539 citations · 6.8k across the 160 of their papers we have counts for
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Columnar Phase in Quantum Dimer Models
Alessandro Giuliani, Elliott H. Lieb
The quantum dimer model, relevant for short-range resonant valence bond physics, is rigorously shown to have long range order in a crystalline phase in the attractive case at low t…
Realization of stripes and slabs in two and three dimensions
Alessandro Giuliani, Elliott H. Lieb, Robert Seiringer
We consider Ising models in two and three dimensions with nearest neighbor ferromagnetic interactions and long range, power law decaying, antiferromagnetic interactions. If the str…
Checkerboards, stripes and corner energies in spin models with competing interactions
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
We study the zero temperature phase diagram of Ising spin systems in two dimensions in the presence of competing interactions, long range antiferromagnetic and nearest neighbor fer…
Modulated phases of a 1D sharp interface model in a magnetic field
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
We investigate the ground states of 1D continuum models having short-range ferromagnetic type interactions and a wide class of competing longer-range antiferromagnetic type interac…
Pattern formation in systems with competing interactions
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
There is a growing interest, inspired by advances in technology, in the low temperature physics of thin films. These quasi-2D systems show a wide range of ordering effects includin…
Striped phases in two dimensional dipole systems
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
We prove that a system of discrete 2D in-plane dipoles with four possible orientations, interacting via a 3D dipole-dipole interaction plus a nearest neighbor ferromagnetic term, h…
The Mathematics of the Bose Gas and its Condensation
Elliott H. Lieb, Robert Seiringer, Jan Philip Solovej +1
This book surveys results about the quantum mechanical many-body problem of the Bose gas that have been obtained by the authors over the last seven years. These topics are relevant…
Ising models with long-range dipolar and short-range ferromagnetic interactions
Alessandro Giuliani, Joel L. Lebowitz, Elliott H. Lieb
We study the ground state of a --dimensional Ising model with both long range (dipole--like) and nearest neighbor ferromagnetic (FM) interactions. The long range interaction is…
Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
M. Aizenman, E. H. Lieb, R. Seiringer +2
One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state compose…
Bose-Einstein Quantum Phase Transition in an Optical Lattice Model
Michael Aizenman, Elliott H. Lieb, Robert Seiringer +2
Bose-Einstein condensation (BEC) in cold gases can be turned on and off by an external potential, such as that presented by an optical lattice. We present a model of this phenomeno…
One-dimensional Bosons in Three-dimensional Traps
Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
Recent experimental and theoretical work has indicated conditions in which a trapped, low-density Bose gas ought to behave like the 1D delta-function Bose gas solved by Lieb and Li…
Polarization of interacting bosons with spin
Eli Eisenberg, Elliott H. Lieb
We demonstrate rigorously that in the absence of explicit spin-dependent forces one of the ground states of interacting bosons with spin is always fully polarized -- however compli…
Ground State Energy of the One-Component Charged Bose Gas
Elliott H. Lieb, Jan Philip Solovej
The model considered here is the `jellium' model in which there is a uniform, fixed background with charge density in a large volume and in which particles of elec…
A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas
Elliott H. Lieb, Robert Seiringer, Jakob Yngvason
We consider the ground state properties of an inhomogeneous two-dimensional Bose gas with a repulsive, short range pair interaction and an external confining potential. In the limi…
Stability of Relativistic Matter With Magnetic Fields
Elliott H. Lieb, Heinz Siedentop, Jan Philip Solovej
Stability of matter with Coulomb forces has been proved for non-relativistic dynamics, including arbitrarily large magnetic fields, and for relativistic dynamics without magnetic f…
Stability of Matter in Magnetic Fields
Elliott Lieb
The proof of the stability of matter is three decades old, but the question of stability when arbitrarily large magnetic fields are taken into account was settled only recently. Ev…
Stability and Instability of Relativistic Electrons in Classical Electro magnetic Fields
Elliott H. Lieb, Heinz Siedentop, Jan Philip Solovej
The stability of matter composed of electrons and static nuclei is investigated for a relativistic dynamics for the electrons given by a suitably projected Dirac operator and with…