Crossover from Luttinger liquid to Coulomb blockade regime in carbon nanotubes

We develop a theoretical approach to the low-energy properties of 1D electron systems aimed to encompass the mixed features of Luttinger liquid and Coulomb blockade behavior observed in the crossover between the two regimes. For this aim we extend the Luttinger liquid description by incorporating the effects of a discrete single-particle spectrum. The intermediate regime is characterized by a power-law behavior of the conductance, but with an exponent oscillating with the gate voltage, in agreement with recent experimental observations. Our construction also accounts naturally for the existence of a crossover in the zero-bias conductance, mediating between two temperature ranges where the power-law behavior is preserved but with different exponent.Comment: 5 pages, 3 figure

Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain

The exact amplitude for the asymptotic correlation function in the S=1/2 Heisenberg antiferromagnetic chain is determined: goes to (-1)^r delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function are also analysed.Comment: 8 pages, 3 figures, added reference and discussio

Effect of Inter-Site Repulsions on Magnetic Susceptibility of One-Dimensional Electron Systems at Quarter-Filling

The temperature dependence of the magnetic susceptibility, \chi (T), is investigated for one-dimensional interacting electron systems at quarter-filling within the Kadanoff-Wilson renormalization-group method. The forward scattering on the same branch (the g_4-process) is examined together with the backward (g_1) and forward (g_2) scattering amplitudes on opposite branches. In connection with lattice models, we show that \chi (T) is strongly enhanced by the nearest-neighbor interaction, an enhancement that surpasses one of the next-nearest-neighbor interaction. A connection between our predictions for \chi (T) and experimental results for \chi (T) in quasi-one-dimensional organic conductors is presented.Comment: 4 pages, 4 figures, to be published in Journal of the Physical Society of Japan, vol. 74, No. 1

Coulomb Gaps in One-Dimensional Spin-Polarized Electron Systems

We investigate the density of states (DOS) near the Fermi energy of one-dimensional spin-polarized electron systems in the quantum regime where the localization length is comparable to or larger than the inter-particle distance. The Wigner lattice gap of such a system, in the presence of weak disorder, can occur precisely at the Fermi energy, coinciding with the Coulomb gap in position. The interplay between the two is investigated by treating the long-range Coulomb interaction and the random disorder potential in a self-consistent Hartree-Fock approximation. The DOS near the Fermi energy is found to be well described by a power law whose exponent decreases with increasing disorder strength.Comment: 4 pages, revtex, 4 figures, to be published in Phys. Rev. B as a Rapid Communicatio

Solitonic excitations in the Haldane phase of a S=1 chain

We study low-lying excitations in the 1D $S=1$ antiferromagnetic valence-bond-solid (VBS) model. In a numerical calculation on finite systems the lowest excitations are found to form a discrete triplet branch, separated from the higher-lying continuum. The dispersion of these triplet excitations can be satisfactorily reproduced by assuming approximate wave functions. These wave functions are shown to correspond to moving hidden domain walls, i.e. to one-soliton excitations.Comment: RevTex 3.0, 24 pages, 2 figures on request by fax or mai

Entanglement and quantum phase transition in the extended Hubbard model

We study quantum entanglement in one-dimensional correlated fermionic system. Our results show, for the first time, that entanglement can be used to identify quantum phase transitions in fermionic systems.Comment: 5 pages, 4 figure

Effects of Umklapp Scattering on Electronic States in One Dimension

The effects of Umklapp scattering on electronic states are studied in one spatial dimension at absolute zero. The model is basically the Hubbard model, where parameters characterizing the normal ($U$) and Umklapp ($V$) scattering are treated independently. The density of states is calculated in the t-matrix approximation by taking only the forward and Umklapp scattering into account. It is found that the Umklapp scattering causes the global splitting of the density of states. In the presence of sufficiently strong Umklapp scattering, a pole in the t-matrix appears in the upper half plane, signalling an instability towards the '$G/2-$pairing' ordered state ($G$ is the reciprocal lattice vector), whose consequences are studied in the mean field approximation. It turns out that this ordered state coexists with spin-density-wave state and also brings about Cooper-pairs. A phase diagram is determined in the plane of $V$ and electron filling $n$.Comment: 22 pages, LaTeX, 17 figures included, uses jpsj.st

Interacting Electrons on a Square Fermi Surface

Electronic states near a square Fermi surface are mapped onto quantum chains. Using boson-fermion duality on the chains, the bosonic part of the interaction is isolated and diagonalized. These interactions destroy Fermi liquid behavior. Non-boson interactions are also generated by this mapping, and give rise to a new perturbation theory about the boson problem. A case with strong repulsions between parallel faces is studied and solved. There is spin-charge separation and the square Fermi surface remains square under doping. At half-filling, there is a charge gap and insulating behavior together with gapless spin excitations. This mapping appears to be a general tool for understanding the properties of interacting electrons on a square Fermi surface.Comment: 25 pages, Nordita preprint 94/22

Bosonization on the lattice: the emergence of the higher harmonics

A general and transparent procedure to bosonize fermions placed on a lattice is presented. Harmonics higher than $k_F$ are shown to appear in the one-paticle Green function, due to the compact character of real electron bands. Quantitative estimations of the role of these higher harmonics are made possible by the bosonization technique presented here.Comment: Pages: 15 (REVTEX 3.0) plus 4 postscript figures appended at the end of the tex