Coherent and dissipative dynamics at quantum phase transitions (2103.02626v5)

Abstract: The many-body physics at quantum phase transitions shows a subtle interplay between quantum and thermal fluctuations, emerging in the low-temperature limit. In this review, we first give a pedagogical introduction to the equilibrium behavior of systems in that context, whose scaling framework is essentially developed by exploiting the quantum-to-classical mapping and the renormalization-group theory of critical phenomena at continuous phase transitions. Then we specialize to protocols entailing the out-of-equilibrium quantum dynamics, such as instantaneous quenches and slow passages across quantum transitions. These are mostly discussed within dynamic scaling frameworks, obtained by appropriately extending the equilibrium scaling laws. We review phenomena at first-order quantum transitions as well, whose peculiar scaling behaviors are characterized by an extreme sensitivity to the boundary conditions, giving rise to exponentials or power laws for the same bulk system. In the last part, we cover aspects related to the effects of dissipative interactions with an environment, through suitable generalizations of the dynamic scaling at quantum transitions. The presentation is limited to issues related to, and controlled by, the quantum transition developed by closed many-body systems, treating the dissipation as a perturbation of the critical regimes, as for the temperature at the zero-temperature quantum transition. We focus on the physical conditions giving rise to a nontrivial interplay between critical modes and various dissipative mechanisms, generally realized when the involved mechanism excites only the low-energy modes of the quantum transitions.

• The paper demonstrates that quantum phase transitions exhibit dual dynamics through coherent and dissipative mechanisms, established by rigorous scaling frameworks and renormalization-group theory.
• It employs numerical studies to validate distinct scaling behaviors in both continuous and first-order transitions, emphasizing boundary condition sensitivities in finite-size systems.
• The findings offer practical insights into quantum computing design by highlighting the role of dissipation as a perturbative factor influencing low-energy excitations.

An Overview of "Coherent and Dissipative Dynamics at Quantum Phase Transitions"

The paper "Coherent and Dissipative Dynamics at Quantum Phase Transitions" by Davide Rossini and Ettore Vicari serves as a comprehensive paper of many-body physics during quantum phase transitions (QPTs). In this detailed review, Rossini and Vicari explore the intricate interplay between coherent and dissipative dynamics, especially in systems undergoing quantum fluctuations at low temperatures.

Key Contributions and Findings

Equilibrium and Out-of-equilibrium Dynamics

Initially, the authors present a pedagogical introduction to equilibrium behavior at QPTs. They utilize quantum-to-classical mapping techniques along with renormalization-group (RG) theory to establish scaling frameworks for critical phenomena at continuous transitions. This analysis elegantly leads to an exploration of out-of-equilibrium quantum dynamics, such as the impact of instantaneous quenches and slow traversals across quantum transitions. The discussion extends beyond continuous transitions to first-order transitions, where scaling behaviors show sensitivity to boundary conditions, leading to exponential or power-law behaviors.

Dissipative Dynamics in Quantum Systems

An essential part of the paper covers the effects of dissipation due to interactions with external environments. The authors employ dynamic scaling frameworks adapted for dissipative systems to reveal a nuanced interplay between critical modes and dissipation. They effectively demonstrate how dissipation acts as a perturbation within critical regimes, particularly influencing the excitation of low-energy modes in closed many-body systems close to QPTs.

Numerical and Conceptual Depth

Rossini and Vicari place considerable emphasis on numerical results and bold theoretical claims. For example, they identify contrasting scaling behaviors at first-order transitions, linked to boundary sensitives that mark a departure from classical intuition. They stress the importance of these numerical studies in validating theoretical scaling frameworks, particularly when addressing finite-size systems and higher-dimensional models.

Implications and Future Outlook

The paper's implications are both practical and theoretical. It provides a detailed characterization of dynamic phenomena relevant for designing quantum computing devices, as coherent control over quantum systems is crucial. The authors speculate future AI developments, which may leverage these insights into quantum coherence and entanglement, aiding in robust quantum AI systems.

Closing Remarks

The paper offers a thorough and sophisticated analysis of QPTs, emphasizing coherent and dissipative dynamics. The insights gained contribute significantly to understanding quantum many-body systems in both theoretical and experimental domains. As technological advancements continue to move forward, especially in quantum computing, the foundations laid by this research will likely be pivotal in realizing efficient and stable quantum devices.

This substantial body of work not only underscores the striking contrast between coherent and dissipative dynamics but also explores emerging questions in critical phenomena, encouraging further research into their broader implications across quantum technologies.