How to fold a spin chain: Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models

TY - JOUR

T1 - How to fold a spin chain

T2 - Integrable boundaries of the Heisenberg XXX and Inozemtsev hyperbolic models

AU - Gomez, Alejandro De La Rosa

AU - MacKay, Niall

AU - Regelskis, Vidas

N1 - 9 pages, 1 figure

PY - 2017/4/25

Y1 - 2017/4/25

N2 - We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a "bottom-up" approach for constructing integrable boundaries and can be applied to any spin chain model.

AB - We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a "bottom-up" approach for constructing integrable boundaries and can be applied to any spin chain model.

KW - math-ph

KW - hep-th

KW - math.MP

KW - nlin.SI

U2 - 10.1016/j.physleta.2017.02.039

DO - 10.1016/j.physleta.2017.02.039

M3 - Article

SN - 0375-9601

VL - 381

SP - 1340

EP - 1348

JO - Physics Letters A

JF - Physics Letters A

IS - 16

ER -