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Slater determinant and exact eigenstates of the two-dimensional Fermi–hubbard model

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Chinese Physics B 2018年第7期27卷 264-267页

作者：任军航叶明勇林秀敏 Fujian Provincial Key Laboratory of Quantum Manipulation and New Energy Materials College of Physics and Energy Fujian Normal University Fuzhou 350117 China Fujian Provincial Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices Xiamen 361005 China

We consider the construction of exact eigenstates of the two-dimensional Fermi-hubbard model defined on an L ×L lattice with a periodic condition. Based on the characteristics of Slater determinants, several methods are introduced to construct exact eigenstates of the model. The eigenstates constructed are independent of the on-site electron interaction and some of them can also represent exact eigenstates of the two-dimensional Bose-hubbard model.

关键词： hubbard model exact eigenstate Slater determinant

Antiferromagnetic Phase Transition in the Quasi-Two-Dimensional hubbard model at Half Filling

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Chinese Physics Letters 2004年第5期21卷 937-940页

作者：刘勤勇田光善闫新中 DepartmentofPhysics PekingUniversityBeijing100871 InstituteofPhysics ChineseAcademyofSciencesPoBox603Beijing100080

We study the antiferromagnetic phase transition in the quasi-two-dimensional hubbard model at half filling for a wide range of the Coulomb interaction U. By using the fluctuation-exchange approximation, we calculate the Néel transition temperature of the system as a function of the Coulomb interaction U. For weak-to-intermediate Coulomb interactions, the present calculation provides a reasonable result for the Néel temperature.

关键词： hubbard model

Structure of Essential Spectra and Discrete Spectrum of the Energy Operator of Six-Electron Systems in the hubbard model. First Quintet and First Singlet States

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Journal of Applied Mathematics and Physics 2022年第11期10卷 3424-3461页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of six-electron systems in the hubbard model and investigate the structure of essential spectra and discrete spectrum of the system in the first quintet and first singlet states in the ... 详细信息

关键词： hubbard model Essential Spectrum Discrete Spectrum Six Electron Systems Octet State Singlet State Quintet State

The pairing correlations in the phased t-U hubbard model

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Chinese Physics B 2004年第2期13卷 229-233页

作者：刘自信刘平刘亚文生辉 DepartmentofPhysics HenanNormalUniversityXinxiang453002China

In this paper we have studied the phased t U hubbard model. Using the constrained path Monte Carlo method,we investigated the effects of phase factor on pairing correlation functions in the ground state, and we found that the long-range correlations are dependent on the choice of phase factor, and for some special values of phase factor there exist long-range pairing correlations only in the strong coupling region.

关键词： hubbard model correlation function

Spectra of the Energy Operator of Four-Electron Systems in the Impurity hubbard model. Triplet State

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Journal of Applied Mathematics and Physics 2021年第11期9卷 2776-2795页

作者： S. M. Tashpulatov R. T. Parmanova Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider the energy operator of four-electron systems in an impurity hubbard model and investigated the structure of essential spectra and discrete spectrum of the system in the first triplet state in a one-dimensional lattice. For investigation the structure of essential spectra and discrete spectrum of the energy operator of four-electron systems in an impurity hubbard model, for which the momentum representation is convenient. In addition, we used the tensor products of Hilbert spaces and tensor products of operators in Hilbert spaces and described the structure of essential spectrum and discrete spectrum of the energy operator of four-electron systems in an impurity hubbard model. The investigations show that there are such cases: 1) the essential spectrum of the system consists of the union of no more than eight segments, and the discrete spectrum of the system consists of no more than three eigenvalues;2) the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues;3) the essential spectrum of the system consists of the union of no more than three segments, and the discrete spectrum of the system is the empty set. Consequently, the essential spectrum of the system consists of the union of no more than sixteen segments, and the discrete spectrum of the system consists of no more than eleven eigenvalues.

