The one-dimensional Hubbard model: A reminiscence

Elliott H. Lieb; F. Y. Wu

doi:10.1016/S0378-4371(02)01785-5

The one-dimensional Hubbard model: A reminiscence

Elliott H. Lieb, F. Y. Wu

Mathematics

Research output: Contribution to journal › Conference article › peer-review

154 Scopus citations

Abstract

In 1968 we published the solution of the ground state energy and wave function of the one-dimensional Hubbard model, and we also showed that there is no Mott transition in this model. Details of the analysis have never been published, however. As the Hubbard model has become increasingly important in condensed matter physics, relating to topics such as the theory of high-T_c superconductivity, it is appropriate to revisit the one-dimensional model and to recall here some details of the solution.

Original language	English (US)
Pages (from-to)	1-27
Number of pages	27
Journal	Physica A: Statistical Mechanics and its Applications
Volume	321
Issue number	1-2
DOIs	https://doi.org/10.1016/S0378-4371(02)01785-5
State	Published - Apr 1 2003
Event	Statphys - Taiwan - 2002: Lattice Models and Complex Systems - Taipei and Taichung, Taiwan, Province of China Duration: May 26 2002 → Jun 1 2002

All Science Journal Classification (ASJC) codes

Statistics and Probability
Condensed Matter Physics

Keywords

Exact solution
Hubbard model
One dimension

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10.1016/S0378-4371(02)01785-5

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title = "The one-dimensional Hubbard model: A reminiscence",

abstract = "In 1968 we published the solution of the ground state energy and wave function of the one-dimensional Hubbard model, and we also showed that there is no Mott transition in this model. Details of the analysis have never been published, however. As the Hubbard model has become increasingly important in condensed matter physics, relating to topics such as the theory of high-Tc superconductivity, it is appropriate to revisit the one-dimensional model and to recall here some details of the solution.",

keywords = "Exact solution, Hubbard model, One dimension",

author = "Lieb, {Elliott H.} and Wu, {F. Y.}",

note = "Funding Information: We are indebted to Daniel Mattis for encouraging us to investigate the jump in the chemical potential as an indicator of the insulator–conductor transition. We also thank Helen Au-Yang and Jacques Perk for helpful discussions. FYW would like to thank Dung-Hai Lee for the hospitality at the University of California at Berkeley and Ting-Kuo Lee for the hospitality at the National Center for Theoretical Sciences, Taiwan, where part of this work was carried out. Work has been supported in part by NSF grants PHY-0139984, DMR-9980440 and DMR-9971503. ; Statphys - Taiwan - 2002: Lattice Models and Complex Systems ; Conference date: 26-05-2002 Through 01-06-2002",

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T2 - Statphys - Taiwan - 2002: Lattice Models and Complex Systems

AU - Lieb, Elliott H.

AU - Wu, F. Y.

N1 - Funding Information: We are indebted to Daniel Mattis for encouraging us to investigate the jump in the chemical potential as an indicator of the insulator–conductor transition. We also thank Helen Au-Yang and Jacques Perk for helpful discussions. FYW would like to thank Dung-Hai Lee for the hospitality at the University of California at Berkeley and Ting-Kuo Lee for the hospitality at the National Center for Theoretical Sciences, Taiwan, where part of this work was carried out. Work has been supported in part by NSF grants PHY-0139984, DMR-9980440 and DMR-9971503.

PY - 2003/4/1

Y1 - 2003/4/1

N2 - In 1968 we published the solution of the ground state energy and wave function of the one-dimensional Hubbard model, and we also showed that there is no Mott transition in this model. Details of the analysis have never been published, however. As the Hubbard model has become increasingly important in condensed matter physics, relating to topics such as the theory of high-Tc superconductivity, it is appropriate to revisit the one-dimensional model and to recall here some details of the solution.

AB - In 1968 we published the solution of the ground state energy and wave function of the one-dimensional Hubbard model, and we also showed that there is no Mott transition in this model. Details of the analysis have never been published, however. As the Hubbard model has become increasingly important in condensed matter physics, relating to topics such as the theory of high-Tc superconductivity, it is appropriate to revisit the one-dimensional model and to recall here some details of the solution.

KW - Exact solution

KW - Hubbard model

KW - One dimension

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M3 - Conference article

AN - SCOPUS:0037380795

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VL - 321

SP - 1

EP - 27

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1-2

Y2 - 26 May 2002 through 1 June 2002

ER -

The one-dimensional Hubbard model: A reminiscence

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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