## Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. LiebThis is the third Selecta of publications of Elliott Lieb, the first two being Stabil ity of Matter: From Atoms to Stars, edited by Walter Thirring, and Inequalities, edited by Michael Loss and Mary Beth Ruskai. A companion fourth Selecta on Statistical Mechanics is also edited by us. Elliott Lieb has been a pioneer of the discipline of mathematical physics as it is nowadays understood and continues to lead several of its most active directions today. For the first part of this selecta we have made a selection of Lieb's works on Condensed Matter Physics. The impact of Lieb's work in mathematical con densed matter physics is unrivaled. It is fair to say that if one were to name a founding father of the field, Elliott Lieb would be the only candidate to claim this singular position. While in related fields, such as Statistical Mechanics and Atomic Physics, many key problems are readily formulated in unambiguous mathematical form, this is less so in Condensed Matter Physics, where some say that rigor is "probably impossible and certainly unnecessary". By carefully select ing the most important questions and formulating them as well-defined mathemat ical problems, and then solving a good number of them, Lieb has demonstrated the quoted opinion to be erroneous on both counts. What is true, however, is that many of these problems turn out to be very hard. It is not unusual that they take a decade (even several decades) to solve. |

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### Contents

i | |

Proof of the Peierls Instability in One Dimension with T Kennedy | 85 |

Affleck T Kennedy and H Tasaki | 253 |

E Thomas | 311 |

Bose Gas | 325 |

Some of the Early History of Exactly Soluble Models | 439 |

of TwoDimensional Ice | 449 |

of a Ferroelectric | 457 |

Ising and Dimer Models | 520 |

The Excitation Spectrum | 617 |

Selecta of Elliott H Lieb | 655 |

### Other editions - View all

Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. Lieb Elliott H. Lieb No preview available - 2010 |

Condensed Matter Physics and Exactly Soluble Models: Selecta of Elliott H. Lieb Elliott H. Lieb No preview available - 2014 |

### Common terms and phrases

antiferromagnetic asymptotic atoms bipartite Bose gas Bose–Einstein condensation bosons boundary conditions calculation chain classical commute configuration consider constant correlation function corresponding defined denote density diagonal dimensions dimerized E. H. Lieb eigenstate eigenvalues electrons Elliott H equations excitation fermions ferromagnetism finite flux free energy given graph ground state energy ground-state half-filled band Hamiltonian Heisenberg Heisenberg model Hubbard model inequality infinite integral interaction Ising model J.P. SOLOVEJ kinetic energy laser lattice Lemma Lett linear long-range order lower bound magnetic MANY-BODY PROBLEM Math mathematical Mattis Néel order obtained one-dimensional operators pair parameter particle number phase transition Phys Physics positive potential proof prove quantum mechanical result rigorous satisfies SEIRINGER solution subspace symmetry temperature Theorem theory thermodynamic limit tion total spin transfer matrix transformation two-dimensional unique Valence Bond vector wave function XY model Yngvason zero