Département de Physique Théorique, Université de Genève, CH-1211 Genève 4, Switzerland.
IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria.
Phys Rev Lett. 2019 Feb 1;122(4):040601. doi: 10.1103/PhysRevLett.122.040601.
We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between thermal and localized phases. We identify the physical MBL transition in the limit of maximal asymmetry, reflecting the instability of MBL against rare thermal inclusions. We find a critical point that is localized with power-law distributed thermal inclusions. The typical size of critical inclusions remains finite at the transition, while the average size is logarithmically diverging. We propose a two-parameter scaling theory for the many-body localization transition that falls into the Kosterlitz-Thouless universality class, with the MBL phase corresponding to a stable line of fixed points with multifractal behavior.
我们提出了一个简单的、完全可解的强随机性重整化群（RG）模型，用于一维的多体局域（MBL）相变。我们的方法依赖于一组 RG 流，这些 RG 流由热相和局域相之间的非对称参数化。我们在最大非对称极限下识别出物理 MBL 相变，反映了 MBL 对稀有热包含物的不稳定性。我们发现了一个临界点，在临界点处存在幂律分布的热包含物。在相变处，临界包含物的典型大小保持有限，而平均大小呈对数发散。我们提出了一个多体局域相变的双参数标度理论，该理论属于科斯特利茨-图尔勒普拉斯（Kosterlitz-Thouless）普适类，其中 MBL 相对应于具有多重分形行为的稳定的固定点线。
