Quantum duality and Bethe-ansatz for the Hofstadter problem on hexagonal lattice

The Hofstadter problem is studied on hexagonal lattice. We first establish a relation between the spectra for the hexagonal lattice and for its dual he triangular lattice. Following the idea of Faddeev and Kashaev, we then obtain the Bethe-ansatz equations for this system.Comment: 8 pages, latex, revised version for Phys. Lett.

Tunneling and orthogonality catastrophe in the topological mechanism of superconductivity

We compute the angular dependence of the order parameter and tunneling amplitude in a model exhibiting topological superconductivity and sketch its derivation as a model of a doped Mott insulator. We show that ground states differing by an odd number of particles are orthogonal and the order parameter is in the d-representation, although the gap in the electronic spectrum has no nodes. We also develop an operator algebra, that allowes one to compute off-diagonal correlation functions.Comment: 4 pages, Revtex, psfig; some references are correcte

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

Lehmann-Symanzik-Zimmermann Reduction Approach to Multi-Photon Scattering in Coupled-Resonator Arrays

We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process in a nano-architecture consisting of the coupled resonator arrays (CRA), which are also coupled to some artificial atoms as the controlling quantum node. By making use of this approach, we find the bound states of single photon for an elementary unit, the T-type CRA, and explicitly obtain its multi-photon scattering S-matrix in various situations. We also use this method to calculate the multi-photon S-matrices for the more complex quantum network constructed with main T-type CRA's, such as a H-type CRA waveguide.Comment: 15 pages, 14 figure

Strongly Correlated Two-Electron Transport in a Quantum Waveguide Having a Single Anderson Impurity

The strongly correlated two-electron transport in one-dimensional channel coupled with an Anderson-type impurity is solved exactly via a Bethe ansatz approach. We show that the transport properties are fundamentally different for spin singlet and triplet states, thus the impurity acts as a novel filter that operates based on the total spin angular momentum of the electron pairs, but not individual spins. The filter provides a deterministic generation of electron entanglement in spin, as well as energy and momentum space.Comment: 12 pages, 3 figure

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

The Toulose limit of the Multi-Channel Kondo model.

We study the Toulouse limit of the multi-channel Kondo model defined as the limit of maximal anisotropy which can be achieved without changing the infrared behaviour of the model. It is shown that when the number of channels exceeds 2, the interactions do not vanish and the Toulouse limit remains a non-trivial field theory. Considerable simplifications take place only for k = 2, where the Bethe ansatz reproduces the results by Emery and Kivelson.Comment: 10 pages, LaTex, a discussion about the magnetic properties is added