Msc defense by Vasileios Moustakis

Integrable Matrix Product State Overlaps from Twisted Yangian Representations

This thesis aims to examine overlaps between Matrix Product States and Bethe states that are relevant to defect versions of N=4 Super Yang-Mills. The relation between conformal operators in the so(6) and su(2) sectors with Bethe states of the corresponding spin chains in the planar limit and at one-loop order is explained through Feynman diagram calculations and the relevance of spin chain overlaps to the dCFT is established.

The Heisenberg model is introduced and solved using the algebraic Bethe ansatz. The Yangian of gl(N) is defined, its connection to the algebraic Bethe ansatz is noted and it is used to derive the Bethe equations for a spin chain in an arbitrary gl(N) representation. The connection between the boundary Yang-Baxter equation and integrable matrix product states is explained and the relation between solutions to that relation and twisted Yangian representations is established. For the (SU(3),SO(3)) and (SO(6),SO(5)) symmetric pairs, twisted Yangian representations are used to reduce ratios of overlaps between the matrix product states and Bethe states to transfer matrix eigenvalues. The transfer matrix eigenvalues are computed.


Censor: Marta Orselli