Exact Drude weight for the one-dimensional Hubbard model at finite temperatures

The Drude weight for the one-dimensional Hubbard model is investigated at finite temperatures by using the Bethe ansatz solution. Evaluating finite-size corrections to the thermodynamic Bethe ansatz equations, we obtain the formula for the Drude weight as the response of the system to an external gauge potential. We perform low-temperature expansions of the Drude weight in the case of half-filling as well as away from half-filling, which clearly distinguish the Mott-insulating state from the metallic state.Comment: 9 pages, RevTex, To appear in J. Phys.

Chiral non-linear sigma-models as models for topological superconductivity

We study the mechanism of topological superconductivity in a hierarchical chain of chiral non-linear sigma-models (models of current algebra) in one, two, and three spatial dimensions. The models have roots in the 1D Peierls-Frohlich model and illustrate how the 1D Frohlich's ideal conductivity extends to a genuine superconductivity in dimensions higher than one. The mechanism is based on the fact that a point-like topological soliton carries an electric charge. We discuss a flux quantization mechanism and show that it is essentially a generalization of the persistent current phenomenon, known in quantum wires. We also discuss why the superconducting state is stable in the presence of a weak disorder.Comment: 5 pages, revtex, no figure

Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires

We study a quantum phase transition which occurs in a system composed of two impurities (or quantum dots) each coupled to a different interacting (Luttinger-liquid) lead. While the impurities are coupled electrostatically, there is no tunneling between them. Using a mapping of this system onto a Kondo model, we show analytically that the system undergoes a Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the Luttinger liquid parameter in the leads and the dot-lead interaction. The phase with low values of the Luttinger-liquid parameter is characterized by an abrupt switch of the population between the impurities as function of a common applied gate voltage. However, this behavior is hard to verify numerically since one would have to study extremely long systems. Interestingly though, at the transition the entanglement entropy drops from a finite value of $\ln(2)$ to zero. The drop becomes sharp for infinite systems. One can employ finite size scaling to extrapolate the transition point and the behavior in its vicinity from the behavior of the entanglement entropy in moderate size samples. We employ the density matrix renormalization group numerical procedure to calculate the entanglement entropy of systems with lead lengths of up to 480 sites. Using finite size scaling we extract the transition value and show it to be in good agreement with the analytical prediction.Comment: 12 pages, 9 figure

Energy Reflection Symmetry of Lie-Algebraic Problems: Where the Quasiclassical and Weak Coupling Expansions Meet

We construct a class of one-dimensional Lie-algebraic problems based on sl(2) where the spectrum in the algebraic sector has a dynamical symmetry E -> - E. All 2j+1 eigenfunctions in the algebraic sector are paired, and inside each pair are related to each other by simple analytic continuation x -> ix, except the zero mode appearing if j is integer. At j-> infinity the energy of the highest level in the algebraic sector can be calculated by virtue of the quasiclassical expansion, while the energy of the ground state can be calculated as a weak coupling expansion. The both series coincide identically.Comment: Latex, 16 pages, 3 figures. Minor styllistic changes made, typos corrected, a remark on the energy-reflection symmetry in the quantum-algebraic Hamiltonians emerging in finite-difference problems added. Final version, to be published in Physical Review

Magnetic properties of the Anderson model: a local moment approach

We develop a local moment approach to static properties of the symmetric Anderson model in the presence of a magnetic field, focussing in particular on the strong coupling Kondo regime. The approach is innately simple and physically transparent; but is found to give good agreement, for essentially all field strengths, with exact results for the Wilson ratio, impurity magnetization, spin susceptibility and related properties.Comment: 7 pages, 3 postscript figues. Latex 2e using the epl.cls Europhysics Letters macro packag

Tunneling in the topological mechanism of superconductivity

We compute the two-particle matrix element and Josephson tunneling amplitude in a two-dimensional model of topological superconductivity which captures the physics of the doped Mott insulator. The hydrodynamics of topological electronic liquid consists of the compressible charge sector and the incompressible chiral topological spin liquid. We show that ground states differing by an odd number of particles are orthogonal and insertion of two extra electrons is followed by the emission of soft modes of the transversal spin current. The orthogonality catastrophe makes the physics of superconductivity drastically different from the BCS-theory but similar to the physics of one-dimensional electronic liquids. The wave function of a pair is dressed by soft modes. As a result the two particle matrix element forms a complex d-wave representation (i.e., changes sign under $90^o$ degree rotation), although the gap in the electronic spectrum has no nodes. In contrast to the BCS-theory the tunneling amplitude has an asymmetric broad peak (much bigger than the gap) around the Fermi surface. We develop an operator algebra, that allows one to compute other correlation functions.Comment: 18 pages, 2 eps figures, revtex, psfig, significant changes have been mad

Anomalous magnetic splitting of the Kondo resonance

The splitting of the Kondo resonance in the density of states of an Anderson impurity in finite magnetic field is calculated from the exact Bethe-ansatz solution. The result gives an estimate of the electron spectral function for nonzero magnetic field and Kondo temperature, with consequences for transport experiments on quantum dots in the Kondo regime. The strong correlations of the Kondo ground state cause a significant low-temperature reduction of the peak splitting. Explicit formulae are found for the shift and broadening of the Kondo peaks. A likely cause of the problems of large-N approaches to spin-1/2 impurities at finite magnetic field is suggested.Comment: 4 pages, 2 eps figures; published versio

Commensurate-Incommensurate Phase Transitions for Multichain Quantum Spin Models: Exact Results

The behavior in an external magnetic field is studied for a wide class of multichain quantum spin models. It is shown that the magnetic field together with the interchain couplings cause commensurate-incommensurate phase transitions between the gapless phases in the ground state. The conformal limit of these models is studied and it is shown that the low-lying excitations for the incommensurate phases are not independent. A scenario for the transition from one to two space dimensions for the integrable multichain models is proposed. The similarities in the external field behavior for the quantum multichain spin models and a wide class of quantum field theories are discussed. The exponents for the gaps caused by relevant perturbations of the models are calculated.Comment: 23 pages, LaTeX, typos correcte

Solution of the Two-Channel Anderson Impurity Model - Implications for the Heavy Fermion UBe13_{13} -

We solve the two-channel Anderson impurity model using the Bethe-Ansatz. We determine the ground state and derive the thermodynamics, obtaining the impurity entropy and specific heat over the full range of temperature. We show that the low temperature physics is given by a line of fixed points decribing a two-channel non Fermi liquid behavior in the integral valence regime associated with moment formation as well as in the mixed valence regime where no moment forms. We discuss relevance for the theory of UBe$_{13}$.Comment: 4 pages, 2 figures, (to be published in PRL

Transport through Quantum Dots: Analytic Results from Integrability

Recent experiments have probed quantum dots through transport measurements in the regime where they are described by a two lead Anderson model. In this paper we develop a new method to analytically compute for the first time the corresponding transport properties. This is done by using the exact solvability of the Anderson Hamiltonian, together with a generalization of the Landauer-Buttiker approach to integrable systems. The latter requires proper identification of scattering states, a complex and crucial step in our approach. In the Kondo regime, our results include the zero-field, finite temperature linear response conductance, as well as the zero-temperature, non-equilibrium conductance in an applied Zeeman field.Comment: 5 pages, 3 figure