XVI Training Course in the Physics of Strongly Correlated Systems
Vietri sul Mare (Salerno) Italy
October 3 - 14, 2011
Participant Seminar Abstracts
Mr. Edmund Bennett
School of Physics & Astronomy, University of St. Andrews, St. Andrews, Scotland
Majorana Dimerised Order in Magnetic Systems
Abstract: My research considers the analysis of quantum critical points (QCPs) using a Majorana fermion [1] representation of spin. Majorana fermions are a useful spin representation as they obey Wick’s theorem and automatically provide the correct (S^{a})^{2} = 1/4 for stationary spin-1/2 lattice spins. I consider a 3D Ising model in an applied transverse field, which is an adequate model of the ferromagnetic material LiHoF_4, which exhibits a QCP. A Majorana dimerisation decoupling and a Ising magnetic decoupling may be used on equal footing in models describing this system and suggest the presence of order above the QCP, therefore giving insight into the behaviour of the material in this regime. I present a mean-field (saddle-point) approximation and gaussian corrections to this theory. [1] W. Mao, P. Coleman, C. Hooley & D. Langreth; PRL, 91, 20, p. 2072031-2072034; 2003
Mr. Andreas Eberlein
Department Quantum Many Body Systems, Max Planck Institute for Solid State Research, Stuttgart, Germany
Functional renormalization group study of fluctuation effects in fermionic superfluids
Abstract: We study ground state properties of the attractive Hubbard model at weak coupling with the aim of finding an efficient description of the effective Nambu two-particle vertex in a singlet superconductor. We decompose the vertex into a sum of interaction channels, each capturing a particular singular dependence on external momenta and frequencies. Using the functional renormalization group, we derive flow equations for the interaction channels on one-loop level. We compute the frequency dependence of the self-energy as well as the momentum and frequency dependence of the two-particle vertex. Our results for the impact of fluctuations on the superconducting gap are in good agreement with the literature.
Mr. Denis Golež
F1, Institute Jozef Stefan IJS, Slovenia, Slovenia
Nonequillibrium dynamics of polaron systems
Abstract: Polaron is a quasi-particle, which is formed by a charged particle and accompanied polarisation field. As electron is moving throught the crystal its interacting with the lattice creates deformation. This deformation acts as a effective potential well, which lowers the mobility of the quasiparticle. In previous years theoretical research was limited on the equilibrium properties of the systems. However, as experiments starts probing physical properties far beyond the linear response regime, the interest on the correlated phenomena out of the equilibrium rapidly starts to grow in fields like the transport in nanosystems, ultra-cold atomic gasses and time resolved optical spectroscopy (pump and probe experiments). I will represent the nonequillibrium dynamics of the Holstein polaron problem driven by a constant or pulse modulated electric field. In the case of constant electric field the crucial condition for emergence of the quasi-stationary current in the system driven by constant electric field is the existence of the bath, which can absorb energy, while for pulse modulated field we can analyse the relaxation dynamics.
Mr. Felix Hofmann
I. Institut für Theoretische Physik, University of Hamburg, Germany
(Non-equilibrium) Self-energy-functional theory and conserving approximations
Abstract: The self-energy-functional theory [1] provides a general framework for the systematic construction of non-perturbative, thermodynamically consistent approximations in order to study strongly correlated systems in the thermodynamical limit in and out of equilibrium and proves to respect particle number and spin conservation laws [2]. On the space of self-energies a functional can be constructed which is stationary at the physical self-energy and equals the physical grand canonical potential when evaluated at the latter. Without approximating the (formally unknown) functional, the variational principle can be evaluated by restricting the self-energies to a subspace of (numerically) solvable reference systems. This is done self consistently, such that the results are obtained in the thermodynamical limit. By choosing appropriate classes of reference systems, theories like variational-cluster-approach (VCA) and dynamical-mean-field-theory (DMFT) can be derived from SFT as well as improved variants. Likewise, SFT allows for studying phases and phase transitions (by numerical means) as for example the Mott metal-insulator transition, magnetic phase transitions or the transition from antiferromagnetic to the superconducting phase in Hubbard-like and spin models. [1] M. Potthoff, AIP Conf. Proc. 1419, pp. 199-258 (2011) [2] F. Hofmann and M. Potthoff, to be published
Mr. Ebad Kamil
Institute for Theoretical Physics, University of Goettingen, Germany
Reduced Density Matrix functional theory- A suitable vehicle to import explicit correlations
Abstract: A variational formulation for the calculation of interacting fermions system based on density matrix functional theory is presented. This formulation allows importing explicit many particle effects into standard density functional theory based calculations and also avoids ambiguities of double counting terms inherent to other approaches. Local approximation for explicit correlations is introduced and the resulting constrained impurity problem is solved using resolvent expansion/Quantum Master equation technique developed in the field of Open quantum system.
