Universal properties of single-particle excitations across the many-body localization transition
Universal properties of single-particle excitations across the many-body localization transition
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多体定位转变中单粒子激发的普遍性质
DOI：
10.1103/physrevb.109.214209
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发表时间：
2022
影响因子：
3.7
通讯作者：
A. Garg
中科院分区：
文献类型：
--
作者：
A. Jana;V. Chandra;A. Garg
理解从离域到多体定域(MBL)阶段的转变的性质是一个重要的悬而未决的问题。为了探索MBL跃迁的本质，我们研究了无序相互作用量子多体系统在高激发多体本征态中产生的单粒子激发的普遍性质。在一类具有随机无序的一维无自旋费米子模型中，我们研究了单粒子局域态密度的典型值与平均值之比的有限尺寸标度以及通过MBL跃迁的散射率。我们的结果表明，这类无自旋费米子的一维模型中的MBL相变本质上是连续的。对于系统中不同的相互作用范围，关联长度在过渡点$W_c$，$\xi\sim|W-W_c|^{-\nu}$的临界指数$\nu$满足Chayes-Chayes-Fisher-Spencer(CCFS)界$\nu\ge 2/d$，其中$d$是系统的物理尺寸。我们还讨论了为什么在单粒子态密度和散射率符合CCFS准则的情况下，从传统的多体局域化诊断的有限尺寸标度获得的临界指数能级间距比强烈违反CCFS界限。
Understanding the nature of the transition from the delocalized to the many-body localized (MBL) phase is an important unresolved issue. To probe the nature of the MBL transition, we investigate the universal properties of single-particle excitations produced in highly excited many-body eigenstates of a disordered interacting quantum many-body system. In a class of one-dimensional spinless fermionic models with random disorder, we study the finite size scaling of the ratio of typical to average values of the single-particle local density of states and the scattering rates across the MBL transition. Our results indicate that the MBL transition in this class of one-dimensional models of spinless fermions is continuous in nature. For various ranges of interactions in the system, the critical exponent $\nu$ with which the correlation length $\xi$ diverges at the transition point $W_c$, $\xi \sim |W-W_c|^{-\nu}$, satisfies the Chayes-Chayes-Fisher-Spencer(CCFS) bound $\nu \ge 2/d$ where $d$ is the physical dimension of the system. We also discuss why the critical exponent obtained from finite-size scaling of the conventional diagnostic of many-body localization, the level-spacing ratio, strongly violates the CCFS bound while the single-particle density of states and scattering rates are consistent with the CCFS criterion.