TY - JOUR
T1 - The integrable (hyper)eclectic spin chain
AU - Ahn, Changrim
AU - Staudacher, Matthias
N1 - Publisher Copyright:
© 2021, The Author(s).
PY - 2021/2
Y1 - 2021/2
N2 - We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of N = 4 Super Yang-Mills Theory.
AB - We refine the notion of eclectic spin chains introduced in [1] by including a maximal number of deformation parameters. These models are integrable, nearest-neighbor n-state spin chains with exceedingly simple non-hermitian Hamiltonians. They turn out to be non-diagonalizable in the multiparticle sector (n > 2), where their “spectrum” consists of an intricate collection of Jordan blocks of arbitrary size and multiplicity. We show how and why the quantum inverse scattering method, sought to be universally applicable to integrable nearest-neighbor spin chains, essentially fails to reproduce the details of this spectrum. We then provide, for n=3, detailed evidence by a variety of analytical and numerical techniques that the spectrum is not “random”, but instead shows surprisingly subtle and regular patterns that moreover exhibit universality for generic deformation parameters. We also introduce a new model, the hypereclectic spin chain, where all parameters are zero except for one. Despite the extreme simplicity of its Hamiltonian, it still seems to reproduce the above “generic” spectra as a subset of an even more intricate overall spectrum. Our models are inspired by parts of the one-loop dilatation operator of a strongly twisted, double-scaled deformation of N = 4 Super Yang-Mills Theory.
KW - AdS-CFT Correspondence
KW - Bethe Ansatz
KW - Integrable Field Theories
UR - http://www.scopus.com/inward/record.url?scp=85107376573&partnerID=8YFLogxK
U2 - 10.1007/JHEP02(2021)019
DO - 10.1007/JHEP02(2021)019
M3 - Article
AN - SCOPUS:85107376573
SN - 1126-6708
VL - 2021
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 2
M1 - 19
ER -