Mesons, Confinement, and Complexity: A Krylov Space Perspective on the Long-Range Ising Chain
Abstract
We investigate the interplay between confinement and Krylov complexity in the long-range transverse-field Ising chain, where power-law interactions ∼ 1/rα generate an effective confining potential between domain walls without an explicit symmetry-breaking field. Using the time-averaged Krylov state complexity after a quench as a diagnostic, we find that the complexity is strongly suppressed and only weakly system size-dependent at small α and small transverse field hx, where confinement is strongest, and crosses over to rapid growth at larger α, where it increases with system size. Within the confined regime, the oscillation frequencies of the complexity agree with the meson masses of an effective two-kink model, with the dominant frequency growing linearly with the lightest meson mass and the time-averaged complexity decreasing approximately as its inverse square. We further study operator Krylov complexity at finite temperature using the Wightman inner product. At low temperature, it exhibits bounded oscillations that directly encode the meson spectrum, whereas this structure is progressively washed out as the temperature increases. These results identify Krylov complexity as a spectroscopic probe of interaction-induced confinement and reproduce, in a microscopic lattice model, the hallmarks of Krylov complexity identified in confining field theories.
Related
BibTeX
@misc{jiang2026mesons,
title = {{Mesons, Confinement, and Complexity: A Krylov Space Perspective on the Long-Range Ising Chain}},
author = {Xuhao Jiang and Jad C. Halimeh and N. S. Srivatsa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36054},
eprint = {2610.36054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36054},
}
RIS
TY - UNPB
TI - Mesons, Confinement, and Complexity: A Krylov Space Perspective on the Long-Range Ising Chain
AU - Xuhao Jiang
AU - Jad C. Halimeh
AU - N. S. Srivatsa
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36054
UR - https://arxiv.org/abs/2610.36054
AB - We investigate the interplay between confinement and Krylov complexity in the long-range transverse-field Ising chain, where power-law interactions ∼ 1/r^α generate an effective confining potential between domain walls without an explicit symmetry-breaking field. Using the time-averaged Krylov state complexity after a quench as a diagnostic, we find that the complexity is strongly suppressed and only weakly system size-dependent at small α and small transverse field h_x, where confinement is strongest, and crosses over to rapid growth at larger α, where it increases with system size. Within the confined regime, the oscillation frequencies of the complexity agree with the meson masses of an effective two-kink model, with the dominant frequency growing linearly with the lightest meson mass and the time-averaged complexity decreasing approximately as its inverse square. We further study operator Krylov complexity at finite temperature using the Wightman inner product. At low temperature, it exhibits bounded oscillations that directly encode the meson spectrum, whereas this structure is progressively washed out as the temperature increases. These results identify Krylov complexity as a spectroscopic probe of interaction-induced confinement and reproduce, in a microscopic lattice model, the hallmarks of Krylov complexity identified in confining field theories.
ER -