The TF Limit for Rapidly Rotating Bose Gases in Anharmonic Traps

Starting from the full many body Hamiltonian we derive the leading order energy and density asymptotics for the ground state of a dilute, rotating Bose gas in an anharmonic trap in the ` Thomas Fermi' (TF) limit when the Gross-Pitaevskii coupling parameter and/or the rotation velocity tend to infinity. Although the many-body wave function is expected to have a complicated phase, the leading order contribution to the energy can be computed by minimizing a simple functional of the density alone

The Ground States of Large Quantum Dots in Magnetic Fields

The quantum mechanical ground state of a 2D $N$-electron system in a confining potential $V(x)=Kv(x)$ ($K$ is a coupling constant) and a homogeneous magnetic field $B$ is studied in the high density limit $N\to\infty$, $K\to \infty$ with $K/N$ fixed. It is proved that the ground state energy and electronic density can be computed {\it exactly} in this limit by minimizing simple functionals of the density. There are three such functionals depending on the way $B/N$ varies as $N\to\infty$: A 2D Thomas-Fermi (TF) theory applies in the case $B/N\to 0$; if $B/N\to{\rm const.}\neq 0$ the correct limit theory is a modified $B$-dependent TF model, and the case $B/N\to\infty$ is described by a ``classical'' continuum electrostatic theory. For homogeneous potentials this last model describes also the weak coupling limit $K/N\to 0$ for arbitrary $B$. Important steps in the proof are the derivation of a new Lieb-Thirring inequality for the sum of eigenvalues of single particle Hamiltonians in 2D with magnetic fields, and an estimation of the exchange-correlation energy. For this last estimate we study a model of classical point charges with electrostatic interactions that provides a lower bound for the true quantum mechanical energy.Comment: 57 pages, Plain tex, 5 figures in separate uufil

Quantum shock waves in the Heisenberg XY model

We show the existence of quantum states of the Heisenberg XY chain which closely follow the motion of the corresponding semi-classical ones, and whose evolution resemble the propagation of a shock wave in a fluid. These states are exact solutions of the Schroedinger equation of the XY model and their classical counterpart are simply domain walls or soliton-like solutions.Comment: 15 pages,6 figure

The ground state of a general electron-phonon Hamiltonian is a spin singlet

The many-body ground state of a very general class of electron-phonon Hamiltonians is proven to contain a spin singlet (for an even number of electrons on a finite lattice). The phonons interact with the electronic system in two different ways---there is an interaction with the local electronic charge and there is a functional dependence of the electronic hopping Hamiltonian on the phonon coordinates. The phonon potential energy may include anharmonic terms, and the electron-phonon couplings and the hopping matrix elements may be nonlinear functions of the phonon coordinates. If the hopping Hamiltonian is assumed to have no phonon coordinate dependence, then the ground state is also shown to be unique, implying that there are no ground-state level crossings, and that the ground-state energy is an analytic function of the parameters in the Hamiltonian. In particular, in a finite system any self-trapping transition is a smooth crossover not accompanied by a nonanalytical change in the ground state. The spin-singlet theorem applies to the Su-Schrieffer-Heeger model and both the spin-singlet and uniqueness theorems apply to the Holstein and attractive Hubbard models as special cases. These results hold in all dimensions --- even on a general graph without periodic lattice structure.Comment: 25 pages, no figures, plainte

Onsager's Inequality, the Landau-Feynman Ansatz and Superfluidity

We revisit an inequality due to Onsager, which states that the (quantum) liquid structure factor has an upper bound of the form (const.) x |k|, for not too large modulus of the wave vector k. This inequality implies the validity of the Landau criterion in the theory of superfluidity with a definite, nonzero critical velocity. We prove an auxiliary proposition for general Bose systems, together with which we arrive at a rigorous proof of the inequality for one of the very few soluble examples of an interacting Bose fluid, Girardeau's model. The latter proof demonstrates the importance of the thermodynamic limit of the structure factor, which must be taken initially at k different from 0. It also substantiates very well the heuristic density functional arguments, which are also shown to hold exactly in the limit of large wave-lengths. We also briefly discuss which features of the proof may be present in higher dimensions, as well as some open problems related to superfluidity of trapped gases.Comment: 28 pages, 2 figure, uses revtex

Comment on "Kagome Lattice Antiferromagnet Stripped to Its Basics"

Density matrix renormalization group (DMRG) calculations on large systems (up to 3096 spins) indicate that the ground state of the Heisenberg model on a 3-chain Kagome strip is spontaneously dimerized. This system has degenerate ground states and a gap to triplet and singlet excitations. These results are in direct contradiction with recent results of Azaria et al (Phys. Rev. Lett. 81, 1694 (1998)) and suggest a need for a reexamination of the underlying field theory.Comment: 1 page, submitted to PR

Exact particle and kinetic energy densities for one-dimensional confined gases of non-interacting fermions

We propose a new method for the evaluation of the particle density and kinetic pressure profiles in inhomogeneous one-dimensional systems of non-interacting fermions, and apply it to harmonically confined systems of up to N=1000 fermions. The method invokes a Green's function operator in coordinate space, which is handled by techniques originally developed for the calculation of the density of single-particle states from Green's functions in the energy domain. In contrast to the Thomas-Fermi (local density) approximation, the exact profiles under harmonic confinement show negative local pressure in the tails and a prominent shell structure which may become accessible to observation in magnetically trapped gases of fermionic alkali atoms.Comment: 8 pages, 3 figures, accepted for publication in Phys. Rev. Let

Ground state energy of the low density Hubbard model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani, our result proves that in the low density limit, the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by $8\pi a \rho_u \rho_d$, where $\rho_{u(d)}$ denotes the density of the spin-up (down) particles, and $a$ is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.Comment: LaTeX2e, 18 page

Incremental expansions for Hubbard-Peierls systems

The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated combining incremental expansion with exact diagonalization of finite chain segments. The ground state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than $3 \cdot 10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site) chain segm ents. For dimerized chains the dimerization order parameter $d$ as a function of the onsite repulsion interaction $U$ has a maximum at nonzero values of $U$, if the electron-phonon coupling $g$ is lower than a critical value $g_c$. The critical value $g_c$ is found with high accuracy to be $g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.Comment: 4 Pages, 3 Figures, REVTE

Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases

This is a continuation of the papers [4] of Bleher and Fokin and [5] of Bleher and Liechty, in which the large $n$ asymptotics is obtained for the partition function $Z_n$ of the six-vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, respectively. In the present paper we obtain the large $n$ asymptotics of $Z_n$ on the critical line between these two phases.Comment: 22 pages, 6 figures, to appear in the Journal of Statistical Physic