Mr. Pasquale Marra
IFW Dresden, Germany
Probing the Phase of the Superconducting Order Parameter via Resonant Inelastic X-ray Scattering
Abstract: The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned Resonant Inelastic X-ray Scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors of various symmetries we show that the low- energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.
Dr. Soumya Mukherjee
Asia-Pacific Center for Theoretical Physics (APCTP), Pohang, South Korea
Possible symmetry of the order parameter in noncentrosymmetric superconductor Li2Pt3B
Abstract: The nature of the order parameter symmetry in the noncentrosymmetric superconducting compound LI2Pt3B seems to be an interesting and long lasting problem as findings of some experiments contradict others. The most nearest in nature of this compound is Li2Pd3B, which shows s-wave kind of behaviour and this is widely accepted and verified. On the other hand the nature of the order parameter in the Pt compound is still full of contradictions. Based on a spin fluctuation mechanism we describe the possible nature and symmetry of the order parameter in this compound which also follow experimental findings. This work predicts some s(+-) type of order parameter with line nodes as the possible candidate. Mystery still remains regarding the explanation of the NMR experiment and this will be explained. More accurate theory/experiment are needed to verify/clarify these prediction/mystery.
Mr. Goran Niksic
University of Zagreb, Faculty of Science - Physics Department, Zagreb, Croatia
SDW and the pseudogap in cuprates
Abstract: We investigate the SDW susceptibility around the pseudogap temperature T* in a realistic three-band model of the CuO_2 planes in high-Tc cuprates. This approach starts from initially empty copper orbitals and metallic oxygen holes which then hybridise with the copper sites. The magnetic scattering of two oxygen holes in the hybridised ground state introduces k-dependent spectral weights and projectors which can lead to a suppression of the logarithmic singularity (commensurate SDW response) even at the van Hove doping, in the presence of even slight disorder. We find the three-band structure, site-selective scattering, and small amount of disorder to be the minimal elements of complexity which cumulatively enable the incommensurate SDW response to survive up to optimal doping without involving superconductivity. The supression of the commensurate response already at one-loop level corresponds to the crossover from the weak-coupling to the strong-coupling regime, characteristic of complex materials.
Mr. David Nozadze
Missouri university of science and technology, USA
Composition-tuned quantum smeared phase transitions
Abstract: Phase transitions in random systems are smeared if individual spatial regions can order independently of the bulk system. We study such smeared phase transitions in substitutional alloys A_{1-x}B_x that can be tuned from an ordered phase at composition x=0 to a disordered phase at x=1. We show that the ordered phase develops a pronounced tail that extends over all compositions x<1. Using optimal fluctuation theory, we derive the composition dependence of the order parameter and other quantities in the tail of the smeared phase transition. We also investigate the influence of spatial disorder correlations on smeared phase transitions. As an example, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in Sr_{1-x}Ca_xRuO_3 is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. We find that the ferromagnetic phase is significantly extended by the disorder and develops a pronounced tail over a broad range of the composition x. These findings are explained by our model of smeared quantum phase transitions in itinerant magnets.
