**XIV
Training Course in the Physics of Strongly Correlated Systems**

*Vietri sul Mare (Salerno) Italy*

*October 5 - 16, 2009*

*Participant Seminar
Abstracts*

**
Mr.
Sergey
Artyukhin
**

Zernike Institute for Advanced Materials, University of Groningen, The Netherlands

**
Ferromagnetic insulator state in iron-doped FeTiO_3**

**Abstract:**
The solid solution of two antiferromagnetic compounds, FeTiO3 and Fe2O3, exhibits an unusual insulating ferromagnetic state appearing around room temperature. FeTiO3 is formed by alternating ferromagnetic planes of magnetic Fe and nonmagnetic Ti ions. In the solid solution some Ti atoms are substituted by Fe dopants, which frustrates the antiferromagnetic spin ordering by inducing a local ferromagnetic coupling between neighboring magnetic layers. The result is a large non-collinear modulation of spins around Fe dopands.
We study properties of these spin polarons and their effect on magnetic properties of (1-x)FeTiO3- xFe2O3.
The polarons carry a large magnetization, which at low doping leads to superparamagnetic behavior, while at larger doping the overlapping spin polarons induce a transition into a ferrimagnetic state. The phase diagram of
(1-x)FeTiO3- xFe2O3 obtained by Monte Carlo simulations agrees well with experimental observations.

**
Mr.
Wojciech
Brzezicki
**

M. Smoluchowski Institute of Physics, Jagiellonian University, Cracov, Poland

**
Quantum compass model on a chain, ladder and finite square clusters**

**Abstract:**
I show the exact solutions for the quantum compass model on a chain and ladder which are based on mapping to quantum Ising models in certain subspaces. I discuss the ground – state and thermodynamic properties of both models. I show the application of the Kernel Polynomial Method to finite compass clusters of the size 4x4 and 5x5. I show the transformation which maps 5x5 compass model to 10 classes of 4x4 models which can be solved by KPM for the ground – state and thermodynamic properties.

**
Dr.
Giacomo
Coslovich
**

Università degli Studi di Trieste, Italy

**
Discontinuities in the ultrafast electronic response of High-Tc Superconductors**

**Abstract:**
Ultrafast optical spectroscopy has been used in the past as a tool to study the strength of electron-electron and electron-phonon interactions in strongly correlated systems and High-temperature superconductors. Recently, the possibility to impulsively photo-induce a collapse of the superconducting state in these materials by means of an ultrashort laser pulse has attracted growing attention [1,2,3]. Non-linear laser intensity dependencies and discontinuities in the ultrafast electronic response are the key experimental features of this new physics, which is barely understood yet.
In this seminar we consider the case of Bi2212 superconductors at different dopings and temperatures. We present both experimental results of the ultrafast electronic response and simulations of the non-equilibrium behavior of a superconducting BCS gap. In the simulations the electronic structure of the Bi2212 sample is considered and several models of the non-equilibrium electron distribution functions are assumed.
The optical control of the electronic phase of a superconducting system opens the way towards the manipulation of matter based on the change of the thermodynamic potential along non-equilibrium pathways. This technique has possible application in other complex and strongly correlated materials. Further on, the possibility to follow the dynamics of such non-equilibrium phase transitions on the femtosecond timescale could help in the understanding of the key mechanisms at the base of the elusive superconducting and pseudogap phases in cuprates.
[1] P. Kusar, V. V. Kabanov, J. Demsar, T. Mertelj, S. Sugai and D. Mihailovic, "Controlled Vaporization of the Superconducting Condensate in Cuprate Superconductors
by Femtosecond Photoexcitation", PRL 101, 227001 (2008)
[2] C. Giannetti, G. Coslovich, F. Cilento, G. Ferrini, H. Eisaki, N. Kaneko, M. Greven, F. Parmigiani: "Discontinuity of the ultrafast electronic response of underdoped superconducting Bi2Sr2CaCu2O8+delta strongly excited by ultrashort light pulses", PRB 79, 224502 (2009)
[3] T. Mertelj, V. V. Kabanov, C. Gadermaier, N. D. Zhigadlo, S. Katrych, J. Karpinski and D. Mihailovic, "Distinct Pseudogap and Quasiparticle Relaxation Dynamics in the Superconducting State of Nearly Optimally Doped SmFeAsO0:8 F0:2 Single Crystals", PRL 102, 117002 (2009)

**
Dr.
Andrea
Di Ciolo
**

Institut für Theoretische Physik, Goethe Universität Frankfurt, Frankfurt am Main, Germany

**
Evaluation of observables using Gutzwiller wave functions **

**Abstract:**
I will discuss about the determination of response functions and projected excitations of Gutzwiller wave functions.
According to my expertise, I will also deliver a short survey of the state of art of the generalized Gutzwiller approaches
for strongly correlated systems (Time-Dependent Gutzwiller Approximation, Renormalized Mean Feld Theory ...)

