Bosonization Method Research Articles

Photoluminescence spectrum of an interacting two-dimensional electron gas atν=1

We report on the theoretical photoluminescence spectrum of the interacting two-dimensional electron gas at filling factor one (\nu=1). We considered a model similar to the one adopted to study the X-ray spectra of metals and solved it analytically using the bosonization method previously developed for the two-dimensional electron gas at \nu=1. We calculated the emission spectra of the right and the left circularly polarized radiations for the situations where the distance between the two-dimensional electron gas and the valence band hole are smaller and greater than the magnetic length. For the former, we showed that the polarized photoluminescence spectra can be understood as the recombination of the so-called excitonic state with the valence band hole whereas, for the latter, the observed emission spectra can be related to the recombination of a state formed by a spin down electron bound to n spin waves. This state seems to be a good description for the quantum Hall skyrmion.

Quantum vs Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains

The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact 00u-type quantum plateau state, is also presented. The phase transition to the classical udu-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.

The Luther-Emery liquid: Spin gap and anomalous flux period

We study the dependence of the ground state energy on an applied Aharonov-Bohm flux $\ensuremath{\Phi}$ for the Luttinger model with large momentum scattering. Employing the method of finite size bosonization, we show that for systems with a spin gap but with gapless charge degrees of freedom, the ground state energy has an exact period of $hc∕2e$, i.e., half a flux quantum, in the limit of large system size $L$. Finite size corrections are found to vanish exponentially in $L$. This behavior is contrasted to that of the spin gapless case, for both even and odd particle number. Generalizations to finite temperature are also discussed.

Magnetization Plateau of theS= 1/2 Frustrated Heisenberg Chain with Period 3 Parity Invariant Exchange Modulation

The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate ↑↑↓-type plateau states in the uniform chain, two of them (↓↑↑↓↑↑... and ↑↓↑↑↓↑... ) turned out to be robust against the period 3 exchange modulation which favors the ○-○ ↑○-○ ↑... phase up to a critical value of the modulation amplitude (○-○ = singlet dimer) resulting in the Z 2 symmetry broken phase. Another ↑↑↓-type state with ↑↑↓↑↑↓... configuration is stabilized for period 3 modulation with opposite sign. The transition between the ○-○↑ ○-○ ↑...-phase and Z 2 -broken phase is the Ising transition and that between the ↑↑↓↑↑↓... -phase and Z 2 broken phase is the first. order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.

Renormalization Group Studies of the Fibonacci Quantum Spin Chains

Renormalization group studies of the ground state properties of the S =1/2 Fibonacci antiferromagnetic XXZ chain are reviewed. In the XY limit, this model can be mapped onto the free fermion chain which has been extensively studied using the renormalization group approach for the transfer matrix. For the XXZ chain with weak Fibonacci modulation, the investigation by means of the bosonization and perturbational renormalization group method is reviewed. Finally, the recent results of the real space renormalization group approach in the strong modulation limit is presented. Combining the real space renormalization group and the weak modulation renormalization group results, the schematic ground state phase diagram is presented.

Application of the Non-Abelian Bosonization to Spin-1 Ladder and Tube in a High Magnetic Field

We review the non-Abelian bosonization method for one-dimensional spin-1 systems, which was first proposed by Tsvelik. As a new application of it, we discuss field-induced critical phases of spin-1 antiferromagnetic 2-leg ladder and 3-leg tube. It is shown that the ground states in both the ladder and the tube become a one-component Tomonaga-Luttinger liquid when the interchain coupling is weak and the external uniform field is sufficiently larger than the lower critical value.

Ferrimagnetic mixed-spin ladders in weak- and strong-coupling limits

We study two similar spin ladder systems with the ferromagnetic leg coupling. First model includes two sorts of spins, s= 1/2 and s= 1, and the second model comprises only s=1/2 legs coupled by a "triangular" rung exchange. The antiferromagnetic (AF) rung coupling destroys the long-range order and eventually makes the systems equivalent to the AF s=1/2 Heisenberg chain. We investigate the situation by different methods in weak and strong rung coupling limits. Particularly we compare the spin-wave theory and the bosonization method in the weak coupling regime of the second model. We analyze the spectra and correlations, and discuss the order parameter of these ladder systems.

Relaxation and Dephasing in a Many-Fermion Generalization of the Caldeira-Leggett Model

We analyze a model system of fermions in a harmonic oscillator potential under the influence of a fluctuating force generated by a bath of harmonic oscillators. This represents an extension of the well-known Caldeira-Leggett model to the case of many fermions. Using the method of bosonization, we calculate Green's functions and discuss relaxation and dephasing of a single extra particle added above the Fermi sea. We also extend our analysis to a more generic coupling between system and bath that results in complete thermalization of the system.

