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Anomalous suppression of the Bose glass at commensurate fillings in the disordered Bose-Hubbard model

机译：在无序的Bose-Hubbard模型中，相应充填处的Bose玻璃异常抑制

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摘要

We study the weakly disordered Bose-Hubbard model on a cubic lattice through a one-loop renormalization-group analysis of the corresponding effective-field theory which is explicitly derived by combining a strong-coupling expansion with a replica average over the disorder. The method is applied not only to generic uncorrelated on-site disorder but also to simultaneous hopping-disorder correlated with the differences of adjacent disorder potentials. Such correlations are inherent in fine-grained optical speckle potentials used as a source of disorder in optical lattice experiments. As a result of strong coupling, the strength of the replica-mixing disorder vertex, responsible for the emergence of a Bose glass, crucially depends on the chemical potential and the Hubbard repulsion and vanishes to leading order in the disorder at commensurate boson fillings. As a consequence, at such fillings a direct transition between the Mott insulator and the superfiuid in the presence of disorder cannot be excluded on the basis of a one-loop calculation. At incommensurate fillings, at a certain length scale, the Mott insulator will eventually become unstable toward the formation of a Bose glass. Phase diagrams as a function of the microscopic parameters are presented and the finite-size crossover between the Mott-insulating state and the Bose glass is analyzed.
机译：我们通过对相应有效场理论进行一环重归一化组分析，研究了立方晶格上的弱无序Bose-Hubbard模型，该分析通过结合强耦合扩展和无序复制平均值而明确得出。该方法不仅适用于通用的不相关的现场障碍，而且适用于与相邻障碍电位的差异相关的同时跳频障碍。此类相关性是在用作晶格实验中无序源的细粒度光学散斑电位中固有的。由于强耦合，导致玻色玻璃出现的复制混合混合顶点的强度关键取决于化学势和Hubbard排斥力，并消失在相应的玻色子填充中。结果，基于单回路计算，不能排除在存在无序情况下在莫特绝缘子和超流体之间的直接过渡。如果填充量不适当，则在一定长度范围内，Mott绝缘子最终将对玻色玻璃的形成变得不稳定。给出了作为微观参数的函数的相图，并分析了莫特绝缘状态和玻色玻璃之间的有限尺寸交叉。

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