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Physical Review C

Large-Nscaling behavior in the pairing model

MARIA LUIZA CESCATO, M. Kyotoku, Maria Carolina Nemes

Published Feb 1, 1992• 3 citations
Publisher

Abstract

A numerical study of the static and dynamical properties of the pairing interaction in a two-level system is presented as a search for a large-N scaling behavior already empirically found in other models of the same class. A scaling behavior is found in the spectra as a function of N, but the dynamical properties show strong dependence on the initial conditions.

DOI
10.1103/physrevc.45.671

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A numerical study of the static and dynamical properties of the pairing interaction in a two-level system is presented as a search for a large-N scaling behavior already empirically found in other models of the same class. A scaling behavior is found in the spectra as a function of N, but the dynamical properties show strong dependence on the initial conditions.
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The scaling properties of the exact wave functions in the two-level pairing model are studied and a well-defined limit, when the number of pairs goes to infinity, is found. An approximate method for obtaining the scaled wave functions is discussed. Well-known methods for relating finite-difference equations with differential ones are used, together with a semiclassical expansion. The approximate results obtained agree well with the exact ones. A comparison with the time-dependent Hartree-Fock approach is also done.
We analyze a model quantum dynamical system subjected to periodic interaction with an environment, which can describe quantum measurements. Under the condition of strong classical chaos and strong decoherence due to large coupling with the measurement device, the spectra of the evolution operator exhibit an universal behavior. A generic spectrum consists of a single eigenvalue equal to unity, which corresponds to the invariant state of the system, while all other eigenvalues are contained in a disk in the complex plane. Its radius depends on the number of the Kraus measurement operators and determines the speed with which an arbitrary initial state converges to the unique invariant state. These spectral properties are characteristic of an ensemble of random quantum maps, which in turn can be described by an ensemble of real random Ginibre matrices. This will be proven in the limit of large dimension.
The first excitation energy in the two-level pairing model is investigated in terms of the equilibrium and the small fluctuation around it. The basic idea is an extension of results presented in a previous paper by the present authors. In this investigation, the result obtained in the previous paper plays a central role: At the limit of the weak and the strong interaction strength, the results are in good agreement with the exact one. The former and the latter are calculated in the framework of the su(2) ⊗ su(1, 1)- and the su(2) ⊗ su(2)-coherent state, respectively. On the basis of the above conclusion, the intermediate region for the interaction strength is described in terms of the idea of the interpolation and it is shown that the agreement of the result with the exact one is quite good. 1 typeset using PTPTEX.cls 〈Ver.0.9 〉 The description of the first excited state in the two-level pairing model for the closed shell system has been regarded as a basic, but a modest problem in many-body physics. For example, the recent investigations can be found in Ref. 1). Following this quiet stream, recently, the present authors have considered this problem from tow slightly different viewpoints. One
We study a partially disordered one-dimensional system with interacting particles. Concretely, we impose a disorder potential to only every other site, followed by a clean site. Our numerical analysis of eigenstate properties is based on the entanglement entropy and density distributions. Most importantly, at large disorder, there exist eigenstates with large entanglement entropies and significant correlations between the clean sites. These states have volume-law scaling, embedded into a sea of area-law states, reminiscent of inverted quantum-scar states. These eigenstate features leave fingerprints in the nonequilibrium dynamics even in the large-disorder regime, with a strong initial-state dependence. We demonstrate that certain types of initial charge-density-wave states decay significantly, while others preserve their initial inhomogeneity, the latter being the typical behavior for many-body localized systems. This initial-condition-dependent dynamics may give extra control over the delocalization dynamics at large disorder strength and should be experimentally feasible with ultracold atoms in optical lattices.