Dupuis Nicolas, Daviet Romain
Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC, F-75005 Paris, France.
Phys Rev E. 2020 Apr;101(4-1):042139. doi: 10.1103/PhysRevE.101.042139.
We study a one-dimensional disordered Bose fluid using bosonization, the replica method, and a nonperturbative functional renormalization-group approach. We find that the Bose-glass phase is described by a fully attractive strong-disorder fixed point characterized by a singular disorder correlator whose functional dependence assumes a cuspy form that is related to the existence of metastable states. At nonzero momentum scale k, quantum tunneling between the ground state and low-lying metastable states leads to a rounding of the cusp singularity into a quantum boundary layer (QBL). The width of the QBL depends on an effective Luttinger parameter K_{k}∼k^{θ} that vanishes with an exponent θ=z-1 related to the dynamical critical exponent z. The QBL encodes the existence of rare "superfluid" regions, controls the low-energy dynamics, and yields a (dissipative) conductivity vanishing as ω^{2} in the low-frequency limit. These results reveal the glassy properties (pinning, "shocks," or static avalanches) of the Bose-glass phase and can be understood within the "droplet" picture put forward for the description of glassy (classical) systems.
我们使用玻色化、复制方法和非微扰泛函重整化群方法研究一维无序玻色流体。我们发现玻色玻璃相由一个完全吸引的强无序不动点描述，其特征是具有奇异的无序关联函数，其函数依赖关系呈现出一种尖点形式，这与亚稳态的存在有关。在非零动量尺度(k)处，基态与低能亚稳态之间的量子隧穿导致尖点奇异性转变为量子边界层（QBL）。QBL的宽度取决于一个有效的卢廷格参数(K_{k}\sim k^{\theta})，该参数随着与动态临界指数(z)相关的指数(\theta = z - 1)而消失。QBL编码了罕见“超流体”区域的存在，控制了低能动力学，并在低频极限下产生一个与(\omega^{2})成比例消失的（耗散）电导率。这些结果揭示了玻色玻璃相的玻璃态性质（钉扎、“冲击”或静态雪崩），并且可以在为描述玻璃态（经典）系统而提出的“液滴”图景中得到理解。
