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Nonequilibrium quantum criticality in bilayer itinerant ferromagnets

机译：双层迭代铁磁体的非平衡量子临界

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We present a theory of nonequilibrium quantum criticality in a coupled bilayer system of itinerant electron magnets. The model studied consists of the first layer subjected to an in-plane current and open to an external substrate. The second layer is subject to no direct external drive, but couples to the first layer via short-ranged spin-exchange interaction. No particle exchange is assumed between the layers. Starting from a microscopic fermionic model, we derive an effective action in terms of two coupled bosonic fields which are related to the magnetization fluctuations of the two layers. When there is no interlayer coupling, the two bosonic modes possess different dynamical critical exponents z with z=2 (z=3) for the first (second) layer. This results in multiscale quantum criticality in the coupled system. It is shown that the linear coupling between the two fields leads to a low-energy fixed point characterized by the larger dynamical critical exponent z=3. We compute the correlation length in the quantum disordered and quantum critical regimes for both the nonequilibrium case and in thermal equilibrium where the whole system is held at a common temperature T. We identify an effective temperature scale T_(eff) with which we define a quantum-to-classical crossover that is in exact analogy with the thermal equilibrium case but with T replaced by T_(eff). However, we find that the leading correction to the correlation length in the quantum critical regime scales differently with respect to T and T_(eff). We also note that the current in the lower layer generates a drift of the magnetization fluctuations, manifesting itself as a parity-breaking contribution to the effective action of the bosonic modes. In this sense, the nonequilibrium drive in this system plays a role which is distinct from T in the thermal equilibrium case. We also derive the stochastic dynamics obeyed by the critical fluctuations in the quantum critical regime and find that they do not fall into the previously identified dynamical universality classes.
机译：我们提出了在流动电子磁体耦合双层系统中的非平衡量子临界理论。研究的模型由经受面内电流并通向外部基板的第一层组成。第二层不受直接外部驱动，而是通过短程自旋交换相互作用耦合到第一层。假设在各层之间没有粒子交换。从微观铁电离子模型出发，我们根据两个耦合的玻色子场得出了一个有效的作用，这两个波子场与两层的磁化涨落有关。当不存在层间耦合时，对于第一层（第二层），两个玻色子模式具有不同的动态临界指数z，其中z = 2（z = 3）。这导致耦合系统中的多尺度量子临界性。结果表明，这两个场之间的线性耦合导致了一个低能量的固定点，其特征在于较大的动态临界指数z = 3。我们针对非平衡情况和整个系统保持在共同温度T下的热平衡情况，计算了量子无序态和量子临界态中的相关长度。我们确定了一个有效的温度标度T_（eff），用以定义一个量子到经典的转换，与热平衡情况完全相似，但用T_（eff）代替T。但是，我们发现，量子临界态中相关长度的前导校正相对于T和T_（eff）具有不同的缩放比例。我们还注意到，较低层中的电流会产生磁化波动的漂移，这本身表现为破坏了对玻色子模式的有效作用的奇偶校验贡献。从这个意义上说，在热平衡情况下，该系统中的非平衡驱动起着不同于T的作用。我们还推导了量子临界状态中的临界波动所服从的随机动力学，发现它们不属于先前确定的动力学普遍性类别。

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