Integrable matrix product states and overlaps

by Tamás Gombor (HUN-REN Wigner RCP)

Friday 6 Mar 2026, 14:00 → 15:00 Europe/Budapest

Integrable matrix product states (MPS) appear in a variety of contexts ranging from quantum statistical physics to the AdS/CFT correspondence. A central quantity associated with these states is their overlap with Bethe eigenstates, which encodes physically important information, for example about quantum quenches and one-point functions in defect conformal field theories. Until recently, these overlaps were known only in a few special cases, but major progress has led to their exact and systematic determination. A key insight is that the overlap functions are governed by the eigenvalues of Casimir operators of reflection algebras, revealing an unexpected and powerful algebraic structure.

In this talk I will give an introduction to the problem, review the main methods for computing MPS–Bethe state overlaps, and outline several applications in integrable quantum systems and holography.

The presentation is based on T. Gombor, Phys. Rev. Lett. 135, 150402.