Mr. Victor Quito
Department of Condensed Matter Physics, Institute of Physics Gleb Wataghin, Unicamp - Campinas, Brazil
Bilinear and biquadratic random spin-1 chain
Abstract: In this talk I will present our results concerning random isotropic spin 1 chains with first neighbor interactions that include the usual bilinear Heisenberg term but additionally consider a biquadratic \left(S_{i}\cdot S_{i+1}\right)^{2} interaction, using the Strong Disorder Renormalization Group technique. I will start reviewing the known results for the bilinear chain in the scope of the SDRG method, either in the limit of strong and weak disorder, showing the different phases that can emerge. Latter I will show our phase diagram as function of the ratio between bilinear and biquadratic terms for the strong disorder regime, particularly for the cases where the system presents the higher SU(3) symmetry.
Mr. Roman Rausch
Institute of Theoretical Physics, University of Hamburg, Hamburg, Germany
Phase diagram of a chemically disordered and magnetically concentrated system
Abstract: We present self-consistent CPA-RKKY calculations of the critical temperatures of the antiferromagnetic phases within the pure Kondo-lattice model (sc and fcc lattices). Extending the results to chemical and magnetic disorder, we are able to calculate the phases of the concentrated spin system Eu1−xGdxS which agree well with the experiment. This substance also shows a spin-glass phase whose origin is briefly discussed from a proposed microscopic principle.
Mr. Esmaeel Sarvestani
Forschungszentrum Juelich GmbH and RWTH Aachen, Germany
Josephson supercurrent in a graphene-superconductor junction
Abstract: Within the tunneling Hamiltonian formulation for the eight-component spinors, the Josephson critical supercurrent has been calculated in a planar superconductor-normal graphene-superconductor junction. Coupling between superconductor regions and graphene is taken into account by a tunneling Hamiltonian which contains two types of tunneling, intravalley and intervalley tunneling. Within the present tunneling approach, we find that the contributions of two kinds of tunneling to the critical supercurrent are completely separable. Therefore, it is possible to consider the effect of the intervalley tunnelings in the critical supercurrent. The incorporation of these type of processes into the tunneling Hamiltonian exposes a special feature of the graphene Josephson junctions. The effect of intervalley tunneling appears in the length dependence plot of critical current in the form of oscillations. We also present the results for temperature dependence of critical supercurrent and compare with experimental results and other theoretical calculations.
Mr. Mohammad Sayad
I. Institut für Theoretische Physik, University of Hamburg , Germany
Mean-Field Theory of the Time-Dependent Kondo Effect
Abstract: We propose a generalization of the hybridization mean-field theory [1,2] to Kondo systems far from thermal equilibrium. This time-dependent mean-field approach is used to study the formation or breaking of a Kondo singlet on the time axis. To this end we consider a Kondo impurity on a one-dimensional tight-binding chain as well as on two- and three-dimensional clusters after a sudden change of the exchange-coupling strength. We present results for the ground-state and the finite-temperature equilibrium phase diagram of the Kondo Hamiltonian and for the non-equilibrium final-state dynamics after a quench through the phase boundary and discuss the time-dependent competition of the Kondo effect with the RKKY interaction for systems with two magnetic impurities. [1] C. Lacroix and M. Cyrot, Phys. Rev. B 20, 1969 (1979) [2] D. Newns and N. Read, Advances in Physics 36, 799 (1987).
Mr. Gerardo Sica
Dipartimento di Fisica "E.R. Caianiello", Università degli Studi di Salerno, Italy
High temperature superconductivity from realistic long-range Coulomb and Fröhlich interactions
Abstract: It has been recently found that in highly polarizable ionic lattices the bare long-range Coulomb and electron-phonon (Fröhlich) interactions almost negate each other resulting in a short-range polaronic spin-exchange Jp(u) of phononic origin that depends on the effective on-site interaction u coming from the competition between repulsive Hubbard-U and attractive on-site Fröhlich interaction. Different from the well-known t-J model, Jp(u) is not responsible for antiferromagnetism but for the formation of small and superlight bound states of two polarons (bipolarons) that condense with a critical temperature well in exceed of 100K. The effective on-site term, limiting the double occupancy, reduces the inter-site polaron exchange Jp resulting in a transition from small to large bipolarons at some critical value of u that accounts for the BEC/BCS crossover.
