# A non-integrable quench from AdS/dCFT

## TL;DR

This paper explores the properties of a matrix product state arising from AdS/dCFT, showing it does not meet integrability criteria but still allows for exact calculations of certain one-point functions.

## Contribution

It introduces a non-integrable matrix product state from AdS/dCFT and derives exact results for one-point functions despite the lack of integrability.

## Key findings

- Matrix product state does not satisfy a recent integrability criterion.
- Overlaps cannot be expressed as factorized determinants.
- Provides exact formulas for one-point functions in large spin-chain limit.

## Abstract

We study the matrix product state which appears as the boundary state of the AdS/dCFT set-up where a probe D7 brane wraps two two-spheres stabilized by fluxes. The matrix product state plays a dual role, on one hand acting as a tool for computing one-point functions in a domain wall version of N=4 SYM and on the other hand acting as the initial state in the study of quantum quenches of the Heisenberg spin chain. We derive a number of selection rules for the overlaps between the matrix product state and the eigenstates of the Heisenberg spin chain and in particular demonstrate that the matrix product state does not fulfill a recently proposed integrability criterion. Accordingly, we find that the overlaps can not be expressed in the usual factorized determinant form. Nevertheless, we derive some exact results for one-point functions of simple operators and present a closed formula for one-point functions of more general operators in the limit of large spin-chain length.