Entropy dynamics of the binary bond disordered Heisenberg chain

TL;DR

This paper introduces a new algorithm to study entanglement dynamics in disordered Heisenberg chains, revealing the absence of a many-body localization transition and identifying a long-time entropy scaling mechanism and a transient Mpemba effect.

Contribution

The paper develops the ancilla TEBD algorithm for entanglement analysis and demonstrates its effectiveness in studying long-time dynamics and localization properties.

Findings

Multifractal dimension shows no critical behavior, ruling out many-body localization.

Long-time von Neumann entropy scaling explained by competition between spin interaction and disorder.

Transient Mpemba effect observed in the disordered Heisenberg chain.

Abstract

In this article, we study the quench dynamics of the binary bond disordered Heisenberg spin chain. First, we develop a new algorithm, the ancilla TEBD method, which combines the purification technique and the time-evolving block decimation (TEBD) algorithm to study the entanglement dynamics of binary bonded disordered spin chains. With the support of exact diagonalization (ED), we calculate the multifaractal dimension of the binary bond disordered Heisenberg spin model and study its dependence on the strength of the disorder potential; we find that the multifaractal dimension shows no critical behavior which rules out the existence of the many body localization transition. Then, we reproduce the long time scaling of the von Neumann entropy at the time scale that is beyond the reach of typical TEBD and time dependent density matrix renormalization group (tDMRG) algorithms. Based on the numerical analysis, we propose that such a long time scaling is due to the competition of the spin interaction and the disorder which can be seen as a new mechanism for the generating of long time scale entropy dynamics. At last, we numerically proved the existence of the transient Mpemba effect in the bond disordered Heisenberg chain.