Effective thermodynamics of reduced density matices

减密度材料的有效热力学

• 批准号: 22K14007
• 负责人: Mikkelsen Mathias
• 金额: $ 2万
• 依托单位: Kindai University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Early-Career Scientists
• 财政年份: 2022
• 资助国家: 日本
• 起止时间: 2022-04-01 至 2024-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-22K14007/
• 关键词: Thermodynamics; Tensor network; Noise correlations; Hubbard model; Dynamics; Quantum chaos; Bose gases; Non-equilibrium Dynamics; Irreversibility; Quantum quench

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.

在这个财政年度，我已经实现了实施我的提案的几个必需步骤，并发表了一篇与所需技术有关的论文，另一篇论文已提交出版。实施有效的热量和有限互动模型的工作需要评估二阶密度矩阵。这是张量网络（TN）方法中相当涉及的过程，但是，在去年，我在Itensor中实施了此过程，并将其用于我最近在PRA中发表的SU（N）系统中的噪声相关性工作。在去年，我还共同撰写了一份手稿，并在Bose-Mixtures中的量子混乱中提交给Scipost。在这里，我们发现了有趣的混乱制度，具体取决于相互作用之间的对称性。这与系统的热力学特性密切相关，并提出了潜在的参数参数，用于研究具有两个可区分组件的系统中有效的热力学。我还使用TN Suzuki-Trotter方法实施了Hubbard模型淬灭动力学，以研究相关扩展。使用ED对BHM中有效的热量和工作的初步研究表明，在强烈混乱和弱混乱的方案中，不同类型的淬火行为在质上有所不同。

项目成果

Resonant superfluidity in the Rabi-coupled spin-dependent Fermi-Hubbard model

拉比耦合自旋相关费米-哈伯德模型中的共振超流性

• DOI: 10.1103/physreva.106.043316
• 发表时间: 2022
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Mikkelsen Mathias;Kaneko Ryui;Kagamihara Daichi;Danshita Ippei
• 通讯作者: Danshita Ippei

Comparison between noise correlations and the spin-structure factor in SU(N) Hubbard models

SU(N) Hubbard 模型中噪声相关性与自旋结构因子的比较

• 发表时间: 2022
• 作者: Kouichi Hayashi;Maximilian Lederer;Yohei Fukumoto;Masashi Goto;Yuta Yamamoto;Naohisa Happo;Masahide Harada;Yasuhiro Inamura;Kenichi Oikawa;Kenji Ohoyama;and Peter Wellmann;Mathias Mikkelsen and Ippei Danshita
• 通讯作者: Mathias Mikkelsen and Ippei Danshita

Relation between the noise correlations and the spin structure factor for Mott-insulating states in SU(N) Hubbard models

SU(N) Hubbard 模型中莫特绝缘态的噪声相关性与自旋结构因子之间的关系

• DOI: 10.1103/physreva.107.043313
• 发表时间: 2023
• 期刊: Physical Review A
• 影响因子: 2.9
• 作者: Koshi Oi;Jiang Pu;Hao Ou;Rei Usami;Takahiko Endo;Yasumitsu Miyata;Keisuke Shinokita;Kazunari Matsuda;Taishi Takenobu;横田紘子，林田健志，北原暖，木村剛;Pradipto and Hisao Hayakawa;Yuzuru Sato;石渡 哲哉;Teppei Ogihara;K. P. Nayak and K. Muhammed Shafi;渡部 善隆;Mathias Mikkelsen and Ippei Danshita
• 通讯作者: Mathias Mikkelsen and Ippei Danshita