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Equilibrium properties of quantum spin systems with nonadditive long-range interactions
1Department of Physics, Graduate School of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study shows that minimizing free energy over coarse-grained magnetization accurately describes quantum spin systems. This finding clarifies when long-range interactions can be simplified to infinite-range interactions in quantum systems.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Quantum Mechanics
Background:
- Quantum spin systems with nonadditive long-range interactions are complex.
- Classical systems use free energy minimization over coarse-grained magnetization for equilibrium.
- The equivalence of canonical and microcanonical ensembles is crucial for thermodynamic descriptions.
Purpose of the Study:
- To investigate equilibrium states of quantum spin systems with long-range interactions using the Kac prescription.
- To determine the validity of replacing actual long-range interactions with infinite-range (Curie-Weiss-type) interactions in quantum systems.
- To analyze the conditions under which canonical and microcanonical ensembles are equivalent in quantum spin systems.
Main Methods:
- Applying the Kac prescription to scale interaction strengths in quantum spin systems.
- Minimizing the free-energy functional over coarse-grained magnetization for quantum systems.
- Examining the Heisenberg XXZ model as a specific case study.
Main Results:
- The free-energy minimization approach is valid for quantum spin systems, mirroring classical systems.
- The replacement of long-range interactions with infinite-range interactions is justified only when canonical and microcanonical ensembles are equivalent.
- Non-equivalence of ensembles indicates limitations in simplifying interactions.
Conclusions:
- The study provides a rigorous framework for understanding equilibrium states in quantum spin systems with long-range interactions.
- It clarifies the conditions for approximating complex interactions with simpler models, crucial for theoretical and experimental advancements.
- The findings have implications for studying phase transitions and critical phenomena in quantum materials.
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