Exact Quench Dynamics from Algebraic Geometry

TL;DR

This paper introduces an algebraic geometry-based method to analytically compute physical observables in finite-length integrable spin chains, avoiding reliance on Bethe roots or numerical methods.

Contribution

It presents a systematic, purely algebraic approach to calculate quench dynamics quantities in integrable spin chains, extending analytical capabilities.

Findings

Derived new analytic formulas for diagonal entropy

Computed Loschmidt echo analytically for the first time

Method applicable to a broad class of physical quantities

Abstract

We develop a systematic approach to compute physical observables of integrable spin chains with finite length. Our method is based on Bethe ansatz solution of the integrable spin chain and computational algebraic geometry. The final results are analytic and no longer depend on Bethe roots. The computation is purely algebraic and does not rely on further assumptions or numerics. This method can be applied to compute a broad family of physical quantities in integrable quantum spin chains. We demonstrate the power of the method by computing two important quantities in quench dynamics: the diagonal entropy and the Loschmidt echo and obtain new analytic results.