Imaginary time instantons and pseudogap state in superconducting cuprates.

我们提出并研究了具有异常序参数的新状态的性质。它的特征是在虚时间内有一个总长度为1/T的瞬子周期链，其中T为温度。我们引入了一个费米子和玻色子相互作用的模型。然后，我们用解析和数值方法证明了新状态可以对应于模型参数的广泛区域内自由能的最小值。这种状态是独特的，并与朗道型理论中的常规相与静态长程阶相形成对比。我们把这种状态称为“瞬子晶体”。我们提出的模型可能源于我们早期发表的描述超导铜酸盐低温特性的有效的“具有重叠热点的自旋费米子模型”。现在我们通过计算实时相关函数继续对瞬态晶体的研究。主要问题是研究物理量相关函数的非衰减实时振荡的可能性。在传统的热力学稳定系统中，它们是衰减的，并且认为在无限体积的极限下，宏观模型中不可能存在非衰减振荡。然而，在瞬态晶体中的情况原则上是不同的，我们用解析和数值方法来研究这个问题。所考虑的模型中环路电流的热力学相关函数，只要实时显示振荡，在中子散射中可以给出有限频率的峰值。此外，我们计划研究动力学物理量，例如电导率，并研究波动的影响。

We propose and investigate properties of a new state with an unusual order parameter. It is characterized by a periodic chain of instantons in the imaginary time with the total length 1/T, where T is temperature. We have introduced a model of interacting fermions and bosonic modes having this new state. Then, we demonstrated both analytically and numerically that the new state can correspond to the minimum of the free energy in a broad region of parameters of the model. This state is unique and contrasts conventional phases in Landau-type theories with static long-range orders. We have called this state "instanton crystal". The model we suggested might originate from an effective "spin-fermion model with overlapping hot spots" developed in our earlier publications for description of low temperature properties of superconducting cuprates.Now we continue our study of the instanton crystal by calculating real-time-dependent correlation functions. The main question concerns investigating a possibility of non-decaying real-time oscillations of correlation functions of physical quantities. In conventional thermodynamically stable systems, they decay and it is believed that the non-decaying oscillations are impossible in macroscopic models in the limit of theinfinite volume. Nevertheless, the situation in the instanton crystal can, in principle, be different and we investigate this question both analytically and numerically. The thermodynamic correlation function of the loop currents in the model considered, provided it shows oscillation in real time, can give peaks at finite frequencies in neutron scattering. Further, we plan to study kinetic physical quantities like, e.g., conductivity and investigate effects of fluctuations.