterlitz--Thouless point of the spin-$\tfrac12$ $J_1$--$J_2$ Heisenberg chain}},
  author = {Wuttichai Pankeaw and Pruet Kalasuwan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16915},
  eprint = {2610.16915},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16915},
}

TY  - UNPB
TI  - Mutual information across the commensurate--incommensurate crossover and near the Kosterlitz--Thouless point of the spin-1/2 J_1--J_2 Heisenberg chain
AU  - Wuttichai Pankeaw
AU  - Pruet Kalasuwan
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16915
UR  - https://arxiv.org/abs/2610.16915
AB  - What quantum mutual information adds to conventional correlation functions is often unclear. We study the spin-1/2 J_1-J_2 Heisenberg chain, using DMRG on infinite chains and periodic rings and an SU(2) decomposition of the mutual information into correlation channels. For singlet ground states the two-site mutual information is an exact function of the spin correlator, so any additional content must come from blocks. In the dimerized phase, blocks resolve bond-energy correlations in the SU(2)-scalar channel without an independent asymptotic length: singlet and triplet correlation lengths agree to about 1%. The scalar channel dominates block mutual information at large distances in the commensurate regime up to J_2/J_1=0.40, but falls to a few percent beyond the disorder point, which coincides numerically with the Majumdar-Ghosh point J_2/J_1=1/2; the structure-factor peak splits only at the Lifshitz point J_2/J_1=0.520622(2). On the gapless side we compare block mutual information on rings extrapolated to infinite size with the two-interval prediction of SU(2)_1 conformal field theory across the Kosterlitz-Thouless point J_2/J_1=0.241167. There, for block lengths l≤6, the correction decays as l^−p with p=1.96-$2.07$, and any logarithmic term is at least 60 times smaller than in the Heisenberg chain. Expanding in the marginal coupling (from level spectroscopy) the first-order coefficient is consistent with l^−2 scaling and the second-order coefficient is positive for x≤1/4, suggesting that the mutual information relative to the field-theory value becomes stationary at the KT point for large blocks. The scalar-channel share approaches 1/4 at small cross ratio x, as expected from SO(4) symmetry; under two stated assumptions its first-order response to the coupling is (3/8)ln x−5/8 at small x, matched by the l=4 data within 1-3% at x≤1/9.
ER  -