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Floating Wigner crystal with no boundary charge fluctuations
Mathieu Lewin, Elliott H. Lieb, Robert Seiringer
We modify the "floating crystal" trial state for the classical Homogeneous Electron Gas (also known as Jellium), in order to suppress the boundary charge fluctuations that are know…
Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices
Yi Li, Elliott H. Lieb, Congjun Wu
We study itinerant ferromagnetism in multi-orbital Hubbard models in certain two-dimensional square and three-dimensional cubic lattices. In the strong coupling limit where doubly…
Possible Lattice Distortions in the Hubbard Model for Graphene
Rupert L. Frank, Elliott H. Lieb
The Hubbard model on the honeycomb lattice is a well known model for graphene. Equally well known is the Peierls type of instability of the lattice bond lengths. In the context of…
Energy Cost to Make a Hole in the Fermi Sea
Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb +1
The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condense…
Binding, Stability, and Non-binding of Multi-polaron Systems
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer +1
The binding of polarons, or its absence, is an old and subtle topic. After defining the model we state some recent theorems of ours. First, the transition from many-body collapse t…
Stability and Absence of Binding for Multi-Polaron Systems
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer +1
We resolve several longstanding problems concerning the stability and the absence of multi-particle binding for N\geq 2 polarons. Fröhlich's 1937 polaron model describes non-relati…
Bi-Polaron and N-Polaron Binding Energies
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer +1
The binding of polarons, or its absence, is an old and subtle topic. Here we prove two things rigorously. First, the transition from many-body collapse to the existence of a thermo…
Mueller's Exchange-Correlation Energy in Density-Matrix-Functional Theory
Rupert L. Frank, Elliott H. Lieb, Robert Seiringer +1
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the H…
Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation
Volker Bach, Elliott H. Lieb, Marcos V. Travaglia
As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to satura…
The one-dimensional Hubbard model: A reminiscence
E. H. Lieb, F. Y. Wu
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 mod…
Phase separation due to quantum mechanical correlations
J. K. Freericks, E. H. Lieb, D. Ueltschi
Can phase separation be induced by strong electron correlations? We present a theorem that affirmatively answers this question in the Falicov-Kimball model away from half-filling,…