Density of states near the Mott-Hubbard transition in the limit of large dimensions

The zero temperature Mott-Hubbard transition as a function of the Coulomb repulsion U is investigated in the limit of large dimensions. The behavior of the density of states near the transition at U=U_c is analyzed in all orders of the skeleton expansion. It is shown that only two transition scenarios are consistent with the skeleton expansion for U<U_c: (i) The Mott-Hubbard transition is "discontinuous" in the sense that in the density of states finite spectral weight is redistributed at U_c. (ii) The transition occurs via a point at U=U_c where the system is neither a Fermi liquid nor an insulator.Comment: 4 pages, 1 figure; revised version accepted for publication in Phys. Rev. Let

A Mean Field Analysis of One Dimensional Quantum Liquid with Long Range Interaction

Bi-local mean field theory is applied to one dimensional quantum liquid with long range $1/r^2$ interaction, which has exact ground state wave function. We obtain a mean field solution and an effective action which expresses a long range dynamics. Based on them the ground state energy and correlation functions are computed. The ground state energy agrees fairly well with the exact value and exponents have weaker coupling constant dependence than that of partly known exact value.Comment: EPHOU-93-002, 10 pages (LaTeX), 3 figures available upon request as hard cop

Nuclear spin-orbit interaction from chiral pion-nucleon dynamics

Using the two-loop approximation of chiral perturbation theory, we calculate the momentum and density dependent nuclear spin-orbit strength $U_{ls}(p,k_f)$. This quantity is derived from the spin-dependent part of the interaction energy $\Sigma_{spin} = {i\over 2} \vec \sigma \cdot (\vec q \times\vec p) U_{ls}(p,k_f)$ of a nucleon scattering off weakly inhomogeneous isospin symmetric nuclear matter. We find that iterated $1\pi$-exchange generates at saturation density, $k_{f0}=272.7$MeV, a spin-orbit strength at $p=0$ of $U_{ls}(0,k_{f0})\simeq 35$ MeVfm$^2$ in perfect agreement with the empirical value used in the shell model. This novel spin-orbit strength is neither of relativistic nor of short range origin. The potential $V_{ls}$ underlying the empirical spin-orbit strength $\widetilde U_{ls}= V_{ls} r_{ls}^2$ becomes a rather weak one, $V_{ls}\simeq 17$ MeV, after the identification $r_{ls}= m_\pi^{-1}$ as suggested by the present calculation. We observe however a strong $p$-dependence of $U_{ls}(p,k_{f0})$ leading even to a sign change above $p=200$MeV. This and other features of the emerging spin-orbit Hamiltonian which go beyond the usual shell model parametrization leave questions about the ultimate relevance of the spin-orbit interaction generated by $2\pi$-exchange for a finite nucleus. We also calculate the complex-valued isovector single-particle potential $U_I(p,k_f)+ i W_I(p,k_f)$ in isospin asymmetric nuclear matter proportional to $\tau_3 (N-Z)/(N+Z)$. For the real part we find reasonable agreement with empirical values and the imaginary part vanishes at the Fermi-surface $p=k_f$.Comment: 20 pages, 10 Figures, Accepted for publication in Nuclear Physics

Diagrammatic theory for Periodic Anderson Model: Stationary property of the thermodynamic potential

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of $f-$ localized electrons as a main parameter of the theory. $f-$ electrons are strongly correlated and $c-$ conduction electrons are uncorrelated. Correlation function for $f-$ and mass operator for $c-$ electrons are determined. The Dyson equation for $c-$ and Dyson-type equation for $f-$ electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential about the variation of the mass operator is established. The result is appropriate as for normal and as for superconducting state of the system.Comment: 12 pages, 10 figure

Conserving Gapless Mean-Field Theory for Bose-Einstein Condensates

We formulate a conserving gapless mean-field theory for Bose-Einstein condensates on the basis of a Luttinger-Ward thermodynamic functional. It is applied to a weakly interacting uniform gas with density $n$ and s-wave scattering length $a$ to clarify its fundamental thermodynamic properties. It is found that the condensation here occurs as a first-order transition. The shift of the transition temperature $\Delta T_c$ from the ideal-gas result $T_{0}$ is positive and given to the leading order by $\Delta T_c = 2.33a n^{1/3}T_0$, in agreement with a couple of previous estimates. The theory is expected to form a new theoretical basis for trapped Bose-Einstein condensates at finite temperatures.Comment: Minor errors remove

Non-perturbative approach to Luttinger's theorem in one dimension

The Lieb-Schultz-Mattis theorem for spin chains is generalized to a wide range of models of interacting electrons and localized spins in one-dimensional lattice. The existence of a low-energy state is generally proved except for special commensurate fillings where a gap may occur. Moreover, the crystal momentum of the constructed low-energy state is $2k_F$, where $k_F$ is the Fermi momentum of the non-interacting model, corresponding to Luttinger's theorem. For the Kondo lattice model, our result implies that $k_F$ must be calculated by regarding the localized spins as additional electrons.Comment: Note added on the rigorous proof given by H. Tasaki; also added some references; 5 pages, REVTEX (no figure

Consistency of Wilsonian effective actions

Wilsonian effective actions are interpreted as free energies in ensembles with prescribed field expectation values and prescribed connected two-point functions. Since such free energies are directly obtained from two-particle-irreducible functionals, it follows that Wilsonian effective actions satisfy elementary perturbative consistency conditions, and non-perturbative convexity conditions. In particular, the exact determination of a Wilsonian action by other means (e.g. supersymmetry) allows one to extract restrictions on the particular cutoff scheme and field reparametrization that would lead to such a Wilsonian action from an underlying microscopic action.Comment: 3 pages, RevTe

Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.Comment: 19 pages, 5 figures. accepted to Int. J. Mod. Phys. B (April 2006

Uncertainty Principle and Off-Diagonal Long Range Order in the Fractional Quantum Hall Effect

A natural generalization of the Heisenberg uncertainty principle inequality holding for non hermitian operators is presented and applied to the fractional quantum Hall effect (FQHE). This inequality was used in a previous paper to prove the absence of long range order in the ground state of several 1D systems with continuous group symmetries. In this letter we use it to rule out the occurrence of Bose-Einstein condensation in the bosonic representation of the FQHE wave function proposed by Girvin and MacDonald. We show that the absence of off-diagonal long range order in this 2D problem is directly connected with the $q^2$ behavior of the static structure function $S(q)$ at small momenta.Comment: 10 pages, plain TeX, UTF-09-9

The absence of finite-temperature phase transitions in low-dimensional many-body models: a survey and new results

After a brief discussion of the Bogoliubov inequality and possible generalizations thereof, we present a complete review of results concerning the Mermin-Wagner theorem for various many-body systems, geometries and order parameters. We extend the method to cover magnetic phase transitions in the periodic Anderson Model as well as certain superconducting pairing mechanisms for Hubbard films. The relevance of the Mermin-Wagner theorem to approximations in many-body physics is discussed on a conceptual level.Comment: 33 pages; accepted for publication as a Topical Review in Journal of Physics: Condensed Matte