Relationship between dynamic, quantum and classical critical phenomena

Giovanni Battimelli, Giovanni Ciccotti, Pietro Greco

Jincheng Zhang

This paper investigates the convergence of quantum and classical phenomena through a model of continuous resonance. We propose a theoretical framework that explicitly defines the conditions under which resonance becomes dominant, offering a novel approach to understanding the intricate relationship between these two fundamental aspects of reality. The core mechanism centers on a dynamic process of amplification and propagation, where small perturbations trigger significant changes, ultimately leading to a critical point. This framework aims to bridge the gap between seemingly disparate concepts, offering a potential pathway towards a deeper understanding of complexity and emergent behavior. The significance of this work lies in its proposed dynamic model, which provides a structured approach to analyzing and predicting the interplay between quantum and classical systems.

Anupam Mitra, Tameem Albash, Philip Daniel Blocher +4 more

Abstract We study the tractability of classically simulating critical phenomena in the quench dynamics of one-dimensional transverse field Ising models (TFIMs) using highly truncated matrix product states (MPSs). We focus on two paradigmatic examples: a dynamical quantum phase transition (DQPT) that occurs in nonintegrable long-range TFIMs, and the infinite-time correlation length of the integrable nearest-neighbor TFIM when quenched to the critical point, where the quantities of interest involve equal time one- and two- point correlation functions, which we associate with macroproperties. For the DQPT, we show that the order parameters can be efficiently simulated with heavy truncation of the MPS bond dimension. This can be used to reliably extract critical properties of the phase transition, including critical exponents, even when the full many-body state is not simulated with high fidelity. The long-time correlation length near the critical point is more sensitive to the full many-body state fidelity, and generally requires a large bond dimension MPS. Nonetheless, this can still be efficiently simulated with strongly truncated MPS because it can be extracted from the short-time behavior of the dynamics where entanglement is low. Our results provide illustrations of scenarios where accurate calculation of the full many-body state (microstate) is intractable due to the volume-law growth of entanglement, yet a precise specification of an exact microstate may not be required when simulating macroproperties that play a role in phases of matter of many-body systems. We also study the tractability of simulation using truncated MPS based on quantum chaos and equilibration in the models. We find a counterintuitive inverse relationship, whereby local expectation values are most easily approximated for chaotic systems whose exact many-body state is most intractable.

L. De Cesare, Dimo I. Uzunov

Amit Dutta, Chakrabarti, B K

Jincheng Zhang

This paper introduces the concept of Quantum Self-Organization Criticality (QSOC), a novel framework for understanding complex quantum systems. The core idea posits that quantum systems, under specific conditions, spontaneously transition to critical states exhibiting a self-organizing behavior. This transition is characterized by a relationship between a critical constant *C* and its amplified version *C**, represented mathematically as [Cq = C*]. The exploration of this phenomenon holds significant potential for discovering new quantum critical phenomena and could ultimately lead to breakthroughs in fundamental physics and potentially impact areas such as quantum computation and materials science. The theoretical framework presented herein provides a foundation for future research into this intriguing area of quantum dynamics. ---