Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

Microwave transport approach to the coherence of interchain hopping in (TMTSF)2PF6

We report a microwave study of the longitudinal and transverse transport properties of the quasi-one-dimensional organic conductor (TMTSF)₂PF₆ in its normal phase. The contactless technique have provided a direct measurement of the temperature profile of the resistivity along the b' direction and in magnetic fields up to 14 T. A characteristic energy scale ( K) has been observed which delimits a transient regime from an insulating to a metallic behavior. This anomalous profile is discussed in terms of the onset of coherent transport properties along the b' direction below 40 K. This is also supported by the observation of a finite longitudinal and transverse magnetoresistances only below 40 K, indicative of a two-dimensional regime. Below T_x, however, strong deviations with respect to a Fermi liquid behavior are evidenced. Received 27 January 1999     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

Microscopic interactions in CuGeO 3 and organic Spin-Peierls systems deduced from their pretransitional lattice fluctuations

CuGeO₃ exhibits a Spin-Peierls (SP) transition, at T _SP = 14.3 K, which is announced above 19 K by an important regime of one-dimensional (1D) pretransitional lattice fluctuations which can be detected until about 40 K using X-ray diffuse scattering investigations. A quantitative analysis of this scattering shows that in this 1D direction the correlation length follows the “universal” behaviour expected for the thermal fluctuations of a real order parameter which characterizes the lattice dimerization. This allows to define a 1D mean-field temperature, T _SP ^MF , of about 60 K and invalidates any mean field scenario for the SP transition of CuGeO₃. As T _SP ^MF is as high as 4 T _SP we propose that the 3D-SP order is achieved by the interchain coupling between 1D solitons which form below about 16-20 K. CuGeO₃ being in the non-adiabatic regime, it is also suggested that the observed pretransitional fluctuations of CuGeO₃ originate from the X-ray scattering on a very broad damped critical response of lower frequency than the “critical” phonon modes. From the quantitative analysis of the 1D fluctuations we also estimate the microscopic parameters of the SP chain. These parameters allow to locate CuGeO₃ close to the quantum critical boundary separating the gapped SP ground state to the ungapped anti-ferromagnetic ground state. The vicinity of a quantum critical point emphasizes the role of the quantum and non-adiabatic fluctuations and the importance of the interchain coupling in the physics of CuGeO₃. Finally we compare these findings with those obtained for the organic SP systems (BCPTTF)₂PF₆, (TMTTF)₂PF₆ and MEM(TCNQ)₂. From a similar analysis of the pretransitional lattice fluctuations it is found that (BCPTTF)₂PF₆ and (TMTTF)₂PF₆ are located on the SP gapped classical-quantum boundary and are in the adiabatic regime where the fluctuations lead to the formation of a pseudo-gap in the spin degrees of freedom. Differently, we place MEM(TCNQ)₂ inside the SP quantum phase around the crossover line between the adiabatic and non-adiabatic regimes. Received 13 September 2000 and Received in final form 6 February 2001     

The Fermi-sea-like limit of the composite fermion wave function

The experimentally observed filling factors of the fractional quantum Hall effect can be described in terms of the composite fermion wave function of the Jastrow-Slater form [0pt] fully projected into the lowest Landau level. The Slater determinant of the above composite fermion wave function represents the filled Landau levels of composite fermions evaluated at the corresponding reduced magnetic field. For a system of fermions studied in the thermodynamic limit, we prove that in the even-denominator-filled state limit (when the number of filled Landau levels of composite fermions becomes infinite), the above composite fermion wave function exactly transforms into the Rezayi-Read Fermi-sea-like wave function [0pt] constructed by attaching 2m flux quanta to the Slater determinant of two-dimensional free fermions at the density corresponding to that filling. We study the composite fermion wave function and its evolution into the Fermi-sea-like wave function for a range of filling factors very close to the even-denominator-filled state. Received 19 March 1999     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