关键词： hubbard model Essential Spectrum Discrete Spectrum Four Electron Systems Quintet State Triplet State Singlet State Spectra

Structure of Essential Spectrum and Discrete Spectra of the Energy Operator of Five-Electron Systems in the hubbard model. Third and Fourth Doublet States

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Journal of Applied Mathematics and Physics 2020年第12期8卷 2886-2918页

作者： S. M. Tashpulatov Institute of Nuclear Physics of Academy of Science of Republic of Uzbekistan Tashkent Uzbekistan

We consider a five-electron system in the hubbard model with a coupling between nearest-neighbors. The structure of essential spectrum and discrete spectrum of the systems in the third and fourth doublet states in a v-dimensional lattice is investigated. We prove that the essential spectrum of the system in a third doublet state consists is the union of at most four segments, and discrete spectrum of the system is empty. We show that the essential spectrum of the system in a fourth doublet state consists of the union of at most seven segments, and discrete spectrum of the system consists of no more than one point.

关键词： Essential Spectrum Discrete Spectrum Five-Electron System Bound State Anti-Bound State hubbard model Doublet State Sextet State Quartet State

Quantum phase transition and von Neumann entropy of quasiperiodic hubbard chains

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Chinese Physics B 2008年第5期17卷 1623-1628页

作者：朱璇童培庆 Department of Physics Nanjing Normal University

The half-filled hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.

关键词： von Neumann entropy quasiperiodicity hubbard model spin-density waves

Recent progress on fabrication and flat-band physics in 2D transition metal dichalcogenides moiré superlattices

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Journal of Semiconductors 2023年第1期44卷 43-55页

作者： Xinyu Huang Xu Han Yunyun Dai Xiaolong Xu Jiahao Yan Mengting Huang Pengfei Ding Decheng Zhang Hui Chen Vijay Laxmi Xu Wu Liwei Liu Yeliang Wang Yang Xu Yuan Huang Advanced Research Institute of Multidisciplinary Science Beijing Institute of TechnologyBeijing 100081China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Integrated Circuits and Electronics MIIT Key Laboratory for Low-Dimensional Quantum Structure and DevicesBeijing Institute of TechnologyBeijing 100081China BIT Chongqing Institute of Microelectronics and Microsystems Chongqing 401332China

Moiré superlattices are formed when overlaying two materials with a slight mismatch in twist angle or lattice constant. They provide a novel platform for the study of strong electronic correlations and non-trivial band topology, where emergent phenomena such as correlated insulating states, unconventional superconductivity, and quantum anomalous Hall effect are discovered. In this review, we focus on the semiconducting transition metal dichalcogenides(TMDs) based moiré systems that host intriguing flat-band physics. We first review the exfoliation methods of two-dimensional materials and the fabrication technique of their moiré structures. Secondly, we overview the progress of the optically excited moiré excitons, which render the main discovery in the early experiments on TMD moiré systems. We then introduce the formation mechanism of flat bands and their potential in the quantum simulation of the hubbard model with tunable doping, degeneracies, and correlation strength. Finally, we briefly discuss the challenges and future perspectives of this field.

关键词： flat-band physics two-dimensional materials moirésuperlattices hubbard model moiréexcitons

Ferromagnetism in an Itinerant Electron System

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Communications in Nonlinear Science and Numerical Simulation 1996年第3期1卷 12-16页

作者： D. F. WAANG(Institut de Physique Theorique Ecole Polytechnique Federale de Lausanne,PHB-Ecublens, CH-1015 Lausanne, Switzerland)E-mail: wang@sidpsg. epfl.ch Institut de Physique Théorique Ecole Polytechnique Fédérale de Lausanne PHB-Ecublens CH-1015 Lausanne Switzerland

In this work, the ground states of the hubbard model on complete graph arestudied, for a finite lattice sise L and arbitrary on-site energy U. We construct explicitlythe ground states of the system when the number of the electrons Ne ≥ L + 1. In particular,for Ne = L + 1, the ground state is ferromagntic with total spin sg = (Ne - 2)/2.

关键词： Ferromagnetism hubbard model Kondo-lattice model