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Fermi liquid theory --- Mathematical models --- Congresses --- Hubbard model --- Mathematical physics

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Hubbard model --- Model, Hubbard --- Electronics and optics of solids --- Solid state physics --- Congresses --- Energy-band theory of solids --- Solid state physics - Congresses --- Hubbard model - Congresses

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The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding many-body problems analytically or numerically, although much insight can be gained from the analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands, and which has been applied to problems as diverse as high-Tc superconductivity, band magnetism, and the metal-insulator transition. This 2005 book presents a coherent, self-contained account of the exact solution of the Hubbard model in one dimension. The early chapters will be accessible to beginning graduate students with a basic knowledge of quantum mechanics and statistical mechanics. The later chapters address more advanced topics, and are intended as a guide for researchers to some of the more topical results in the field of integrable models.

Hubbard model --- Quantum theory --- Hubbard model. --- Quantum theory. --- Statistical mechanics. --- Mechanics --- Mechanics, Analytic --- Quantum statistics --- Statistical physics --- Thermodynamics --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Model, Hubbard --- Energy-band theory of solids

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One of the most active areas in atomic, molecular and optical physics is the use of ultracold atomic gases in optical lattices to simulate the behaviour of electrons in condensed matter systems. The larger mass, longer length scale, and tuneable interactions in these systems allow the dynamics of atoms moving in these systems to be followed in real time, and resonant light scattering by the atoms allows this motion to be probed on a microscopic scale using site-resolved imaging. This book reviews the physics of Hubbard-type models for both bosons and fermions in an optical lattice, which give rise to a rich variety of insulating and conducting phases depending on the lattice properties and interparticle interactions. It also discusses the effect of disorder on the transport of atoms in these models, and the recently discovered phenomenon of many-body localization. It presents several examples of experiments using both density and momentum imaging and quantum gas microscopy to study the motion of atoms in optical lattices. These illustrate the power and flexibility of ultracold-lattice analogues for exploring exotic states of matter at an unprecedented level of precision.

Hubbard model. --- Many-body problem. --- Quantum theory. --- Low temperatures. --- Optical lattices. --- Quantum physics (quantum mechanics & quantum field theory) --- SCIENCE / Physics / Quantum Theory.

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Antiferromagnetism --- Antiferromagnetisme --- Haute température [Superconductivité à ] --- High Tc superconductivity --- High critical temperature superconductivity --- High temperature superconductivity --- Hoge temperatuur superconductiviteit --- Hubbard model --- Modèle d'Hubbard --- Superconductiviteit [Hoge temperatuur ] --- Superconductivité à haute température --- Temperatuur superconductiviteit [Hoge ] --- Température [Superconductivité à haute ] --- antiferromagnétisme --- 538.94 --- 530.19 --- Model, Hubbard --- Energy-band theory of solids --- Superconductivity --- Ferromagnetism --- Quantum liquids and solids --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- Antiferromagnetism. --- High temperature superconductivity. --- Hubbard model. --- 530.19 Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc. --- 538.94 Quantum liquids and solids --- Fundamental functions in general. Potential. Gradient. Intensity. Capacity etc