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Researchers derived exact formulas for hyperbolic functions, simplifying analysis of finite-size Ising spin chains. These findings offer new methods for calculating quantum critical points and enabling rapid system driving.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Mathematical Physics

Background:

  • Ising spin chains are fundamental models in statistical mechanics and quantum information.
  • Understanding finite-size effects is crucial for realistic physical systems.
  • Closed-form expressions are highly valuable for analytical and computational studies.

Purpose of the Study:

  • To derive exact closed-form expressions for sums involving hyperbolic functions.
  • To apply these expressions to the analysis of finite-size Ising spin chains.
  • To generalize and extend existing mathematical results.

Main Methods:

  • Derivation of exact closed-form expressions for specific mathematical sums.
  • Application of these sums to physical models, specifically Ising spin chains.
  • Utilizing hyperbolic function identities and summation techniques.

Main Results:

  • Exact closed-form expressions for sums leading to hyperbolic functions.
  • Closed-form expressions for fidelity susceptibility at quantum critical points.
  • Closed-form expressions for counterdiabatic Hamiltonian coefficients for rapid adiabatic driving.

Conclusions:

  • The derived formulas provide powerful tools for studying finite-size Ising spin chains.
  • These results offer new analytical pathways for quantum critical phenomena and quantum control.
  • The work extends and generalizes known mathematical series and integrals.