Exact Overlaps for All Integrable Matrix Product States of Rational Spin Chains

The overlaps between integrable matrix product states (MPSs) and Bethe states are important in both the nonequilibrium statistical physics and the AdS/CFT duality. We present the general MPS overlap formula. The result is a product of a ratio of Gaudin determinants and a prefactor. The Gaudin determinants depend on the spin chain but not on the MPS. The MPS dependent prefactor is given for all integrable MPSs of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi mathvariant="fraktur">gl</a:mi></a:mrow><a:mrow><a:mi>N</a:mi></a:mrow></a:msub></a:mrow></a:math>, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msub><d:mi mathvariant="fraktur">o</d:mi><d:mi>N</d:mi></d:msub></d:math>, and <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi mathvariant="fraktur">sp</g:mi></g:mrow><g:mrow><g:mi>N</g:mi></g:mrow></g:msub></g:mrow></g:math> symmetric spin chains with arbitrary representations.