Effective thermodynamics of reduced density matices

在这个财政年度，我已经完成了实施我的建议的几个必要步骤，并发表了一篇与所需技术相关的论文，另一篇论文已经提交发表。实现有限相互作用模型的有效热和功需要二阶密度矩阵的计算。在张量网络（TN）方法中，这是一个相当复杂的过程，然而，在去年，我在ITensor中实现了这一过程，并将其用于我最近在PRA上发表的SU(N)系统中的噪声相关性研究。去年，我还与人合著了一篇关于玻色混合物中的量子混沌的手稿，并提交给scipost。这里我们发现了有趣的混沌状态，取决于相互作用之间的对称性。这与系统的热力学性质密切相关，并为研究具有两个可区分成分的系统中的有效热力学提供了潜在的参数制度。此外，我已经实现了Bose-Hubbard模型（BHM）使用精确对角化（ED）的有效热和功的计算。为了研究相关扩散，我还使用TN Suzuki-Trotter方法实现了Hubbard模型淬火动力学。对BHM的有效热和功的初步研究表明，不同类型的淬火在强混沌和弱混沌状态下的行为有质的不同。

In this financial year I have achieved several required steps for implementing my proposal and published one paper related to the required techniques, with another paper having been submitted for publication.Implementing the effective heat and work for a model with finite interactions requires the evaluation of the second-order density matrix. This is a rather involved process in the tensor network (TN) approach, however, during the last year I implemented this in ITensor and used it for my work on noise correlations in SU(N) systems which was recently published in PRA. In the last year I have also co-authored a manuscript, submitted to scipost, on quantum chaos in Bose-mixtures. Here we found interesting chaotic regimes, depending on the symmetry between interactions. This is closely related to the thermodynamic properties of the system and suggests potential parameter regimes of interest for investigating effective thermodynamics in systems with two distinguishable components.Additionally, I have implemented the calculation of effective heat and work for the Bose-Hubbard model (BHM) using exact diagonalization (ED). I have also implemented Hubbard model quench dynamics using the TN Suzuki-Trotter approach in order to study correlation spreading. Preliminary investigations of the effective heat and work in the BHM using ED suggests that the behavior for different types of quenches in strongly chaotic and weakly chaotic regimes are qualitatively different.