Emergent Hamiltonian description for dynamics of interacting integrable models

Nikola Burić, Slobodan Prvanović, Milan Radonjić

Constrained Hamiltonian dynamics is exploited to provide the mathematical framework of a coarse-grained description of the quantum system of two interacting qubits and of nonlinear interacting oscillators. The coarse-graining is treated as an equivalence relation on the set of quantum states resulting in the emergence of the classical phase-space. The equivalence relation imposes constraints on the Hamiltonian dynamics of the quantum system. It is seen that the evolution of the coarse-grained system preserves constant and minimal quantum fluctuations of the fundamental observables. This leads to the emergence of typical classical properties, like the relation between symmetry and integrability, and in the case of oscillators in the macro-limit implies the emergence of the classical system.

R. Bullough, D. J. Pilling, JUSSI TIMONEN

Olalla A. Castro-Alvaredo, Benjamin Doyon, Takato Yoshimura

Understanding the general principles underlying strongly interacting quantum states out of equilibrium is one of the most important tasks of current theoretical physics.With experiments accessing the intricate dynamics of many-body quantum systems, it is paramount to develop powerful methods that encode the emergent physics.Up to now, the strong dichotomy observed between integrable and nonintegrable evolutions made an overarching theory difficult to build, especially for transport phenomena where spacetime profiles are drastically different.We present a novel framework for studying transport in integrable systems: hydrodynamics with infinitely many conservation laws.This bridges the conceptual gap between integrable and nonintegrable quantum dynamics, and gives powerful tools for accurate studies of spacetime profiles.We apply it to the description of energy transport between heat baths, and provide a full description of the current-carrying nonequilibrium steady state and the transition regions in a family of models including the Lieb-Liniger model of interacting Bose gases, realized in experiments.

Ning Wu, Tunan Ruan

Aydın Cem Keser, Sriram Ganeshan, Gil Refael +1 more

We investigate dynamical many-body localization and delocalization in an integrable system of periodically-kicked, interacting linear rotors. The linear-in-momentum Hamiltonian makes the Floquet evolution operator analytically tractable for arbitrary interactions. One of the hallmarks of this model is that depending on certain parameters, it manifests both localization and delocalization in momentum space. We present a set of ``emergent'' integrals of motion, which can serve as a fundamental diagnostic of dynamical localization in the interacting case. We also propose an experimental scheme, involving voltage-biased Josephson junctions, to realize such many-body kicked models.

Guo-Qiang Wang, Chang-Ling Zou, Guang-Can Guo +1 more

The universality of dynamical scaling laws constitutes a cornerstone in the theoretical understanding of quantum many-body systems, particularly in non-equilibrium settings. Recent advancements have proposed a phenomenological ansatz based on spontaneous symmetry breaking (SSB) to unify the description of charge transport in open quantum systems. However, it remains unclear under which conditions it fails to capture the emergent hydrodynamics and if it does break down, whether nontrivial dynamics emerge. In this work we show that Kardar-Parisi-Zhang (KPZ) dynamics in an open integrable model (the B3 model), rather than diffusion from SSB, emerges. We find that the B3 model is equivalent to two interacting asymmetric XXZ spin chains and the ansatz can only capture the influence of the inter-chain interactions. When the initial state is appropriate, the asymmetric XXZ structure dominates the dynamics, which gives KPZ scaling behavior even when the hopping rate becomes negative. Our work motivates theory of charge transport in open systems beyond the ansatz based on SSB.