**
Mr.
Mark
Fischer
**

Institute for Theoretical Physics, ETH Zürich, Switzerland

**
Effects of spin-orbit coupling on the metamagnetic transition in Sr$_3$Ru$_2$O$_7**

**Abstract:**
Ultra-clean crystals of Sr$_3$Ru$_2$O$_7$ undergo a metamagnetic transition at low temperatures. This transition shows a strong anisotropy in the applied field direction with the critical field $H^*$ ranging from $\sim 5.1$T for $H\perp c$ to $\sim 8$T for $H\parallel c$. In addition, studies on ultra-pure samples revealed a splitting of the metamagnetic transition into at least two magnetization anomalies for fields in $c$-direction. It has been suggested that a nematic phase emerges between the magnetization jumps.\\
The aim of our study is to explain the field anisotropy of these phenomena. Based on a microscopic tight-binding model, we introduce the metamagnetic transition by means of a van Hove singularity scenario and we describe the low-temperature phase as a nematic state favored by forward scattering processes. The rotation of the O-octahedra around the $c$-axis observed in this material introduces a staggered spin-orbit coupling within the planes and naturally leads to an anisotropy of the magnetic response in accordance to observation. Moreover, the spin-orbit coupling shows a strong influence on both, the critical field $H^*$ and the occurence of the nematic phase.

**
Miss
Olga
Howczak
**

M. Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland

**
de Haas-van Alphen magnetization oscillations and spin-dependent masses in a two-dimensional Fermi liquid of correlated quasiparticles **

**Abstract:**
We consider the magnetic properties of two-dimensional Fermi liquid of quasiparticles with spin dependent masses in periodic crystal potential. To determine thermodynamic properties of this Hofstadter like model we use quantum transfer-matrix method developed by T. Xiang and collaborators. The de Haas-van Alphen oscillation of magnetization is calculated at finite temperatures.

**
Dr.
Anna
Kauch
**

Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, Germany

**
Strong coupling approximation of the Bosonic Dynamical Mean-Field Theory equations**

**Abstract:**
The bosonic dynamical mean-field theory (B-DMFT), recently formulated by Byczuk and Vollhardt (Phys. Rev. B 77, 235106 (2008)), provides a comprehensive and thermodynamically consistent description of correlated lattice bosons. Within the B-DMFT normal and Bose-Einstein condensed bosons are treated on equal footing. In the B-DMFT the lattice bosonic problem is replaced by a single impurity coupled to two bosonic baths (corresponding to normal and condensed bosons, respectively). This yields a set of B-DMFT equations which have to be solved self-consistently. We propose here an approximate method to solve the B-DMFT equations for the bosonic Hubbard model by performing a renormalized strong-coupling perturbation expansion (linked-cluster expansion) around the atomic limit. We investigate the validity of this approach by comparing our results to the known phase diagram of the Hubbard model.

**
Dr.
Ivan
Leonov
**

Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, Germany

**
Structural transformations caused by electronic correlations**

**Abstract:**
The electronic structure of materials can often be described
quite accurately by density functional theory in the
local density approximation (LDA) or the generalized
gradient approximation (GGA). However, these
methods usually fail to predict the correct electronic and
structural properties of materials where electronic correlations
play a role. Extensions of LDA, e.g., LDA + U
and self-interaction correction LDA, can improve the
results, e.g., the band gap value and local moment, but only
for solids with long-range order. Hence the computation of
electronic, magnetic, and structural properties of strongly
correlated paramagnetic materials remains a great challenge.
Here, we present a computational scheme [1] for the
investigation of complex materials with strongly interacting
electrons which
is able to treat atomic displacements, and hence structural
transformation, caused by electronic correlations.
It combines ab initio band structure and dynamical
mean-field theory and is implemented in terms of plane-wave
pseudopotentials. With this approach, we address electronic
and structural properties of paramagnetic perovskites KCuF3,
K2CuF4, and LaMnO3, the prototypical materials for orbital
ordering and cooperative Jahn-Teller distortion.
[1] I. Leonov, N. Binggeli, Dm. Korotin, V. I. Anisimov, N. Stojic,
and D. Vollhardt, Phys. Rev. Lett. 101, 096405 (2008).

