Disorder free many-body localization transition in two quasiperiodically coupled Heisenberg spin chains

K. G. S. H. Gunawardana, Bruno Uchoa
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Abstract

Disorder free many-body localization (MBL) can occur in interacting systems that can dynamically generate their own disorder. We address the thermal-MBL phase transition of two isotropic Heisenberg spin chains that are quasi-periodically coupled to each other. The spin chains are incommensurate and are coupled through a short range exchange interaction of the $XXZ$ type that decays exponentially with the distance. Using exact diagonalization, matrix product states and density matrix renormalization group, we calculate the time evolution of the entanglement entropy at long times and extract the inverse participation ratio in the thermodynamic limit. We show that this system has a robust MBL phase. We establish the phase diagram with the onset of MBL as a function of the interchain exchange coupling and of the incommensuration between the spin chains. The Ising limit of the interchain interaction optimizes the stability of the MBL phase over a broad range of incommensurations above a given critical exchange coupling. Incorporation of interchain spin flips significantly enhances entanglement between the spin chains and produces delocalization, favoring a pre-thermal phase whose entanglement entropy grows logarithmically with time.
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两个准周期耦合海森堡自旋链中的无序多体局域化转变
无序多体定位(MBL)可以发生在能够动态产生自身无序的相互作用系统中。我们研究了两个各向同性海森堡自旋链的热-MBL 相变,这两个自旋链准周期性地相互耦合。这两条自旋链互不相称,通过 XXZ$ 类型的短程交换相互作用耦合,这种相互作用随距离呈指数衰减。利用精确对角化、矩阵乘积态和密度矩阵重正化群,我们计算了长时间纠缠熵的时间演化,并提取了热力学极限的反参与比。我们证明该系统具有稳健的 MBL 相。我们以链间交换耦合和自旋链间不相容的函数建立了 MBL 开始的相图。链间相互作用的伊辛极限优化了 MBL 相在给定临界交换耦合度以上的广泛同调范围内的稳定性。链间自旋翻转的加入大大增强了自旋链之间的纠缠并产生了脱局域,有利于热前阶段,其纠缠熵随时间呈对数增长。
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