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Physics of Atomic Nuclei

Do we understand the role of incoherent interactions in many-body physics?

Vladimir Zelevinsky, Declan Mulhall, Alexander Volya

Published Mar 1, 2001• 12 citations
Publisher

Abstract

Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.

DOI
10.1134/1.1358477

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Recent developments in many-body quantum chaos show that a quantum system with strong incoherent interactions can still be described with the aid of mean quasiparticle occupation numbers as in Fermi liquid theory. We use these ideas and the geometric chaoticity of angular momentum coupling to explain the predominance of ground states with zero spin and the maximum possible spin for a system of randomly interacting fermions in a rotationally invariant mean field (an analog of the Hund rule). We show that spin ordering coexists with the chaotic features of the ground-state wave functions.
Recent developments in many-body quantum chaos have raised the issue of correlations between different families of levels in the spectra of random fermionic systems. It seems that rotational invariance is sufficient to force an otherwise random system to have statistically ordered spectra where the ground state can have zero spin or the maximum spin allowed a huge portion of the time. We have tackled this question and have characterized the role of ``geometric chaoticity'' and pairing in random systems. We have shown how the geometry gives rise to such a distribution of ground state spins and examined the coexistence of these regularities with chaotic wave functions.
Numerical simulations show that the ground state spin of a finite many-body system with random but rotationally invariant interactions is predominantly zero. This means that it is not sufficient to explain the zero ground state spin of even-even nuclei only by pairing correlations. Simple explanations based on a statistical multiplicity, width of the level density, effective pairing, formation of condensates etc. do not work. We suggest statistical theory based on the effective mean field and geometric chaoticity of angular momentum coupling of individual particles. The results show a significant role of symmetry arguments in finite systems.
Many-body systems that saturate the quantum bound on chaos are attracting interest across a wide range of fields. Notable examples include the Sachdev-Ye-Kitaev model and its variations, all characterized by some form or randomness and all-to-all couplings. Here, we study many-body quantum chaos in a quantum impurity model showing non-Fermi-liquid physics, the overscreened multichannel S U ( N ) Kondo model. We exactly compute the low-temperature behavior of the out-of-time order correlator in the limit of large N and large number of channels, K , at a fixed ratio γ = K / N . Because of strong correlations at the impurity site, the spin fractionalizes in auxiliary fermions and bosons. We show that all the degrees of freedom of our theory acquire a Lyapunov exponent that is linear in temperature as T → 0 , with a prefactor that depends on γ . Remarkably, for N = K , the impurity spin displays maximal chaos, while bosons and fermions only reach half of the maximal Lyapunov exponent. Our results highlight two key features: a nondisordered model that is maximally chaotic due to strong correlations at its boundary, with the maximal chaos appearing in a composite gauge-invariant operator, the impurity spin, and not in the auxiliary single-particle degrees of freedom.
Dynamics of a many-body quantum system of strongly interacting constituents is traditionally considered in a hierarchy of approximations: mean field—quasiparticles—collective excitations—large amplitude motion. Incoherent collision-like processes can be included on the level of kinetics as the mechanism for thermalization. On the other hand, starting from some excitation energy, local spectral properties can always be practically described by random matrix theory. Deep interrelation between two seemingly opposite pictures is not fully understood. This is discussed below, including unresolved problems and possible ways to better theory. Along the road I show how the ideas of quantum chaos can serve as a powerful conceptual, theoretical, experimental and computational tool.
In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.