Kondo Physics and Exact Solvability of Double Dots Systems

We study two double dot systems, one with dots in parallel and one with dots in series, and argue they admit an exact solution via the Bethe ansatz. In the case of parallel dots we exploit the exact solution to extract the behavior of the linear response conductance. The linear response conductance of the parallel dot system possesses multiple Kondo effects, including a Kondo effect enhanced by a nonpertubative antiferromagnetic RKKY interaction, has conductance zeros in the mixed valence regime, and obeys a non-trivial form of the Friedel sum rule.Comment: 4 pages, 2 figures; v2: published form to appear in August 2007 issue of Phys. Rev. Let

Orbital Dependence of Quasiparticle Lifetimes in Sr2RuO4

Using a phenomenological Hamiltonian, we investigate the quasiparticle lifetimes and dispersions in the three low energy bands, gamma, beta, and alpha of Sr2RuO4. Couplings in the Hamiltonian are fixed so as to produce the mass renormalization as measured in magneto-oscillation experiments. We thus find reasonable agreement in all bands between our computed lifetimes and those measured in ARPES experiments by Kidd et al. [1] and Ingle et al. [2]. In comparing computed to measured quasiparticle dispersions, we however find good agreement in the alpha-band alone.Comment: 7 pages, 5 figure

Understanding the entanglement entropy and spectra of 2D quantum systems through arrays of coupled 1D chains

We describe an algorithm for studying the entanglement entropy and spectrum of 2D systems, as a coupled array of $N$ one dimensional chains in their continuum limit. Using the algorithm to study the quantum Ising model in 2D, (both in its disordered phase and near criticality) we confirm the existence of an area law for the entanglement entropy and show that near criticality there is an additive piece scaling as $c_{eff}\log (N)/6$ with $c_{eff} \approx 1$. \textcolor{black}{Studying the entanglement spectrum, we show that entanglement gap scaling can be used to detect the critical point of the 2D model. When short range (area law) entanglement dominates we find (numerically and perturbatively) that this spectrum reflects the energy spectrum of a single quantum Ising chain.Comment: 8 pages (4 + supplementary material). 10 figure

Glimmers of a Quantum KAM Theorem: Insights from Quantum Quenches in One Dimensional Bose Gases

Real-time dynamics in a quantum many-body system are inherently complicated and hence difficult to predict. There are, however, a special set of systems where these dynamics are theoretically tractable: integrable models. Such models possess non-trivial conserved quantities beyond energy and momentum. These quantities are believed to control dynamics and thermalization in low dimensional atomic gases as well as in quantum spin chains. But what happens when the special symmetries leading to the existence of the extra conserved quantities are broken? Is there any memory of the quantities if the breaking is weak? Here, in the presence of weak integrability breaking, we show that it is possible to construct residual quasi-conserved quantities, so providing a quantum analog to the KAM theorem and its attendant Nekhoreshev estimates. We demonstrate this construction explicitly in the context of quantum quenches in one-dimensional Bose gases and argue that these quasi-conserved quantities can be probed experimentally.Comment: 21 pages with appendices; 13 figures; version accepted by PR

Studying the Perturbed Wess-Zumino-Novikov-Witten SU(2)k Theory Using the Truncated Conformal Spectrum Approach

We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the model is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $k\gg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $\lambda$. Moreover for $\lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.Comment: 30 pages, 19 eps figures, LaTeX2e file. Version 2: manuscript accepted for publication; small changes in text and in one of the figure

Interference effects in interacting quantum dots

In this paper we study the interplay between interference effects in quantum dots (manifested through the appearance of Fano resonances in the conductance), and interactions taken into account in the self-consistent Hartree-Fock approximation. In the non-interacting case we find that interference may lead to the observation of more than one conductance peak per dot level as a function of an applied gate voltage. This may explain recent experimental findings, which were thought to be caused by interaction effects. For the interacting case we find a wide variety of different interesting phenomena. These include both monotonous and non-monotonous filling of the dot levels as a function of an applied gate voltage, which may occur continuously or even discontinuously. In many cases a combination of the different effects can occur in the same sample. The behavior of the population influences, in turn, the conductance lineshape, causing broadening and asymmetry of narrow peaks, and determining whether there will be a zero transmission point. We elucidate the essential role of the interference between the dot levels in determining these outcomes. The effects of finite temperatures on the results are also examined.Comment: 11 pages, 9 fugures, REVTeX

Magnetic Response in the Underdoped Cuprates

We examine the dynamical magnetic response of the underdoped cuprates by employing a phenomenological theory of a doped resonant valence bond state where the Fermi surface is truncated into four pockets. This theory predicts a resonant spin response which with increasing energy (0 to 100meV) appears as an hourglass. The very low energy spin response is found at (pi,pi +- delta) and (pi +- delta,pi) and is determined by scattering from the pockets' frontside to the tips of opposite pockets where a van Hove singularity resides. At energies beyond 100 meV, strong scattering is seen from (pi,0) to (pi,pi). This theory thus provides a semi-quantitative description of the spin response seen in both INS and RIXS experiments at all relevant energy scales

Superconductivity generated by coupling to a Cooperon in a 2-dimensional array of 4-leg Hubbard ladders

Starting from an array of four-leg Hubbard ladders weakly doped away from half-filling and weakly coupled by inter-ladder tunneling, we derive an effective low energy model which contains a partially truncated Fermi surface and a well defined Cooperon excitation formed by a bound pair of holes. An attractive interaction in the Cooper channel is generated on the Fermi surface through virtual scattering into the Cooperon state. Although the model is derived in the weak coupling limit of a four-leg ladder array, an examination of exact results on finite clusters for the strong coupling t-J model suggests the essential features are also present for a strong coupling Hubbard model on a square lattice near half-filling.Comment: 20 pages, 4 figure