Bosonization Method Research Articles

Aharonov–Bohm effect in one-dimensional systems

With usual bosonization method, we study a single transverse-mode ring with an Aharonov–Bohm flux, and show that the ground state energy and persistent current of the system are periodic functions of the flux with a basic period Φ 0= hc/ e, and depend on the parity of the fermion number. Moreover, we show the persistent current is increasing with the fermion interaction strength in the weak repulsive interaction region, which is different from previous calculations in which the persistent current decreases as increasing the fermion interaction strength.

Dynamical Properties of One-Dimensional Multicomponent Quantum Liquids in Metallic Phase

We investigate low-energy dynamical properties of one-dimensional multicomponent quantum liquids with the short-range interaction as well as the $1/x$-type long-range interaction. By calculating the single-particle spectrum and the dynamical spin susceptibility by means of the bosonization method, we discuss how the orbital degeneracy and the band splitting affect the dynamical response functions. The effect of the long-range interaction is also addressed. Although the long-range interaction suppresses charge fluctuations, it effectively enhances spin fluctuations via the formation of the Wigner crystal.

Thermodynamic potential of the periodic Anderson model with the X-boson method: chain approximation

The Periodic Anderson Model (PAM) in the $U\to\infty$ limit has been studied in a previous work employing the cumulant expansion with the hybridization as perturbation (M. S. Figueira, M. E. Foglio and G. G. Martinez, Phys. Rev. B \textbf{50}, 17933 (1994)). When the total number of electrons $N_{t}$ is calculated as a function of the chemical potential $\mu$ in the ``Chain Approximation'' (CHA), there are three values of the chemical potential $\mu$ for each $N_{t}$ in a small interval of $N_{t}$ at low $T$ (M. S Figueira, M. E Foglio, Physica A 208 (1994)). We have recently introduced the ``X-boson'' method, inspired in the slave boson technique of Coleman, that solves the problem of non conservation of probability (completeness) in the CHA as well as removing the spurious phase transitions that appear with the slave boson method in the mean field approximation. In the present paper we show that the X-boson method solves also the problem of the multiple roots of $N_{t}(\mu)$ that appear in the CHA.

OPTICAL CONDUCTIVITY OF ONE-DIMENSIONAL NARROW-GAP SEMICONDUCTORS

The optical conductivities of two one-dimensional narrow-gap semiconductors, anticrossing quantum Hall edge states and carbon nanotubes, are studied using bosonization method. A lowest order renormalization group analysis indicates that the bare band gap can be treated perturbatively at high frequency/temperature. At very low energy scale the optical conductivity is dominated by the excitonic contribution, while at temperature higher than a crossover temperature the excitonic features are eliminated by thermal fluctuations. In case of carbon nanotubes the crossover temperature scale is estimated to be 300 K.

Soliton Lattice State of Spin- Antiferromagnetic Chain in an External Magnetic Field**The project supported by National Natural Science Foundation of China

One-dimensional spin- anisotropic Heisenberg antiferromagnet in a longitudinal external magnetic field is studied using bosonization method and Gaussian wave functional techniques which take account of the spatial structure. The magnetization and the energy of the ground state which depend on the external magnetic field are calculated. For the case of anisotropic parameter , increasing of the external magnetic field above the threshold value leads to the appearance of the soliton lattice state in the ground state, until to an another critical field where the ground state changes to the canted state phase. Therefore, with increasing external magnetic field, the ground state experiences four different phases successively, namely, antiferromagnetic Ising, soliton lattice state canted state, and magnetization saturated phases. When , the soliton lattice state phase does not appear, with increasing external field, the paramagnetic phase smoothly evolves into the canted state phase, finally reaches magnetization saturated phase.

Hubbard chains network on corner-sharing tetrahedra: Origin of the heavy-fermion state inLiV2O4

We investigate the Hubbard chains network model defined on corner-sharing tetrahedra (the pyrochlore lattice) which is a possible microscopic model for the heavy fermion state of LiV_2O_4. Based upon this model, we can explain transport, magnetic, and thermodynamic properties of LiV_2O_4. We calculate the spin susceptibility, and the specific heat coefficient, exploiting the Bethe ansatz exact solution of the 1D Hubbard model and bosonization method. The results are quite consistent with experimental observations. We obtain the large specific heat coefficient $\gamma\sim 222 {\rm mJ/mol K^2}$.