Damping of zero sound in Luttinger liquids

We calculate the damping γ_q of collective density oscillations (zero sound) in a one-dimensional Fermi gas with dimensionless forward scattering interaction F and quadratic energy dispersion k² / 2 m at zero temperature. Using standard many-body perturbation theory, we obtain γ_q from the expansion of the inverse irreducible polarization to first order in the effective screened (RPA) interaction. For wave-vectors | q| /k_F ≪F (where k_F = m v_F is the Fermi wave-vector) we find to leading order γ_q ∝| q |³ /(v_F m²). On the other hand, for F ≪| q| /k_F most of the spectral weight is carried by the particle-hole continuum, which is distributed over a frequency interval of the order of q²/m. We also show that zero sound damping leads to a finite maximum proportional to |k - k_F | ^{-2 + 2 η} of the charge peak in the single-particle spectral function, where η is the anomalous dimension. Our prediction agrees with photoemission data for the blue bronze K_0.3MoO₃. We comment on other recent calculations of γ_q.     

The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given. Received 2 March 1999     

Determination of the chemical potential and the energy of the ν=1/2 FQHE system for low temperatures

We consider the energy density of a spin polarized ν = 1/2 system for low temperatures. We show that due to the elimination of the magnetic field and the field of the positive background charge in the calculation of the grand canonical potential of Chern-Simons systems through a mean field formalism one gets corrections to the well known equations which determine the chemical potential and the energy from the grand canonical potential. We use these corrected equations to calculate the chemical potential and the energy of the ν = 1/2 system at low temperatures in two different approximations. Received 14 March 2001     

Single hole dynamics in the one-dimensional - model

We present a new finite-temperature quantum Monte Carlo algorithm to compute imaginary-time Green functions for a single hole in the t-J model on non-frustrated lattices. Spectral functions are obtained with the Maximum Entropy method. Simulations of the one-dimensional case show that a simple charge-spin separation Ansatz is able to describe the overall features of the spectral function such as the bandwidth and the compact support of the spectral function, over the whole energy range for values of J / t from 1/3 to 4. This is contrasted with the two-dimensional case. The quasiparticle weight Z_k is computed on lattices up to L =128 sites in one dimension, and scales as . Received 15 February 2000     

Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

We consider one-dimensional (1D) interacting spinless fermions with a non-linear spectrum in a clean quantum wire (non-linear bosonization). We compute diagrammatically the 1D dynamical structure factor, S(ω,q), beyond the Tomonaga approximation focusing on it's tails, |ω| ≫vq, i.e. the 2-pair excitation continuum due to forward scattering. Our methodology reveals three classes of diagrams: two “chiral” classes which bring divergent contributions in the limits ω→±vq, i.e. near the single-pair excitation continuum, and a “mixed” class (so-called Aslamasov-Larkin or Altshuler-Shklovskii type diagrams) which is crucial for the f-sum rule to be satisfied. We relate our approach to the T=0 ones present in the literature. We also consider the case and show that the 2-pair excitation continuum dominates the single-pair one in the range: |q|T/k_F ≪ω±vq ≪T (substantial for q ≪k_F). As applications we first derive the small-momentum optical conductivity due to forward scattering: σ∼1/ω for T ≪ω and σ∼T/ω² for T ≫ω. Next, within the 2-pair excitation continuum, we show that the attenuation rate of a coherent mode of dispersion Ω_q crosses over from , e.g. γ_q ∼|q|³ for an acoustic mode, to , independent of Ω_q, as temperature increases. Finally, we show that the 2-pair excitation continuum yields subleading curvature corrections to the electron-electron scattering rate: , where V is the dimensionless strength of the interaction.     

Charge localization in organic conductors (TM)X: The influence of anion ordering

An investigation of the different contributions leading to charge localization in a 1/2 or 1/4 filled band 1D conductor has been conducted through a study of transport properties in the solid solution [(TMTSF)_1-x (TMTTF) _x]₂ReO₄. The existence of an ordering transition of the anions allows to identify two contributions to the electronic potential with wave vector 4k_F. A dominant on-site 4k_F potential besides the bond contribution is revealed when Umklapp scattering is pertinent via the weakening of the localization arising at the (0, 1/2, 1/2) anion ordering which is stabilized under pressure in the compound [(TMTSF) _0.5 (TMTTF)_0.5]₂ReO₄ at variance with the enhancement of localization observed in the homomolecular (TMTTF)₂ReO ₄ material. Received: 13 May 1998 / Revised: 8 July 1998 / Accepted: 9 July 1998     

