Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions (1706.00838v3)

Abstract: We study the spreading of information in a wide class of quantum systems, with variable-range interactions. We show that, after a quench, it generally features a double structure, whose scaling laws are related to a set of universal microscopic exponents that we determine. When the system supports excitations with a finite maximum velocity, the spreading shows a twofold ballistic behavior. While the correlation edge spreads with a velocity equal to twice the maximum group velocity, the dominant correlation maxima propagate with a different velocity that we derive. When the maximum group velocity diverges, as realizable with long-range interactions, the correlation edge features a slower-than-ballistic motion. The motion of the maxima is, instead, either faster-than-ballistic, for gapless systems, or ballistic, for gapped systems. The phenomenology that we unveil here provides a unified framework, which encompasses existing experimental observations with ultracold atoms and ions. It also paves the way to simple extensions of those experiments to observe the structures we describe in their full generality.

Overview of Universal Scaling Laws for Correlation Spreading in Quantum Systems with Short- and Long-Range Interactions

The paper presents a detailed exploration of correlation spreading after a quantum quench in lattice systems, focusing on both short-range and long-range interactions. Through a unifying quasi-particle framework, the authors identify scaling laws that describe the propagation of correlations, elucidating the complex structures known as correlation cones. These scaling laws are vital for understanding how quantum information and entanglement evolve in different types of quantum systems.

Core Contributions

1. Quasi-Particle Framework: The paper employs a quasi-particle framework to derive universal scaling laws for correlation spreading. It identifies crucial differences in correlation dynamics based on the boundedness of the quasi-particle group velocities.
2. Short-Range Interactions: For systems with short-range interactions, the propagation of correlations follows ballistic dynamics, as previously described by Lieb and Robinson bounds. The paper further distinguishes between the correlation edge and correlation maxima, which move at different velocities, determined by group and phase velocities.
3. Long-Range Interactions: In contrast, systems with long-range interactions exhibit more complex behavior. The correlation edge propagates sub-ballistically due to diverging group velocities in the quasi-particle spectrum. However, local correlation maxima can move faster than ballistic in gapless systems or ballistic in gapped systems. This finding reconciles previous experimental and numerical results and provides a consistent framework for predicting correlation spreading in long-range systems.

Numerical and Experimental Implications

The paper's numerical analysis on various models, such as the Bose-Hubbard model and long-range spin models, supports the theoretical predictions of correlation dynamics. The findings highlight the importance of observing the inner correlation structure, which can provide insights into the presence of energy gaps and the nature of quasi-particle excitations, thereby serving as a witness to the elementary excitations of the quantum system.

The theoretical development offers significant implications for future experiments in quantum simulations using trapped ions, Rydberg atoms, polar molecules, and more. Understanding the dynamics of correlation spreading will facilitate the design of experiments aimed at probing quantum systems' internal characteristics, potentially impacting the fields of quantum computing and information science.

Future Work and Open Questions

While the paper sheds light on the correlation spreading in quantum systems with various interaction ranges, further research is required to explore the implications of these findings in higher dimensions and non-integrable models. Investigating more complex systems and broadening the scope to incorporate non-linear interactions may reveal additional structures and scaling behaviors, advancing both theoretical understanding and practical applications in quantum technologies.

In conclusion, this work advances our comprehension of quantum dynamics, providing a solid foundation for studying correlation propagation and signaling future directions for experimental and theoretical research in quantum systems.