Two-component Fermi gas in a one-dimensional harmonic trap

A many body theory for a two-component system of spin polarized interacting fermions in a one-dimensional harmonic trap is developed. The model considers two different states of the same fermionic species and treats the dominant interactions between the two using the bosonization method for forward scattering. Asymptotically exact results for the one-particle matrix elements at zero temperature are given. Using them, occupation probabilities of oscillator states are discussed. Particle and momentum densities are calculated and displayed. It is demonstrated how interactions modify all these quantities. An asymptotic connection with Luttinger liquids is suggested. The relation of the coupling constant of the theory to the dipole-dipole interaction is also discussed.

Ising transition in a one-dimensional quarter-filled electron system with dimerization

We examine critical properties of the quarter-filled one-dimensional Hubbard model with dimerization and with the onsite and nearest-neighbor Coulomb repulsion U and V. By utilizing the bosonization method, it is shown that the system exhibits an Ising quantum phase transition from the Mott insulating state to the charge-ordered insulating state. It is also shown that the dielectric permittivity exhibits a strong enhancement as decreasing temperature with power-law dependence at the Ising critical point.

A New Bosonization Method for Photoexcited Electronic States and Its Application to Nonlinear Optical Responses

We derive a bosonized Hamiltonian for a semiconductor quantum well with a light field by a new bosonization method taking exactly into account the composite-particle effects of excitons. Then we apply the bosonized Hamiltonian to the four-wave-mixing (FWM) processes. The obtained Hamiltonian describes two-boson states corresponding to bound and unbound two-exciton states and guarantees exclusion of unphysical states, which cannot exist in the fermionic space due to the Pauli exclusion principle. Calculated results of the FWM signals are in good agreement with the experimental ones, and therefore, the bosonized Hamiltonian turns out to be able to describe two-exciton correlations effectively.

Multichannel Electronic Transport Through a Kondo Dot

Electronic transport through the quantum dot with two energy levels is studied by means of the non-equilibrium Green functions and the slave boson method. Special attention is focused on an interplay between quantum inference of traveling waves and electronic correlations. It is shown that if impurity states are far below the Fermi level the transport is through the highest state only. Interference processes become relevant when the levels are shifted towards the mixed valence regime.

Boson representation of two-exciton correlations: An exact treatment of composite-particle effects

We derive a bosonized Hamiltonian describing two-exciton correlation of semiconductor-photon coupled systems with a bosonization method, which takes into full account an effect of deviation of the excitons from ideal bosons. This deviation effect stems from the fact that excitons are composite particles, whose character appears clearly in the case where the excitons overlap each other. We call this effect a composite-particle effect (CPE). To our knowledges this effect was not considered completely in previous theoretical works on exciton-exciton interaction. The Hamiltonian introduced in this paper includes the results of the previous works as low-order terms of the CPE. After the introduction of a general theory of the bosonization method for arbitrary dimension and electron-hole mass ratio, we also demonstrate an application to a semiconductor bulk system coupled with a photon field in the heavy-hole limit. The bosonized Hamiltonian shows that the CPE brings about an enhancement of the exciton-exciton scattering strength and a qualitative change of the photo transition amplitude. It is also shown that the Hamiltonian describes two-exciton bound and scattering states.

Competition of random and periodic potentials in interacting fermionic systems and classical equivalents: The Mott glass

We study the competition between a random potential and a commensurate potential on interacting fermionic and bosonic systems using a variety of methods. We focus on one-dimensional interacting fermionic systems, but higher-dimensional bosonic and fermionic extensions, as well as classical equivalents, are also discussed. Our methods, which include the bosonization method, the replica variational method, the functional renormalization group method, and perturbation around the atomic limit, go beyond conventional perturbative expansions around the Luttinger liquid in one dimension. All these methods agree on the prediction in these systems of a phase, the Mott glass, intermediate between the Anderson (compressible, with a pseudogap in the optical conductivity) and the Mott (incompressible with a gap in the optical conductivity) insulator. The Mott glass, which was unexpected from a perturbative renormalization-group point of view has a pseudogap in the conductivity while remaining incompressible. Having derived the existence of a Mott glass phase in one dimension, we show qualitatively that its existence can also be expected in higher dimensions. We discuss the relevance of this phase to experimental systems such as disordered classical elastic systems and dirty bosons.