Ground state energy calculations of the ν=1/2 and the ν=5/2 FQHE system

We reconsider energy calculations of the spin polarized ν = 1/2 Chern-Simons theory. We show that one has to be careful in the definition of the Chern-Simons path integral in order to avoid an IR divergent magnetic ground state energy in RPA as in [J. Dietel et al, Eur. Phys. J. B 5, 439 (1998)]. We correct the path integral and get a well behaved magnetic energy by considering the energy of the maximal divergent graphs as well as the Hartree-Fock graphs. Furthermore, we consider the ν = 1/2 and the ν = 5/2 system with spin degrees of freedom. In doing this we formulate a Chern-Simons theory of the ν = 5/2 system by transforming the interaction operator to the next lower Landau level. We calculate the Coulomb energy of the spin polarized as well as the spin unpolarized ν = 1/2 and the ν = 5/2 system as a function of the interaction strength in RPA. These energies are in good agreement with numerical simulations of interacting electrons in the first as well as in the second Landau level. Furthermore, we calculate the compressibility, the effective mass and the excitations of the spin polarized ν = 2 + 1/ systems where is an even number. Received 13 June 2000     

Semiconductor quantum dots in high magnetic fields

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called Λ levels).     

Non perturbative calculations for three particles in a linear chain within the generalized Hubbard model

A real-space method has been introduced to study the pairing problem within the generalized Hubbard Hamiltonian. This method includes the bond-charge interaction term as an extension of the previously proposed mapping method [1] for the Hubbard model. The generalization of the method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space, where the problem can be solved exactly. In a one-dimensional lattice, we analyzed the three particle correlation by calculating the binding energy at the ground state, using different values of the bond-charge, the on-site (U) and the nearest-neighbor (V) interactions. A pairing asymmetry is found between electrons and holes for the generalized hopping amplitude, where the hole pairing is not always easier than the electron case. For some special values of the hopping parameters and for all kinds of interactions in the Hubbard Hamiltonian, an analytical solution is obtained. Received 21 January 2000 and Received in final form 18 July 2000     

A dynamic scattering approach for a gated interacting wire

A scattering approach for correlated one-dimensional systems is developed. The perfect contact to charge reservoirs is encoded in time-dependent boundary conditions. The conductance matrix for an arbitrary gated wire, respecting charge conservation, is expressed through a dynamic scattering matrix. Two applications are developed. First, it is shown that the dc conductance is equal to e ²/h for any model with conserved total left- and right-moving charges. Second, the ac conductance matrix is explicitly computated for the Tomonaga-Luttinger model (TLL). Received 31 August 1998     

The Gutzwiller approximation for degenerate bands: a formal derivation

We present a detailed derivation of the Gutzwiller approximation for multi-band Hubbard models with density-density Coulomb interactions. For the one-band Hubbard model we introduce a mathematically well-defined formalism which is easily generalized to the multi-band case. In contrast to earlier attempts, our approach allows us to include inter-orbital hopping terms in the Hamiltonian. Received: 9 December 1997 / Revised and accepted: 6 March 1998     

Integrable correlated electron model with next-nearest-neighbour interactions

The exactly solvable model of supersymmetric t - J chains (STJC) of correlated electrons with next-nearest-neighbour (NNN) interactions is proposed and studied. The model with interactions between nearest neighbours and NNN interactions in one chain can also be considered as a two-chain model with zigzag-like coupling between the chains. The NNN interaction (coupling between chains) causes the onset of additional Dirac seas for low-lying charge and/or spin excitations. These Dirac seas change the low-energy (conformal) behavior of the model. The filling of those seas depends on the values of the NNN coupling (interactions between chains), external magnetic field and applied voltage. We identify the new ground state phases which appear due to the NNN as incommensurate ones. The NNN coupling in the incommensurate phases induces spontaneous magnetization and/or spontaneous filling of the Dirac sea for charge excitations (“spontaneous charge ordering”). The onset of this order implies a first order quantum phase transition driven by the field with hysteresis phenomena. Received 13 September 2000