Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.Comment: Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures

Non-equilibrium dynamics of a system with Quantum Frustration

Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the TLS is coupled symmetrically to both bath. A critical asymmetry angle separates the localized from the delocalized phase. On the other hand, real-time decoherence of a non-equilibrium initial state is for a generic initial state faster for a coupling to two baths than for a single bath.Comment: 22 pages, 9 figure

Signatures of nematic quantum critical fluctuations in the Raman spectra of lightly doped cuprates

We consider the lightly doped cuprates Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ and La$_{2-x}$Sr$_x$CuO$_4$ (with $x=0.02$,0.04), where the presence of a fluctuating nematic state has often been proposed as a precursor of the stripe (or, more generically, charge-density wave) phase, which sets in at higher doping. We phenomenologically assume a quantum critical character for the longitudinal and transverse nematic, and for the charge-ordering fluctuations, and investigate the effects of these fluctuations in Raman spectra. We find that the longitudinal nematic fluctuations peaked at zero transferred momentum account well for the anomalous Raman absorption observed in these systems in the $B_{2g}$ channel, while the absence of such effect in the $B_{1g}$ channel may be due to the overall suppression of Raman response at low frequencies, associated with the pseudogap. While in Y$_{0.97}$Ca$_{0.03}$BaCuO$_{6.05}$ the low-frequency lineshape is fully accounted by longitudinal nematic collective modes alone, in La$_{2-x}$Sr$_x$CuO$_4$ also charge-ordering modes with finite characteristic wavevector are needed to reproduce the shoulders observed in the Raman response. This different involvement of the nearly critical modes in the two materials suggests a different evolution of the nematic state at very low doping into the nearly charge-ordered state at higher doping.Comment: 12 pages with 10 figures, to appear in Phys. Rev. B 201

Comment on "Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh2Si2"

In Phys. Rev. Lett. 106, 137002 (2011), A. Hackl and M. Vojta have proposed to explain the quantum critical behavior of YbRh2Si2 in terms of a Zeeman-induced Lifshitz transition of an electronic band whose width is about 6 orders of magnitude smaller than that of conventional metals. Here, we note that the ultra-narrowness of the proposed band, as well as the proposed scenario per se, lead to properties which are qualitatively inconsistent with the salient features observed in YbRh2Si2 near its quantum critical point.Comment: 3 page

Spectral signatures of critical charge and spin fluctuations in cuprates

We discuss how Raman spectra of high temperature superconducting cuprates are affected by nearly-critical spin and charge collective modes, which are coupled to charge carriers near a stripe quantum critical point. We find that specific fingerprints of nearly-critical collective modes can be observed and that the selectivity of Raman spectroscopy in momentum space may be exploited to distinguish the spin and charge contribution. We apply our results to discuss the spectra of high-T_c superconducting cuprates finding that the collective modes should have masses with substantial temperature dependence in agreement with their nearly critical character. Moreover spin modes have larger masses and are more diffusive than charge modes indicating that in stripes the charge is nearly ordered, while spin modes are strongly overdamped and fluctuating with high frequency.Comment: 6 pages and 3 figures, invited paper to the conference SCES 08, Buzios/Rio, Brazi

Nonequilibrium Spin Dynamics in the Ferromagnetic Kondo Model

Motivated by recent experiments on molecular quantum dots we investigate the relaxation of pure spin states when coupled to metallic leads. Under suitable conditions these systems are well described by a ferromagnetic Kondo model. Using two recently developed theoretical approaches, the time-dependent numerical renormalization group and an extended ow equation method, we calculate the real-time evolution of a Kondo spin into its partially screened steady state. We obtain exact analytical results which agree well with numerical implementations of both methods. Analytical expressions for the steady state magnetization and the dependence of the long-time relaxation on microscopic parameters are established. We find the long-time relaxation process to be much faster in the regime of anisotropic Kondo couplings. The steady state magnetization is found to deviate significantly from its thermal equilibrium value.Comment: 4 pages, 3 figures, final version as accepted by Physical Review Letter

New theoretical approaches for correlated systems in nonequilibrium

Abstract.: We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations. In agreement with the flow equation approach they show that for weak coupling the system relaxes to a "prethermalized” intermediate state instead of rapid thermalization. We discuss the description of nonthermal steady states with generalized Gibbs ensemble

Topological phase transition in a RNA model in the de Gennes regime

We study a simplified model of the RNA molecule proposed by G. Vernizzi, H. Orland and A. Zee in the regime of strong concentration of positive ions in solution. The model considers a flexible chain of equal bases that can pairwise interact with any other one along the chain, while preserving the property of saturation of the interactions. In the regime considered, we observe the emergence of a critical temperature T_c separating two phases that can be characterized by the topology of the predominant configurations: in the large temperature regime, the dominant configurations of the molecule have very large genera (of the order of the size of the molecule), corresponding to a complex topology, whereas in the opposite regime of low temperatures, the dominant configurations are simple and have the topology of a sphere. We determine that this topological phase transition is of first order and provide an analytic expression for T_c. The regime studied for this model exhibits analogies with that for the dense polymer systems studied by de GennesComment: 15 pages, 4 figure

Charge transfer fluctuation, d−d-wave superconductivity, and the B1gB_{1g} Raman phonon in the Cuprates: A detailed analysis

The Raman spectrum of the $B_{1g}$ phonon in the superconducting cuprate materials is investigated theoretically in detail in both the normal and superconducting phases, and is contrasted with that of the $A_{1g}$ phonon. A mechanism involving the charge transfer fluctuation between the two oxygen ions in the CuO$_2$ plane coupled to the crystal field perpendicular to the plane is discussed and the resulting electron-phonon coupling is evaluated. Depending on the symmetry of the phonon the weight of different parts of the Fermi surface in the coupling is different. This provides the opportunity to obtain information on the superconducting gap function at certain parts of the Fermi surface. The lineshape of the phonon is then analyzed in detail both in the normal and superconducting states. The Fano lineshape is calculated in the normal state and the change of the linewidth with temperature below T$_{c}$ is investigated for a $d_{x^{2}-y^{2}}$ pairing symmetry. Excellent agreement is obtained for the $B_{1g}$ phonon lineshape in YBa$_{2}$Cu$_{3}$O$_{7}$. These experiments, however, can not distinguish between $d_{x^{2}-y^{2}}$ and a highly anisotropic $s$-wave pairing.Comment: Revtex, 21 pages + 4 postscript figures appended, tp