scholarly journals Comparative study of quantum dynamics of a few bosons in a one-dimensional split hard-wall trap: exact results versus Bose–Hubbard-model approximations

2011 ◽  
Vol 44 (19) ◽  
pp. 195002 ◽  
Author(s):  
Hongli Guo ◽  
Xiangguo Yin ◽  
Shu Chen
Keyword(s):  
Comparative Study ◽  
Hubbard Model ◽  
Quantum Dynamics ◽  
Exact Results ◽  
Hard Wall ◽  
One Dimensional

Exact Results for Highly Correlated Electron Systems in One Dimension

1997 ◽  
Vol 11 (04n05) ◽  
pp. 355-667 ◽  
Author(s):  
P. Schlottmann
Keyword(s):  
Hubbard Model ◽  
One Dimension ◽  
Correlated Electrons ◽  
Exact Results ◽  
Electron Systems ◽  
Persistent Currents ◽  
Correlated Electron Systems ◽  
One Dimensional ◽  
Correlated Electron ◽  
Highly Correlated

One-dimensional conductors are a long-standing topic of research with direct applications to organic conductors and mesoscopic rings. The discovery of the ceramic high-temperature superconductors has revitalized the interest in low-dimensional charge and spin fluctuations of highly correlated electron systems. Several mechanisms proposed to explain the high-T c superconductors invoke properties of the two-dimensional Hubbard model, but probably also some one-dimensional aspects are relevant. Numerous one-dimensional models for correlated electrons have been studied with various approximate, asymptotically exact and exact methods. These results lead to the concept of Luttinger liquid for interacting electron gases without excitation gaps (metallic systems). Characteristic of Luttinger liquids are the charge and spin separation, marginal Fermi liquid properties, e.g. the absence of quasiparticles in the vicinity of the Fermi surface, nonuniversal power-law singularities in the one-particle spectral function and the related absence of a discontinuity in the momentum distribution at the Fermi level, the power-law decay of correlation functions for long times and large distances, persistent currents in finite rings, etc. Due to the peculiarities of the phase space in one dimension some of the models have sufficient conserved currents to be completely integrable. We review exact results derived within the framework of Bethe's ansatz for integrable one-dimensional models of correlated electrons. The Bethe-ansatz method is presented by explicitly showing the steps leading to the solution of the N-component electron gas interacting via a δ-function potential (repulsive and attractive interaction), which is probably the simplest model of correlated electrons. Emphasis is given to the procedure to extract the groundstate properties, the classification of states, the excitation spectrum, the thermodynamics and finite size effects, such as critical exponents of correlation functions and persistent currents. The method is then applied to numerous other models, e.g. (i) a two-band model involving attractive and repulsive potentials and crystalline fields splitting the bands, (ii) the traditional Hubbard chain with attractive and repulsive U, (iii) the degenerate Hubbard model with repulsive U, which displays a metal–insulator transition at a finite U, (iv) a two-band Hubbard model with repulsive U, (v) the traditional supersymmetric t–J model (vi) a two-band supersymmetric t–J model with band-splitting and (vii) the N-component supersymmetric t–J model. Finally, results for models with long-range interactions, in particular r-2 and sinh -2(r) potentials, are briefly reviewed.

scholarly journals Ground-state properties of the one-dimensional attractive Hubbard model with confinement: A comparative study

2010 ◽  
Vol 82 (1) ◽  
Author(s):  
Ji-Hong Hu ◽  
Jing-Jing Wang ◽  
Gao Xianlong ◽  
Masahiko Okumura ◽  
Ryo Igarashi ◽  
...  
Keyword(s):  
Comparative Study ◽  
Hubbard Model ◽  
Ground State ◽  
One Dimensional ◽  
Ground State Properties ◽  
Attractive Hubbard Model ◽  
The One

Variational Many Body States for the U=∞ Hubbard Model

1991 ◽  
Vol 05 (10) ◽  
pp. 1791-1800 ◽  
Author(s):  
C. Stephen Hellberg ◽  
E. J. Mele
Keyword(s):  
Hubbard Model ◽  
General Class ◽  
Exact Results ◽  
Strongly Correlated ◽  
Many Body ◽  
Local Constraints ◽  
Double Occupancy ◽  
One Dimensional ◽  
Lattice Fermions ◽  
The One

We study a general class of variational wavefunctions for strongly correlated lattice fermions. The wavefunctions considered here automatically satisfy local constraints of no double occupancy and include correlations between opposite spin particles in a very physical way. We calculate the energy and correlation functions for the one dimensional U=∞ Hubbard model, where a comparison with exact results is made. We briefly report on preliminary results for the t-J model.

scholarly journals CRITICAL EXPONENTS IN THE ONE-DIMENSIONAL HUBBARD MODEL

1994 ◽  
Vol 08 (04) ◽  
pp. 403-415 ◽  
Author(s):  
Holger Frahm ◽  
V. E. Korepin
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Asymptotic Behaviour ◽  
Hubbard Model ◽  
Critical Exponents ◽  
Correlation Functions ◽  
Exact Results ◽  
Quantum Field ◽  
One Dimensional ◽  
The One

Exact Bethe Ansatz results on the spectrum of large but finite Hubbard chains in conjunction with methods from conformal quantum field theory can be used to obtain exact results for the asymptotic behaviour of correlation functions. We review this method and discuss some interesting consequences of the results.

scholarly journals Antiferromagnetic fluctuations in the one-dimensional Hubbard model

AIP Advances ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 125127
Author(s):  
Václav Janiš ◽  
Antonín Klíč ◽  
Jiawei Yan
Keyword(s):  
Hubbard Model ◽  
One Dimensional ◽  
The One
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