Bosonization Method Research Articles

An Impurity in One-Dimensional Interacting Fermion System11The project, supported by National Natural Science Foundation of China

The bosonization method is applied to the problem of the one-dimensional interacting fermion system with an impurity. The phase transition at zero temperature of this system is investigated by the renormalization group method.

The Extended Conformal Theory of Luttinger Systems

We described the recently introduced method of algebraic bosonization of the (1 + 1)-dimensional Luttinger systems by discussing in detail the specific case of the Calogero–Sutherland model, and mentioning the treatment of the hard-core Bose gas. We also compare our findings with the exact Bethe Ansatz results.

A study of quasi-one-dimensional conductors based on two coupled chains

Based on the bosonization method, we show that the phase transition between SDW and superconductivity of the quasione-dimensional organic conductors can be understood by the crossover in the two coupled chains. Further, remarkable behaviors of the charge and spin susceptibilities with the transverse wavenumber τ are calculated as a function of the longitudinal wavenumber and the frequency.

Bosonization Approach to the One-Dimensional Kondo Lattice Model at Half Filling: Reexamination

Low-energy properties of the one-dimensional Kondo lattice model are investigated by using bosonization and renormalization group methods. The formation of the spin and charge excitation gaps at half-filling is discussed in detail both for antiferromagnetic and ferromagnetic Kondo couplings. Also, the effect of the interaction between conduction electrons on the gap formation is studied both for the Kondo insulating phase and for the Haldane gap phase. It is found that while the repulsive interaction changes the dependence of the excitation gap on the Kondo exchange coupling, the attractive interaction can drive the Kondo (or Haldane) insulating phase to a completely different phase of massless metallic states.

THE BOSONIZATION FORM AND NEW CRITICAL REGION OF THE QUANTUM ASHKIN-TELLER CHAIN

In the continuum limit, the critical phenomenon of the quantum Ashkin-Teller(A-T) chain is discussed by the bosonization method. A new critical region of the A-T chain besides the Ising decoupling point has been found.

Solvable model for an impurity spin coupled to a one-dimensional superconductor.

A solvable model for a magnetic impurity in a one-dimensional superconductor is proposed. The model consists of the impurity spin coupled to the edge of a quantum wire. The electron gas in the wire is dominated by attractive mutual interactions and forms a gapped state with a short-range superconducting order. In a restricted (but nontrivial) region of parameters, the model is solved by means of bosonization methods. The spectrum and thermodynamic functions are calculated. \textcopyright{} 1996 The American Physical Society.

Superconducting Proximity Effect on a One-Dimensional Interacting Electron Gas

A one-dimensional interacting electron gas (N) in contact with a bulk superconductor (S) is studied theoretically using a bosonization method. We calculate various correlation functions in the case of the complete Andreev reflection at zero temperature. It is found that a tendency towards singlet superconductivity is enhanced in the vicinity of the NS interface, while spin-density-wave correlation is shown to be suppressed. We calculate the conductance of the NS interface in the presence of a barrier potential. This interface conductance shows relatively strong temperature dependence compared with conductance through a single barrier in the absence of the proximity effect. This is a manifestation of interplay between the proximity effect and the mutual interaction.

Superconducting properties of the attractive Hubbard model: A slave-boson study.

The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.

Aspects of the normal-state phase of copper oxide planes in high-Tc superconductors.

We examine various aspects of the normal-state phase of Cu${\mathrm{O}}_{2}$ planes in the high-${T}_{c}$ superconductors. In particular, within the context of the three band Hubbard model, we study as a function of doping the competition between a charge density wave phase induced by oxygen breathing modes, antiferromagnetic order, and paramagnetism. To account for the strong electronic interactions, we use the finite $U$ slave boson method of Kotliar and Ruckenstein.

Pion Observables in the Extended NJL Model with Vector and Axial-Vector Mesons

The momentum-space bosonization method of a Nambu and Jona-Lasinio type model with vector and axial-vector mesons is applied toππscattering. Unlike the case in earlier published papers, we obtain theππscattering amplitude using the linear and nonlinear realizations of chiral symmetry and fully taking into account the momentum dependence of meson vertices. We show the full physical equivalence between these two approaches. The chiral expansion procedure in this model is discussed in detail. Chiral expansions of the quark mass, pion mass and constantfπare obtained. The low-energyππphase shifts are compared to the available data. We also study the scalar form factor of the pion.

Toulouse points and non-Fermi-liquid states in the mixed-valence regime of the generalized Anderson model.

We study the mixed valence regime of a generalized Anderson impurity model using the bosonization approach. This single impurity problem is defined by the $U=\infty$ Anderson model with an additional density-density interaction, as well as an explicit exchange interaction, between the impurity and conduction electrons. We find three points in the interaction parameter space at which all the correlation functions can be calculated explicitly. These points represent the mixed valence counterparts of the ususal Toulouse point for the Kondo problem, and are appropriately named the Toulouse points of the mixed valence problem. Two of the Toulouse points exhibit the strong coupling, Fermi liquid behavior. The third one shows spin-charge separation; here, the spin-spin correlation functions are Fermi-liquid-like, the charge-charge correlation functions and the single particle Green function have non-Fermi-liquid behaviors, and a pairing correlation function is enhanced compared to the Fermi liquid case. This third Toulouse point describes the novel intermediate mixed valence phase we have previously identified. In deriving these results, we emphasize the importance of keeping track of the anticommutation relation between the fermion fields when the bosonization method is applied to quantum impurity problems.