Free energy and Green function for the multi-coupled spin system

The free energy and Green function of the multi-coupled spin chain in low-energy theory are given by using the functional bosonization method. We deduce that 2m coupled spinless chains (m = 0,1,2,...), by using a series of unitary transformations, can be reduced to some uncoupled chains, but for other numbers of coupled spinless chains we need to solve a series of inverse matrices generally; for either case, the system can be formally separated into the charge and spin parts.

Nonlinear ac transport and local fields in quantum wires

Nonlinear frequency-dependent transport in a single-channel quantum wire with a potential barrier in the presence of electron interaction is investigated. The bosonization method for treating the electron-electron interaction is used. The polarization and tunneling currents are evaluated in the weak tunneling region. Harmonic generation is studied. The corresponding longitudinal and transverse electromagnetic fields are evaluated. The importance of screening and local fields is discussed. It is concluded that apart from the influence of induced external screening currents, local longitudinal field corrections are automatically included if the interaction between electrons is taken into account exactly.

Finite-temperature bosonization

Abstract Finite-temperature properties of a non-Fermi-liauid system is one of the most challenging problems in the current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liauids is in one dimension, where the concept of a Luttinger liauid has arisen. The existence of a critical point at zero temperature in one-dimensional systems, and the fact that experiments are all undertaken at finite temperatures, implies a need for these one-dimensional systems to be examined at finite temperatures. Accordingly, we extended the well-known bosonization method of one-dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite-temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.

Finite-temperature bosonization

Finite temperature properties of a non-Fermi liquid system is one of the most challenging probelms in current understanding of strongly correlated electron systems. The paradigmatic arena for studying non-Fermi liquids is in one dimension, where the concept of a Luttinger liquid has arisen. The existence of a critical point at zero temperature in one dimensional systems, and the fact that experiments are all undertaken at finite temperature, implies a need for these one dimensional systems to be examined at finite temperature. Accordingly, we extended the well-known bosonization method of one dimensional electron systems to finite temperatures. We have used this new bosonization method to calculate finite temperature asymptotic correlation functions for linear fermions, the Tomonaga-Luttinger model, and the Hubbard model.

Dynamical Peierls' energy gap generation in one-dimensional charge-density waves systems

Abstract Using bosonization methods we consider the Lagrangian model describing the electron–phonon system using a slowly-varying phonon amplitude approximation. The phase of the phonon field is fermionized and the effective model is mapped into the chiral Gross–Neveu model with two Fermi field species. The chiral density of the electron field and the phase of the phonon field condensate as a soliton order parameter. The incommensurate charge-density wave can be pictured as a collective excitation of the combined motion of both the electrons and lattice ions, accomplished by a dynamical electron–lattice energy redistribution (Peierls' energy gap generation).

Quasiperiodic spin chains in a magnetic field

We study the interplay between a (quasi) periodic coupling array and an external magnetic field in a spin-$\frac{1}{2}$ $\mathrm{XXZ}$ chain. A new class of magnetization plateau is obtained by means of Abelian bosonization methods which gives rise to a sufficient quantization condition. The investigation of magnetic phase diagrams via exact diagonalization of finite clusters finds a complete agreement with the continuum treatment in a variety of situations.

Consistency of superconducting correlations with one-dimensional electron interactions in carbon nanotubes.

We show that a model of interacting electrons in one dimension is able to explain the order of magnitude as well as the temperature dependence of the critical supercurrents recently measured in nanotube samples placed between superconducting contacts. We use bosonization methods to deal with the long-range Coulomb interaction, ending up with a picture in which the critical current does not follow the temperature dependence of the gap in the contacts. Our results also reveal the presence of a short-range attractive interaction in the nanotubes, which accounts for a significant enhancement of the critical supercurrents.

A new method for bosons in anisotropic traps

A systemic method is present to study the vortex and the ground states of the dilute gases of alkali atoms in the anisotropic magnetic traps. By employing the simulated annealing technique, the semi-analytic, semi-numerical solutions for the condensates with different particle numbers are obtained. Some other interesting physical quantities, such as the critical angular velocity of the vortex state, can also be calculated easily.