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Exact edge singularities and dynamical correlations in spin-1/2 chains.

Rodrigo G Pereira¹, Steven R White, Ian Affleck

¹Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1.

Physical Review Letters

|February 1, 2008

Summary

Researchers derived exact formulas for spin chain dynamics, revealing critical exponents from Bethe ansatz solutions. This work precisely calculates the dynamical structure factor using advanced computational methods.

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Area of Science:

Condensed matter physics
Quantum magnetism
Statistical mechanics

Background:

The S=1/2 XXZ spin chain is a fundamental model in quantum magnetism.
Understanding its dynamical properties, particularly in the critical regime, is crucial.
Previous studies often lacked exact analytical solutions for all parameters.

Purpose of the Study:

To derive exact formulas for the singularities of the dynamical structure factor, Szz(q,omega).
To express critical exponents in terms of exactly known phase shifts from the Bethe ansatz.
To study the long-time asymptotics of the self-correlation function.

Main Methods:

Exact analytical derivation of formulas for Szz(q,omega) singularities.
Utilizing Bethe ansatz solutions for exact phase shifts.
Combining analytical results with time-dependent density matrix renormalization group (TD-DMRG) calculations.

Main Results:

Exact formulas for Szz(q,omega) singularities at all q, anisotropy, and magnetic field in the critical regime.
Exponents of singularities are expressed in terms of known Bethe ansatz phase shifts.
High-precision calculation of Szz(q,omega) for short to moderate times.

Conclusions:

The study provides a complete analytical solution for the critical dynamics of the S=1/2 XXZ spin chain.
The findings bridge analytical theory and numerical simulations for highly accurate results.
This work offers a benchmark for understanding quantum critical phenomena in magnetic systems.