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Exact quench dynamics from algebraic geometry.

Yunfeng Jiang1, Rui Wen2, Yang Zhang3,4

  • 1Shing-Tung Yau Center and School of Physics, Southeast University, Nanjing 210096, China.

Physical Review. E
|September 19, 2023
PubMed
Summary
This summary is machine-generated.

We present a new algebraic method to calculate physical properties of finite integrable quantum spin chains. This approach yields analytic results for quantities like diagonal entropy and Loschmidt echo without relying on numerical approximations.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Computational Physics

Background:

  • Integrable quantum spin chains are crucial models in condensed matter physics.
  • Calculating physical observables in these systems, especially for finite lengths, presents significant challenges.
  • Existing methods often rely on approximations or numerical techniques.

Purpose of the Study:

  • To develop a systematic, analytic approach for computing physical observables in finite integrable spin chains.
  • To provide a method independent of Bethe roots and numerical computations.
  • To demonstrate the applicability to key quantities in quantum quench dynamics.

Main Methods:

  • Utilizing the Bethe ansatz solution inherent to integrable spin chains.
  • Employing computational algebraic geometry for the calculations.
  • Developing a purely algebraic framework for deriving physical quantities.

Main Results:

  • An analytic method for computing physical observables in finite integrable spin chains.
  • Results are independent of specific Bethe roots, offering a general solution.
  • Successful computation of diagonal entropy and Loschmidt echo in quench dynamics.

Conclusions:

  • The developed method offers a powerful, purely algebraic tool for analyzing integrable quantum spin chains.
  • It provides exact, analytic results for a wide range of physical quantities.
  • This approach significantly advances the theoretical understanding of quantum dynamics in these systems.