Interplay of Lattice Dimerization and Charge Ordering in One-Dimensional Quarter-Filled Electron Systems

The effect of charge ordering on lattice dimerization has been investigated in the one-dimensional extended Peierls–Hubbard model at quarter filling. We estimate the strength of the lattice dimerization by applying the bosonization method and the perturbative renormalization-group method. In the ground state, it is shown that a first-order phase transition takes place between the dimerized insulator and the charge-ordered insulator. The lattice dimerization disappears in the charge-ordered state, while the lattice dimerization is appreciably suppressed even in the dimerized insulating state due to charge fluctuations. The phase diagram at finite temperature is also discussed.

Gapped spin-liquid states in a one-dimensional Hubbard model with antiferromagnetic exchange interaction

We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange J. This Mott-insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is U_c\sim J/2. However, as J increases, the spin-charge couplings become important and the critical point U_c is significantly suppressed and eventually tends to zero as J\to \infty. Away from half-filling, the charge gap completely collapses but the spin gap persists.

Slave-boson approach to the infinite-UAnderson-Holstein impurity model

The infinite-$U$ Anderson-Holstein impurity model is studied with a focus on the interplay between the strong electron correlation and the weak electron-phonon interaction. The slave boson method has been employed in combination with the large degeneracy expansion (1/N) technique. The charge and spin susceptibilities and the phonon propagator are obtained in the approximation scheme where the saddle point configuration and the Gaussian 1/N fluctuations are taken into account. The spin susceptibility is found not to be renormalized by electron-phonon interaction, while the charge susceptibility is renormalized. From the renormalized charge susceptibility the Kondo temperature is found to increase by the electron-phonon interaction. It turns out that the bosonic 1/N Gaussian fluctuations play a very crucial role, in particular, for the phonon propagator.

Effect of Hund coupling in the one-dimensional SU(4) Hubbard model

The one-dimensional SU(4) Hubbard model perturbed by Hund coupling is studied, away from half-filling, by means of renormalization group and bosonization methods. A spectral gap is always present in the spin-orbital sector irrespective of the magnitude of the Coulomb repulsion. We further distinguish between two qualitatively different regimes. At small Hund coupling, we find that the symmetry of the system is dynamically enlarged to SU(4) at low energy with the result of {\it coherent} spin-orbital excitations. When the charge sector is not gapped, a superconducting instability is shown to exist. At large Hund coupling, the symmetry is no longer enlarged to SU(4) and the excitations in the spin sector become {\it incoherent}. Furthermore, the superconductivity can be suppressed in favor of the conventional charge density wave state.

Boundary contributions to specific heat and susceptibility in the spin-12 XXZchain

Exact low-temperature asymptotic behavior of boundary contribution to specific heat and susceptibility in the one-dimensional spin-$\frac{1}{2}$ $\mathrm{XXZ}$ model with exchange anisotropy $1/2<\ensuremath{\Delta}<~1$ is analytically obtained using the Abelian bosonization method. The boundary spin susceptibility is divergent in the low-temperature limit. This singular behavior is caused by the first-order contribution of a bulk leading irrelevant operator to boundary free energy. The result is confirmed by numerical simulations of finite-size systems. The anomalous boundary contributions in the spin isotropic case are universal.

Resonant tunneling between Luttinger liquids: a solvable case.

We discuss the conductance of a Luttinger liquid interrupted by a quantum dot containing a single resonant level. Using bosonization and refermionization methods, we find a mapping to a Kondo-type problem which possesses a nontrivial Toulouse-type solvable point. At this point, we obtain an analytic expression for the nonlinear current-voltage characteristics and analyze the differential conductance and the width of the resonance peak as functions of bias and gate voltages, temperature, and barrier asymmetry. We also determine the exact scaling function for the linear conductance.

Propagator for a spin–Bose system with the Bose field coupled to a reservoir of harmonic oscillators

We consider the general problem of a single two-level atom interacting with a multimode radiation field (without the rotating-wave approximation), and additionally take the field to be coupled to a thermal reservoir. Using the method of bosonization of the spin operators in the Hamiltonian, and working in the Bargmann representation for all the boson operators, we obtain the propagator for the composite system using the techniques of functional integration, under a reasonable approximation scheme. The propagator is explicitly evaluated for a simplified version of the system with one spin and a dynamically coupled single-mode field. The results are also checked on the known problem of quantum Brownian motion.

Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap

An asymptotically exact many body theory for spin polarized interacting fermions in a one-dimensional harmonic atom trap is developed using the bosonization method and including backward scattering. In contrast to the Luttinger model, backscattering in the trap generates one-particle potentials which must be diagonalized simultaneously with the two-body interactions. Inclusion of backscattering becomes necessary because backscattering is the dominant interaction process between confined identical one-dimensional fermions. The bosonization method is applied to the calculation of one-particle matrix elements at zero temperature. A detailed discussion of the validity of the results from bosonization is given, including a comparison with direct numerical diagonalization in fermionic Hilbert space. A model for the interaction coefficients is developed along the lines of the Luttinger model with only one coupling constant $K$. With these results, particle densities, the Wigner function, and the central pair correlation function are calculated and displayed for large fermion numbers. It is shown how interactions modify these quantities. The anomalous dimension of the pair correlation function in the center of the trap is also discussed and found to be in accord with the Luttinger model.

One-dimensional spin–orbital model perturbed by Hund coupling

The one-dimensional spin–orbital model perturbed by Hund coupling is studied by renormalization group and bosonization methods. The Hund coupling breaks the SU(4) spin–orbital symmetry into SU(2) spin× U(1) orbital at weak coupling fixed point. The one-loop renormalization group analysis shows that the Hund coupling is relevant irrespective of Coulomb repulsion. When Coulomb repulsion is larger than Hund coupling, the spin–orbital physics in strong coupling regime is described by SO(6) Gross–Neveu model, where the spin and orbital excitations are gapped. When the Hund coupling is much larger than the Coulomb repulsion, the strong coupling regime is described by the two coupled SO(3) spin×SO(3) orbital Gross–Neveu model, where again the spin and orbital excitations are gapped.

Charge Gap in One-Dimensional Extended Hubbard Model**The project supported by National Natural Science Foundation of China (No. 19975031) and the Research Fund for the Doctoral Program of Higher Education (No. 1999024833)

By using the bosonization and renormalization group methods, we have studied the low energy physical properties in one-dimensional extended Hubbard model. The formation of charge and spin gaps is investigated at the half-filled electron band. An analytical expression for the charge gap in terms of the Coulomb repulsive interaction strength U and the nearest-neighbour interaction parameter V is obtained.

Generalized two-leg Hubbard ladder at half filling: Phase diagram and quantum criticalities

The ground-state phase diagram of the half-filled two-leg Hubbard ladder with inter-site Coulomb repulsions and exchange coupling is studied by using the strong-coupling perturbation theory and the weak-coupling bosonization method. Considered here as possible ground states of the ladder model are four types of density-wave states with different angular momentum (s-density-wave state, p-density-wave state, d-density-wave state, and f-density-wave state) and four types of quantum disordered states, i.e., Mott insulating states (S-Mott, D-Mott, S'-Mott, and D'-Mott states, where S and D stand for s- and d-wave symmetry). The s-density-wave state, the d-density-wave state, and the D-Mott state are also known as the charge-density-wave (CDW) state, the staggered-flux (SF) state, and the rung-singlet state, respectively. Strong-coupling approach naturally leads to the Ising model in a transverse field as an effective theory for the quantum phase transitions between the SF state and the D-Mott state and between the CDW state and the S-Mott state, where the Ising ordered states correspond to doubly degenerate ground states in the staggered-flux or the charge-density-wave state. From the weak-coupling bosonization approach it is shown that there are three cases in the quantum phase transitions between a density-wave state and a Mott state: the Ising (Z_2) criticality, the SU(2)_2 criticality, and a first-order transition. The quantum phase transitions between Mott states and between density-wave states are found to be the U(1) Gaussian criticality. The ground-state phase diagram is determined by integrating perturbative renormalization-group equations. It is shown that the S-Mott state and the SF state exist in the region sandwiched by the CDW phase and the D-Mott phase.

Numerical study of alternating quantum spin- chains

Abstract We have investigated the S= 1 2 alternating anti-ferromagnetic Heisenberg chain (AHC) and the XXZ chain using the bosonization and Lanczos methods. For the AHC, the asymptotic behavior of the ground state energy per site is obtained and a new finite size scaling procedure is proposed to extrapolate the energy gap to bulk limit. The results show a good agreement with the theoretical prediction, especially for the dependence of the energy gap on the dimerization parameter, the 2 3 power law with logarithmic correction anticipated by the renormalization group theory is confirmed. We also calculate the scaling dimensions of various operators in the XXZ chain for different anisotropic parameters Δ(0⩽Δ⩽1).