随机跳跃的类Hubbard电子晶格模型中无序和相互作用的复合效应引起的金属-绝缘体相变
Metal-insulator transition from combined disorder and interaction effects in Hubbard-like electronic lattice models with random hopping
摘要：
我们发现了一类多费米子系统的扩散费米液相中的无序驱动的不稳定性，表明一级类型的金属-绝缘体转变，这完全是由于淬火无序和粒子间相互作用之间的竞争。我们的结果预计是相关的足够强的无序在d = 3的空间维度。具体来说，我们研究了一类半满的，Hubbard类模型的无自旋费米子（复杂）随机跳跃和短程相互作用的二分晶格，在d > 1。在给定的实现中，跳跃无序打破了时间反演不变性，但保留了负责弹道费米液体的电荷密度波不稳定性的特殊"嵌套“对称性。这种疾病可能会出现，例如，从随机磁场的应用到其他干净的模型。我们推导出这类无序、相互作用费米子系统的低能有效场论描述，其形式为芬克尔斯坦非线性西格玛模型[A. M. Finkel'stein，Zh. Eksp. Teor.菲兹84，168（1983），Sov. JETP 57，97（1983）]。我们分析Finkel'stein西格玛模型使用微扰，一个循环的重整化群分析控制通过d = 2 + π维的ε展开。我们发现，在d = 2维，相互作用不稳定的导电相已知存在于无序的，非相互作用的系统。我们在d > 2维中发现的金属-绝缘体转变发生在无序强度为1/2的情况下，因此在1/2 << 1的情况下可以微扰实现。我们强调，无序系统在没有相互作用的情况下没有定域相，因此定域相以及向定域相的过渡只能由于相互作用的存在而出现。
英文摘要：
We uncover a disorder-driven instability in the diffusive Fermi liquid phase of a class of many-fermion systems, indicative of a metal-insulator transition of first order type, which arises solely from the competition between quenched disorder and interparticle interactions. Our result is expected to be relevant for sufficiently strong disorder in d = 3 spatial dimensions. Specifically, we study a class of half-filled, Hubbard-like models for spinless fermions with (complex) random hopping and short-ranged interactions on bipartite lattices, in d > 1. In a given realization, the hopping disorder breaks time reversal invariance, but preserves the special ``nesting'' symmetry responsible for the charge density wave instability of the ballistic Fermi liquid. This disorder may arise, e.g., from the application of a random magnetic field to the otherwise clean model. We derive a low energy effective field theory description for this class of disordered, interacting fermion systems, which takes the form of a Finkel'stein non-linear sigma model [A. M. Finkel'stein, Zh. Eksp. Teor. Fiz. 84, 168 (1983), Sov. Phys. JETP 57, 97 (1983)]. We analyze the Finkel'stein sigma model using a perturbative, one-loop renormalization group analysis controlled via an epsilon-expansion in d = 2 + epsilon dimensions. We find that, in d = 2 dimensions, the interactions destabilize the conducting phase known to exist in the disordered, non-interacting system. The metal-insulator transition that we identify in d > 2 dimensions occurs for disorder strengths of order epsilon, and is therefore perturbatively accessible for epsilon << 1. We emphasize that the disordered system has no localized phase in the absence of interactions, so that a localized phase, and the transition into it, can only appear due to the presence of the interactions.
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