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Tamas Gombor1

  • 1HUN-REN Wigner Research Centre for Physics, Eötvös Loránd University, MTA-ELTE "Momentum" Integrable Quantum Dynamics Research Group, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary and , Konkoly-Thege Miklós u. 29-33, 1121 Budapest, Hungary.

Physical Review Letters
|October 25, 2025
PubMed
Summary

We derived a general formula for overlaps between integrable matrix product states (MPSs) and Bethe states. This formula, crucial for nonequilibrium physics and AdS/CFT, involves Gaudin determinants and a novel MPS-dependent prefactor.

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Area of Science:

  • Quantum Many-Body Physics
  • High-Energy Physics
  • Statistical Mechanics

Background:

  • Integrable matrix product states (MPSs) and Bethe states are key concepts in quantum many-body theory.
  • Their overlaps are fundamental for understanding nonequilibrium statistical physics and the AdS/CFT correspondence.
  • Existing methods for calculating these overlaps are limited in scope.

Purpose of the Study:

  • To derive a general formula for calculating the overlaps between integrable matrix product states and Bethe states.
  • To provide a unified framework applicable to various symmetric spin chains.
  • To extend the understanding of quantum systems in and out of equilibrium.

Main Methods:

  • The study employs techniques from the theory of integrable systems.
  • Gaudin determinants are utilized as a core component of the formula.
  • A novel prefactor is derived to account for the specifics of the matrix product states.

Main Results:

  • A general formula for the MPS-Bethe state overlap is presented.
  • The formula is expressed as a product of Gaudin determinants and an MPS-dependent prefactor.
  • The derived prefactor is valid for all integrable MPSs of glN, oN, and spN symmetric spin chains with arbitrary representations.

Conclusions:

  • The presented formula offers a significant advancement in calculating MPS-Bethe state overlaps.
  • This work provides essential tools for studying complex quantum phenomena in diverse physical contexts.
  • The findings facilitate deeper insights into the connections between condensed matter systems and quantum gravity.