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.

在本财政年度，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，另一篇论文已提交发表。为实现有限相互作用模型的有效热和功，需要评估二阶密度矩阵。这在张量网络(TN)方法中是一个相当复杂的过程，然而，在过去的一年里，我将其实现在ITInterer中，并将其用于我最近在PRA上发表的关于SU(N)系统中噪声关联的工作。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，并提交给了科学发帖。在这里，我们发现了有趣的混沌体系，这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组分的系统的有效热力学提供了潜在的参数区域。此外，我还使用精确对角化方法(ED)实现了玻色-哈伯德模型(BHM)有效热和功的计算。我还使用TN Suzuki-Trotter方法实现了Hubbard模型的猝灭动力学，以研究相关扩展。用ED对BHM中的有效热和功的初步研究表明，不同类型的猝灭在强混沌和弱混沌区域的行为是本质上不同的。

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

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

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