Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
Many-body localization phase transition: A simplified strong-randomness approximate renormalization group
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多体定位相变：简化的强随机性近似重整化群
DOI：
10.1103/physrevb.93.224201
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发表时间：
2016
影响因子：
3.7
通讯作者：
D. Huse
中科院分区：
文献类型：
--
作者：
Liangsheng Zhang;Bo Zhao;T. Devakul;D. Huse
我们提出了一个简化的强随机性重正化群（RG），它捕获了一般无序一维系统中多体定位（MBL）相变的某些方面。该 RG 可以通过解析方式表示，并且通过求解积分微分方程可以获得数值精度的临界不动点分布和临界指数（满足 Chayes 不等式）。这再现了许多（但不是全部）MBL 相变的定性特征，这些特征是由之前的数值工作和近似 RG 研究提出的：我们的 RG 可以作为未来 RG 研究的“零阶”近似。我们强调的一个有趣的特征是罕见的格里菲斯区域是分形的。对于 MBL 相内的热格里菲斯区域，我们的 RG 可以定性地正确捕获此特征。如果这是正确的超出我们的近似，那么这些格里菲斯效应比之前假设的要强。
We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically, and the critical fixed point distribution and critical exponents (that satisfy the Chayes inequality) are obtained to numerical precision by solving integro-differential equations. This reproduces many, but not all, of the qualitative features of the MBL phase transition that are suggested by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.