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Correlation Decay in Fermionic Lattice Systems with Power-Law Interactions at Nonzero Temperature.
Senaida Hernández-Santana1, Christian Gogolin1,2, J Ignacio Cirac2
1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain.
Physical Review Letters
|September 27, 2017
Summary
We establish bounds on correlations in fermionic lattice systems with long-range interactions. Our findings show correlations decay algebraically with distance, even at high temperatures.
Area of Science:
- Condensed matter physics
- Quantum many-body systems
- Statistical mechanics
Background:
- Understanding correlations in fermionic systems is crucial for condensed matter physics.
- Long-range interactions significantly impact the behavior of quantum systems.
- Thermal equilibrium properties are key to characterizing many-body systems.
Purpose of the Study:
- To investigate correlation decay in fermionic lattice systems with long-range interactions.
- To establish theoretical bounds on correlations between anticommuting operators.
- To generalize existing Lieb-Robinson-type bounds for long-range interactions.
Main Methods:
- Proving a bound on correlation decay for anticommuting operators.
- Generalizing Lieb-Robinson-type bounds to systems with algebraic long-range interactions.
- Utilizing high-temperature expansion and numerical analysis.
Main Results:
- Correlations decay algebraically with distance in the studied systems.
- The decay exponent is closely related to the interaction decay exponent (α ≥ 2D).
- Bounds are shown to be asymptotically tight.
Conclusions:
- The established bounds provide a fundamental understanding of correlation decay in fermionic systems.
- Results are applicable to systems at any non-zero temperature.
- Demonstrated applicability in the one-dimensional Kitaev chain model.
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