Localization dynamics in a centrally coupled system

TL;DR

This paper investigates the dynamics of a central qudit coupled to a disordered spin bath, revealing scaling behaviors and signs of localization through advanced tensor network simulations, extending system size beyond previous methods.

Contribution

It adapts the ML-MCTDH tensor network method to simulate large-scale central-bath systems, enabling the study of localization and dynamics beyond previous computational limits.

Findings

Thermodynamic limit behavior observed in qudit dynamics.

Scaling collapse in spin glass order parameter and entanglement entropy.

Signs of localization persist with unscaled system-bath coupling.

Abstract

In systems where interactions couple a central degree of freedom and a bath, one would expect signatures of the bath's phase to be reflected in the dynamics of the central degree of freedom. This has been recently explored in connection with many-body localized baths coupled with a central qubit or a single cavity mode -- systems with growing experimental relevance in various platforms. Such models also have an interesting connection with Floquet many-body localization via quantizing the external drive, although this has been relatively unexplored. Here we adapt the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) method, a well-known tree tensor network algorithm, to numerically simulate the dynamics of a central degree of freedom, represented by a $d$-level system (qudit), coupled to a disordered interacting 1D spin bath. ML-MCTDH allows us to reach $\approx 10^2$ lattice sites, a far larger system size than what is feasible with exact diagonalization or kernel polynomial methods. From the intermediate time dynamics, we find a well-defined thermodynamic limit for the qudit dynamics upon appropriate rescaling of the system-bath coupling. The spin system shows similar scaling collapse in the Edward-Anderson spin glass order parameter or entanglement entropy at relatively short times. At longer time scales, we see slow growth of the entanglement, which may arise from dephasing mechanisms in the localized system or long-range interactions mediated by the central degree of freedom. Similar signs of localization are shown to appear as well with unscaled system-bath coupling.