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Asymptotic Freedom and Large Spin Antiferromagnetic Chains
Samuel Gozel1, Frédéric Mila1, Ian Affleck2
1Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
Physical Review Letters
|August 7, 2019
Summary
We derived analytic expressions for spin-spin correlations in large-spin quantum systems. These findings, applicable at short distances or high energies, are supported by quantum Monte Carlo simulations.
Area of Science:
- Condensed Matter Physics
- Quantum Magnetism
- Statistical Mechanics
Background:
- Large-spin (S) quantum chains can be mapped to the O(3) nonlinear sigma model.
- This model exhibits asymptotic freedom and Elitzur's conjecture regarding infrared finiteness.
Purpose of the Study:
- Derive analytic expressions for spin-spin correlations in the large-S limit.
- Validate these expressions using numerical simulations.
Main Methods:
- Utilized the Holstein-Primakoff representation.
- Mapped spin chains to the O(3) nonlinear sigma model.
- Employed quantum Monte Carlo simulations for validation.
Main Results:
- Derived analytic expressions for equal-time and dynamical spin-spin correlations.
- Identified validity regimes: distances < S⁻¹exp(πS) or energies > JS²exp(-πS).
- Static correlations align with quantum Monte Carlo simulations for S=5/2.
Conclusions:
- The derived analytic expressions provide accurate descriptions of spin correlations in large-S systems.
- The study confirms the applicability of the nonlinear sigma model in this regime.
- Numerical simulations support the theoretical predictions for spin dynamics.
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