The Heisenberg XX spin chain and low-energy QCD
Abstract
By using random matrix models we uncover a connection between the low energy sector of four dimensional QCD at finite volume and the Heisenberg XX model in a 1d spin chain. This connection allows to relate crucial properties of QCD with physically meaningful properties of the spin chain, establishing a dictionary between both worlds. We predict for the spin chain a third-order phase transition and a Tracy-Widom law in the transition region. We postulate that this dictionary goes beyond the particular example analyzed here and can be applied to other QFT and spin chain models. We finally comment on possible numerical implications of the connection as well as on possible experimental implementations.
Keywords
Cite
@article{arxiv.1305.3877,
title = {The Heisenberg XX spin chain and low-energy QCD},
author = {David Pérez-García and Miguel Tierz},
journal= {arXiv preprint arXiv:1305.3877},
year = {2014}
}
Comments
12 pages. v3 Final version to appear in Phys. Rev. X; discussion on experimental accessibility extended; title modified in journal