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Non-local propagation of correlations in quantum systems with long-range interactions
Philip Richerme1, Zhe-Xuan Gong1, Aaron Lee1
1Joint Quantum Institute, University of Maryland Department of Physics and National Institute of Standards and Technology, College Park, Maryland 20742, USA.
Nature
|July 11, 2014
Summary
Information propagation speed in quantum systems with long-range interactions is crucial for understanding correlations and numerical simulations. This study analyzes variable-range spin chains to measure correlation propagation, revealing insights into otherwise intractable quantum many-body dynamics.
Area of Science:
- Quantum many-body physics
- Condensed matter theory
- Statistical mechanics
Background:
- The maximum speed of information propagation, or quantum speed limit, dictates correlation dynamics in quantum systems.
- Existing bounds (e.g., Lieb-Robinson) are established for short-range interactions, limiting understanding of long-range systems.
- Analytic solutions are rare for long-range interacting systems, hindering accurate dynamical timescale descriptions.
Purpose of the Study:
- To investigate information propagation speeds in quantum many-body systems with variable long-range interactions.
- To determine the shape of the effective 'light cone' and measure correlation propagation velocities.
- To provide a framework for studying dynamics in complex quantum systems.
Main Methods:
- Application of variable-range Ising and XY spin chain Hamiltonians.
- Simulation of far-from-equilibrium quantum many-body system time evolution.
- Analysis of spatial and time-dependent correlations to extract light cone properties and propagation velocities.
Main Results:
- Quantification of correlation propagation speeds across different interaction ranges in the studied spin models.
- Empirical determination of the effective 'light cone' shape for variable long-range interactions.
- Demonstration of a method to study dynamics in systems previously considered intractable.
Conclusions:
- The study provides crucial insights into the dynamics of quantum many-body systems with long-range interactions.
- The developed methods enable the exploration of a wider range of quantum phenomena and system types.
- This research advances the understanding of information transport and correlation spreading in complex quantum systems.
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