The Hubbard Model

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Daniel P. Arovas ◽  
Erez Berg ◽  
Steven A. Kivelson ◽  
Srinivas Raghu
Keyword(s):  
Hubbard Model ◽  
Approximate Solutions ◽  
Annual Review ◽  
Publication Date ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Open Questions ◽  
Spatial Dimensions ◽  
Primary Focus

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 13 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Strongly Correlated Electron Systems: Spin-Reflection Positivity and Some Rigorous Results

1998 ◽  
Vol 12 (07n08) ◽  
pp. 709-779 ◽  
Author(s):  
Shun-Qing Shen
Keyword(s):  
Hubbard Model ◽  
Long Range ◽  
Strongly Correlated Electron Systems ◽  
Strongly Correlated ◽  
Electron Systems ◽  
Strongly Correlated Electron ◽  
Rigorous Results ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Generalized Hubbard Model

Theory of spin-reflection positivity developed in recent years is reviewed. This theory makes use of symmetries in an electron system and theory of matrix to investigate the ground state properties. Existences of anti- and ferromagnetic long-range orders in itinerant electron systems, and of off-diagonal long-range order are two successful applications of the theory. In this article, the author attempt to summarize exact results proved by utilizing this theory and related topics. First a general theory and basic theorems are introduced. Second, based on the band structures of conduction electrons, existences of a singlet state with strongly antiferromagnetic correlation, a state with both anti- and ferromagnetic long-range orders, and a fully saturated ferromagnetic state are proved. The theory is applied to several of the main theoretical models for strongly correlated electron systems, such as the Heisenberg model, the Hubbard model, the Anderson model, the single- and multichannel Kondo model, and the generalized Hubbard model, and a series of rigorous results are found in these models. Third, it is proved that off-diagonal long-range order and charge-density wave exist in the ground states of the attractive Hubbard model and the generalized Hubbard model. A relation between pseudospin symmetry and the uniform density theorem is introduced. Fourth, the theory is applied successfully to explain experimental observations of oscillatory interlayer magnetic coupling in ultrathin magnetic films. Finally several unsolved problems are discussed. All results introduced in this article are mathematically exact.

scholarly journals Superconductivity, Antiferromagnetism, and Kinetic Correlation in Strongly Correlated Electron Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Takashi Yanagisawa
Keyword(s):  
High Temperature ◽  
Hubbard Model ◽  
High Temperature Superconductivity ◽  
Spin Fluctuation ◽  
Coulomb Repulsion ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Antiferromagnetic Correlation ◽  
The Stability

We investigate the ground state of two-dimensional Hubbard model on the basis of the variational Monte Carlo method. We use wave functions that include kinetic correlation and doublon-holon correlation beyond the Gutzwiller ansatz. It is still not clear whether the Hubbard model accounts for high-temperature superconductivity. The antiferromagnetic correlation plays a key role in the study of pairing mechanism because the superconductive phase exists usually close to the antiferromagnetic phase. We investigate the stability of the antiferromagnetic state when holes are doped as a function of the Coulomb repulsionU. We show that the antiferromagnetic correlation is suppressed asUis increased exceeding the bandwidth. High-temperature superconductivity is possible in this region with enhanced antiferromagnetic spin fluctuation and pairing interaction.

scholarly journals SUPERCONDUCTING IN THE NEAR HALF-FILLING HUBBARD MODEL

1995 ◽  
Vol 09 (11n12) ◽  
pp. 711-717
Author(s):  
HOANG ANH TUAN ◽  
NGUYEN TOAN THANG ◽  
NGUYEN NGOC THUAN
Keyword(s):  
Hubbard Model ◽  
Functional Integral ◽  
Strongly Correlated Electron Systems ◽  
Strongly Correlated ◽  
Electron Systems ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Functional Integral Method ◽  
Half Filling

The Hubbard model of strongly correlated electron systems is considered near half-filling within the framework of a new functional integral method without slave bosons. A dynamical system of equations determining the superconducting phase of the Hubbard model is derived. Both singlet and triplet Cooper pairings are studied.

scholarly journals Propagation of shear stress in strongly interacting metallic Fermi liquids enhances transmission of terahertz radiation

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
D. Valentinis ◽  
J. Zaanen ◽  
D. van der Marel
Keyword(s):  
Shear Stress ◽  
Terahertz Radiation ◽  
Fermi Liquid ◽  
Zero Sound ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron ◽  
Collisionless Regime ◽  
Propagating Shear ◽  
Mass Enhancement

AbstractA highlight of Fermi-liquid phenomenology, as explored in neutral $$^3$$ 3 He, is the observation that in the collisionless regime shear stress propagates as if one is dealing with the transverse phonon of a solid. The existence of this “transverse zero sound” requires that the quasiparticle mass enhancement exceeds a critical value. Could such a propagating shear stress also exist in strongly correlated electron systems? Despite some noticeable differences with the neutral case in the Galilean continuum, we arrive at the verdict that transverse zero sound should be generic for mass enhancement higher than 3. We present an experimental setup that should be exquisitely sensitive in this regard: the transmission of terahertz radiation through a thin slab of heavy-fermion material will be strongly enhanced at low temperature and accompanied by giant oscillations, which reflect the interference between light itself and the “material photon” being the actual manifestation of transverse zero sound in the charged Fermi liquid.

scholarly journals Electrical transport properties and Kondo effect in La1−xPrxNiO3−δ thin films

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Van Hien-Hoang ◽  
Nak-Kwan Chung ◽  
Heon-Jung Kim
Keyword(s):  
Thin Films ◽  
Electrical Transport ◽  
Kondo Effect ◽  
Magnetic Moments ◽  
Structural Disorder ◽  
Strongly Correlated ◽  
Electrical Transport Properties ◽  
Strongly Correlated Electron ◽  
Correlated Electron Systems ◽  
Correlated Electron

AbstractThe Kondo effect has been a topic of intense study because of its significant contribution to the development of theories and understanding of strongly correlated electron systems. In this work, we show that the Kondo effect is at work in La1−xPrxNiO3−δ (0 ≤ x ≤ 0.6) thin films. At low temperatures, the local magnetic moments of the 3d eg electrons in Ni2+, which form because of oxygen vacancies, interact strongly with itinerant electrons, giving rise to an upturn in resistivity with x ≥ 0.2. Observation of negative magnetoresistance, described by the Khosla and Fisher model, further supports the Kondo picture. This case represents a rare example of the Kondo effect, where Ni2+ acts as an impurity in the background of Ni3+. We suggest that when Ni2+ does not participate in the regular lattice, it provides the local magnetic moments needed to scatter the conduction electrons in the Kondo effect. These results offer insights into emergent transport behaviors in metallic nickelates with mixed Ni3+ and Ni2+ ions, as well as structural disorder.

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