Critical properties of the transition between the Haldane phase and the large-Dphase of the spin- ferromagnetic - antiferromagnetic Heisenberg chain with on-site anisotropy

We analytically study the ground-state quantum phase transition between the Haldane phase and the large-$D$ (LD) phase of the $S=1/2$ ferromagnetic-antiferromagnetic alternating Heisenberg chain with on-site anisotropy. We transform this model into a generalized version of the alternating antiferromagnetic Heisenberg model with anisotropy. In the transformed model, the competition between the transverse and longitudinal bond alternations yields the Haldane-LD transition. Using the bosonization method, we show that the critical exponents vary continuously on the Haldane-LD boundary. Our scaling relations between critical exponents very well explains the numerical results by Hida.

Dirac fermions with disorder in two dimensions: Exact results.

Dirac fermions on a two-dimensional lattice with disorder are considered. The Dirac mass, which controls the gap between the two bands of the fermions, is subject to random fluctuations. Another type of disorder is discussed presented by a random vector potential. It is shown that the imaginary part of the one-particle Green's function can be written as the imaginary part of another Green's function which has only poles on the lower half-plane. Therefore, it is possible to perform a Cauchy integration for a Lorentzian distribution in analogy with the Lloyd model. The results are compared with calculations performed in the continuum limit based on renormalization group and bosonization methods.

Boundary effects on spectral properties of interacting electrons in one dimension.

The single electron Green's function of the one-dimensional Tomonaga-Luttinger model in the presence of open boundaries is calculated with bosonization methods. We show that the critical exponents of the local spectral density and of the momentum distribution change in the presence of a boundary. The well understood universal bulk behavior always crosses over to a boundary dominated regime for small energies or small momenta. We show this crossover explicitly for the large-U Hubbard model in the low-temperature limit. Consequences for photoemission experiments are discussed.

Electron-phonon induced superconductivity in correlated systems

The issue of electron—phonon induced superconductivity in strongly correlated systems has been discussed. To treat correlation and strong coupling effects we use slave boson method in theU=∞ limit and Eliashberg type of theory. Short range Coulomb interactions severally modify Eliashberg equations making possibles, p andd—wave symmetry of the order parameter. At hole dopings δ≤0.3 andd—wave component of the coupling constant is the largest one.

Two kinds of phase transition in 1-D backward scattering

The one-dimensional Fermion system with backward scattering has been analyzed by use of the methods of bosonization and Gaussian wave functional. We find that there exist two kinds of phase transitions in the spin density degree according to the interaction parameters: one is a Kosterlitz-Thouless type transition and the other is a first order phase transition when backward scattering becomes sufficiently strong.

Gap-formation mechanism of the Kondo-necklace model.

We investigate a gap-formation mechanism of the one-dimensional Kondo-necklace model at zero temperature. An analytic treatment using the bosonization method shows that the model undergoes the Kosterlitz-Thouless transition at the critical coupling ${J}_{c}=0$, which is described by the quantum sine-Gordon model. This result is contrary to the previous investigations on the ground-state phase transition, where some finite critical coupling values have been predicted. To clarify the validity of our analytic calculation result, we estimate the singlet-triplet gap by employing White's density matrix renormalization group method; the numerical calculation is carried out for the systems up to 200 sites with open boundary condition. As a result, we find that the excitation gap observed in the large $J$ region becomes smaller quickly with the decrease of $J$. However, the data show the existence of a small gap for $Jg~0.25$, which seems to support ${J}_{c}=0$.

Numerical Study on the Ground-State Phase Diagram of theS=1/2 XXZ Ladder Model

The ground-state phase diagram of the S =1/2 X X Z ladder model is investigated by using the density-matrix renormalization-group method. This model is composed of two S =1/2 X X Z chains with ferromagnetic rung couplings (λ) and intra-chain anisotropy (Δ), and continuously changes from the two independent S =1/2 X X Z chains at λ=0 to the S =1 X X Z chain in the limit of λ→∞ . It is shown that there exist edge states at Δ=1 and λ=1 in relation to the four-fold degeneracy of the ground state and that an excitation gap opens nearly at λ=0 for 0.8≤Δ≤1. In addition, it is clarified that the transition between the Haldane phase and the antiferromagnetic phase occurs at λ=1.15 ±0.01 for Δ=1. A possible phase diagram in the λ-Δ plane is proposed, which is consistent with the scaling analysis based on the bosonization method.

Critical exponents of the one-dimensional continuum Heisenberg-Ising model

The continuum generalization of the one-dimensional Heisenberg-Ising model is studied by the bosonization method. With reference to the results of the renormalization group theory, we are able to obtain the critical exponents by considering the influence of the large momentum transfer and improve Luther and Peschel's results to the next order. A comparison of the exact result of the lattice model with that of the continuum model by various treatments are also given.

Roles of Interchain Hopping in Two Coupled Chains of Tomonaga Model

Two chains of interacting spinless fermions in the presence of interchain hopping are investigated by use of phase Hamiltonian based on bosonization method. Excitation spectrum and phase diagram at absolute zero temperature are obtained by means of renormalization group method. Momentum distribution functions are also calculated. It is shown that the interchain hopping gives rise to drastic effects on properties of ground state compared to interchain interaction and is crucial to appearance of ordered states in higher dimensions.