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arXiv:1412.2617 · Journal of Physics Conference Series

Partial and quasi dynamical symmetries in quantum many-body systems

A. Leviatan

Published Apr 13, 2015• 2 citations
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Abstract

We introduce the notions of partial dynamical symmetry (PDS) and quasi dynamical symmetry (QDS) and demonstrate their relevance to nuclear spectroscopy, to quantum phase transitions and to mixed systems with regularity and chaos. The analysis serves to highlight the potential role of PDS and QDS towards understanding the emergent "simplicity out of complexity" exhibited by complex many-body systems.

DOI
10.1088/1742-6596/597/1/012003

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We generalize the notion of partial dynamical symmetry (PDS) to a system of interacting bosons and fermions. In a PDS, selected states of the Hamiltonian are solvable and preserve the symmetry exactly, while other states are mixed. As a first example of such novel symmetry construction, spectral features of the odd-mass nucleus 195Pt^{195}\mathrm{Pt}195Pt are analyzed.
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
In this paper, the dynamical symmetry concept is used to investigate the quantum integrability of nuclear many-body systems. It is found that such systems are generally nonintegrable due to the complicated inherent interactions. In fact, in certain regions of the intrinsic parameters, the time-dependent mean-field solution can be chaotic. However, when subdynamical symmetries, e.g., certain excitation modes, dominate, the corresponding dynamics will be rendered regular, thus signaling that the nuclear many-body system is not fully chaotic. Chaotic behavior emerges in the transitional region between the excitation modes where subdynamical symmetries are broken and accompanied by structural phase transitions.
Non-equilibrium quantum many-body systems have attracted considerable attention in the past decades. The scope of the research of this kind of novel system involves interdisciplinary research of condensed matter, atomic and molecular physics, quantum optics, quantum information and quantum computation, as well as the non-equilibrium statistical physics. The non-equilibrium phenomena emerging from the aforementioned quantum systems can exhibit rich and universal behaviors, which have far from being well understood due to the novelties and complexities of these systems, and hence the quantum many-body physics becomes the research highlight. At the same time, with the rapid development of quantum techniques, the understanding of these complex systems is of important practical significance due to their potential applications in quantum computation and quantum manipulation. In this paper, we show our recent progress of non-equilibrium quantum many-body systems. We focus on the novel phenomena closely related to the temporary symmetry breaking, including the exotic quantum matter, quasi-particles as well as the dynamical universality classes in non-equilibrium quantum many-body systems.
Symmetries play a pivotal role in our understanding of the properties of quantum many-body systems. While there are theorems and a well-established toolbox for systems in thermal equilibrium, much less is known about the role of symmetries and their connection to dynamics out of equilibrium. This arises due to the direct link between a system’s thermal state and its Hamiltonian, which is generally not the case for nonequilibrium dynamics. Here we present a pathway to identify the effective symmetries and to extract them from data in nonequilibrium quantum many-body systems. Our approach is based on exact relations between correlation functions involving different numbers of spatial points, which can be viewed as nonequilibrium versions of (equal-time) Ward identities encoding the symmetries of the system. We derive symmetry witnesses, which are particularly suitable for the analysis of measured or simulated data at different snapshots in time. To demonstrate the potential of the approach, we apply our method to numerical and experimental data for a spinor Bose gas. We investigate the important question of a dynamical restoration of an explicitly broken symmetry of the Hamiltonian by the initial state. Remarkably, it is found that effective symmetry restoration can occur long before the system equilibrates. We also use the approach to define and identify spontaneous symmetry breaking far from equilibrium, which is of great relevance for applications to nonequilibrium phase transitions. Our work opens new avenues for the classification and analysis of quantum as well as classical many-body dynamics in a large variety of systems, ranging from ultracold quantum gases to cosmology.