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Lieb-Robinson bound at finite temperatures
Zhiqiang Huang1, Xiao-Kan Guo1
1Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China and University of the Chinese Academy of Sciences, Beijing 100049, China.
Physical Review. E
|July 18, 2018
Summary
This study extends the Lieb-Robinson bound to finite temperatures, revealing how information propagates in quantum systems. The findings detail correlation clustering and its dependence on interaction range for quantum information science.
Area of Science:
- Quantum physics
- Condensed matter theory
- Statistical mechanics
Background:
- The Lieb-Robinson bound establishes a finite speed limit for information propagation in nonrelativistic quantum lattice systems.
- This bound implies the clustering of correlations, a fundamental property in quantum many-body systems.
Purpose of the Study:
- To extend the Lieb-Robinson bound to quantum systems operating at finite temperatures.
- To analyze the behavior of dynamical correlation functions at nonzero temperatures.
Main Methods:
- Calculation of dynamical correlation functions at nonzero temperatures.
- Analysis of systems with short-range, exponentially decaying, and long-range interactions.
- Utilizing combinatoric generating functions of graphs for cluster counting in cluster expansions.
Main Results:
- The study successfully extends the Lieb-Robinson bound to finite-temperature quantum systems.
- Demonstrates how correlation clustering is affected by temperature and interaction range.
- Introduces an efficient graph-theoretic method for cluster expansion analysis.
Conclusions:
- The generalized Lieb-Robinson bound provides crucial insights into information transport in realistic, warm quantum systems.
- The findings are applicable to various quantum technologies and theoretical frameworks.
- Discusses limitations and potential applications of the derived bounds in quantum information science.
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