Dr. Sergey Slizovskiy
Dept. of Physics, Loughborough University, UK
Nonlinear magnetization in graphene
Abstract: We discuss the magnetization of graphene in a strong magnetic field on a free-electron level. We show that the magnetization exhibits non-linear behaviour as a function of the applied field, reflecting the strong non-analyticity of the two-dimensional effective action of Dirac electrons. The necessary values of the magnetic field to observe this non-linearity vary from a few Teslas for clean samples to few tens of Teslas for lower-quality samples. In the light of these calculations, we discuss the effects of disorder and interactions as well as the experimental conditions under which the predictions can be observed.
Mr. Bruno Tomasello
SEPnet: Kent University & ISIS (STFC spallation facility at the Rutherford Appleton Laboratory), UK
Quantum Dynamics in Spin Ice
Abstract: Spin Ice is one of hottest spots in condensed matter physics. This class of magnetic pyrochlores, namely Ho2Ti2O7 and Dy2Ti2O7 , exhibits a wide variety of exotic features at very low temperatures. These are mainly driven by the macroscopic degeneracy that characterizes the ground state [1]. Such degeneracy arises because of the particular arrangement of the Rear Earth (RE) ions (Ho3+or Dy3+) along the pyrochlore lattice (corner-sharing tetrahedra). Each of the magnetic dipoles (spins) sits, indeed, on the vertex of a tetrahedron and is forced, by a strong Crystal Field (CF), to point along the local <111> direction (easy axis). Hence every spin has only two possible configurations: to be pointing inward or outward of the tetrahedron. These geometrical constraints on the spins, together with their magnetic interactions, is what gives Spin Ice its characteristic geometrical frustration [1]. Such frustration not only accounts for a broad range of experimental measurements, it represents also the keystone for the most remarkable feature in Spin Ice: the emergent magnetic monopoles [2]. These quasiparticles attracts a lot of interest both from a fundamental point of view (as an example of fractionalisation in three dimensions) as well as, more speculatively, for the possibility of new technologies exploiting them ("magnetricity" [3,4] ). However, despite the variety of experiments [3-7], a complete and unique description for the dynamics of such monopoles is still missing . Indeed the theoretical models studied to date feature classical Ising spins and therefore the only mechanism for monopole transport in these models is thermal diffusion. In contrast some experiments [6] suggest that the temperature dynamics are characterised by intrinsic temperature-independent timescales.Here we investigate the role of quantum dynamics for the monopoles in the low temperature regime. In Spin Ice, indeed, the hopping of a magnetic monopole, from one site to the next, consists of the flip of a large spin from a configuration, along the easy axis, to the opposite one. At very low temperatures, this requires quantum-mechanical tunnelling through a large anisotropy barrier. Starting from a single RE3+ ion picture we analyze the interplay between the Crystal Field environment ( measured via neutron scattering on RE-titanates; RE2Ti2O7) and internal magnetic fields (from Montecarlo simulations) acting on the spin. We found that quantm mechanics gives very interesting insights in the zero-temperature physics of this system. In particular, by means of fields transverse to the easy axis, we find a quantum spin flip (tunnelling) between the two opposite configurations. Remarkably when the transverse field is tuned across the values obtained by the Montecarlo simulations the range of frequencies spans the same order of magnitudes found among the different experiments. These results suggest that our quantum-mechanical theory provides a self consistent description for the hopping of monopoles, and more in general may also give an important contribution in interpreting some of the current experimental puzzles about dynamics in these systems. [1] S.Bramwell and M.Gingras, Science 294 (2001); [2] C.Castelnovo et al. Nature 451 (2008) ; [3] S.Bramwell et al. Nature 461 (2009) ; [4] S.Giblin et al. Nature-Phys 7 (2011); [5] S.Dunsiger et al PRL 107 (2011) ; [6] K.Matsushira et al. JPSJ 80 (2011) ; [7] S.Blundell PRL 108 (2012) ;
