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Physical Review Research

Structured ground states of randomly interacting bosons

Charles White, Alexander Volya, Declan Mulhall, Vladimir Zelevinsky

Published Feb 13, 2023• 2 citations
Publisher

Abstract

Bosonic degrees of freedom and their emergence as part of complex quantum many-body dynamics, symmetries, collective behavior, clustering, and phase transitions play an important role in modern studies of quantum systems. In this paper, we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.

DOI
10.1103/physrevresearch.5.013109

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Bosonic degrees of freedom and their emergence as part of complex quantum many-body dynamics, symmetries, collective behavior, clustering, and phase transitions play an important role in modern studies of quantum systems. In this paper, we present a systematic study of many-boson systems governed by random interactions. Our findings show that ground states of randomly interacting bosons are not random, being dominated by a few collective configurations containing condensates of clusters.
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Low-lying collective states in nuclei are investigated in the framework of the interacting boson model using an ensemble of random many-body interactions. It is shown that whenever the number of bosons is sufficiently large compared to the rank of the interactions, the spectral properties are characterized by a dominance of LP=0+{L}^{P}{=0}^{+}LP=0+ ground states and the occurrence of both vibrational and rotational band structures. This indicates that these features represent a general and robust property of the collective model space.
While modern computational methods provide a powerful approach to predict the behavior of physical systems, gaining intuition of emergent phenomena requires almost invariably the use of approximation methods. The ideas and methods of semiclassical physics presented in this thesis provide a systematic road to address non-perturbative regimes, where classical information find its way into the description of quantum properties of systems of few to many interacting particles. The first part of the thesis provides a semiclassical description of few-particle systems using cluster expansions and novel analytic results for short-range interacting bosons in one and three dimensions are derived. In the second part, complementary approaches for many-particle systems are used to study the non-equilibrium scrambling dynamics in quantum-critical bosonic systems with large particle numbers, revealing an unscrambling mechanism due to criticality that is verified in extensive numerical simulations.
In this paper, we report our systematic calculations of angular momentum I ground state probabilities P(I)P(I)P(I) of boson systems with spin l in the presence of random two-body interactions. It is found that the P(0)P(0)P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0)P(0)P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the P(Imax){P(I}_{\mathrm{max}})P(Imax​)'s of bosons with spin l do not follow the 1/N1/N1/N (N=l+1,(N=l+1,(N=l+1, referring to the number of independent two-body matrix elements) relation. The properties of the P(I)P(I)P(I)'s obtained in boson systems with spin l are discussed.