**
Mr.
Jan
Kaczmarczyk
**

Condensed Matter Theory and Nanophysics Department, Jagiellonian University, Cracow, Poland

**
Superconductivity in a correlated system of quasiparticles with spin-dependent masses**

**Abstract:**
I will discuss a paired state of quasiparticles with spin dependent masses, which were observed recently in the CeCoIn_5 system. In the same strongly-correlated system the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase appears. I will show that the spin-dependent masses essentially extend the regime of applied field and temperatures under which the FFLO phase is stable. We believe that the mechanism of stabilization of the FFLO phase by the spin-dependent masses is generic. Therefore, FFLO phases should be searched for in the same systems in which spin-dependent masses were observed and vice versa. I will compare results of our model calculations with the experiment.

**
Mr.
Zhou
Li
**

Department of Physics, University of Alberta, Edmonton, Canada

**
Refinements of Lanczos method to solve the Holstein Model**

**Abstract:**
We proposed two simple refinements of Lanczos method to solve the Holstein model. 1. By starting from the unperturbed state in the strong-coupling limit instead of the bare electron state, we speed up the convergence considerably in the intermediate and strong coupling regime. 2. By starting from the well converged strong coupling regime, each step we lower the value of electron phonon coupling (or phonon energy) with a small amount, use as a starting wave function the previous solution, truncate to include components with some minimal amplitude (so that a few hundred basis states at most are used), then converge the solution for this value of electron phonon coupling. This process can be continued until the desired range is covered.
As is known, in the adiabatic limit, there is phase transition from a small polaron localized state to a free electron delocalized state, in dimensions two and higher. Nonetheless, as is known through other considerations, for any nonzero phonon frequency, the crossover is smooth.
By using these two refinements, we have obtained numerical exact results for a wide range of parameters. In particular, we obtain well converged results over all coupling strengths and for low phonon frequencies. The results for low frequencies in particular illustrate a rather abrupt crossover to a regime where multi-phonon processes are prevalent.
REFERENCES
1)J. Bonca, S.A. Trugman and I.Batistic, Phys.Rev.B 60, 1633 (1999)
2)H.Fehske and S.A. Trugman, “Polarons in Advanced Materials”, edited by A.S.Alexandrov, Springer Series in Material Sciences 103 pp. 393-461, Springer Verlag, Dordrecht (2007).

**
Dr.
Giovanni
Mazzarella
**

Dipartimento di Fisica "Galileo Galilei", Universita' degli Studi di Padova, Italy

**
Atomic Josephson junction with two bosonic species**

**Abstract:**
We study an atomic Josephson junction (AJJ) in presence of two interacting Bose-Einstein condensates (BECs) confined in a double well trap. We assume that bosons of different species interact with each other. The macroscopic wave functions of the two components obey to a system of two 3D coupled Gross-Pitaevskii equations (GPE). We write the Lagrangian of the system, and from this we derive a system of coupled ordinary differential equations (ODE), for which the coupled pendula represent the mechanic analogous. These differential equations control the dynamical behavior of the fractional imbalance and of the relative phase of each bosonic component. We perform the stability analysis around the points which preserve the symmetry and get an analytical formula for the oscillation frequency around the stable points. Such a formula could be used as an indirect measure of the inter-species s-wave scattering length. We also study the oscillations of each fractional imbalance around zero and non zero - the macroscopic quantum self-trapping (MQST) - time averaged values. For different values of the inter-species interaction amplitude, we carry out this study both by directly solving the two GPE and by solving the corresponding coupled pendula equations. We show that, under certain conditions, the predictions of these two approaches are in good agreement. Moreover, we calculate the crossover value of the inter-species interaction amplitude which signs the onset of MQST.

**
Mr.
Rubem
Mondaini
**

Solid State Physics Department, Federal University of Rio de Janeiro, Brazil

**
Electronic correlations in disordered honeycomb lattices**

**Abstract:**
In the past few years, much attention has been given to the study of honeycomb lattices. Beyond the experimental motivation due to the recent fabrication of graphene sheets, this importance also arises from the fact that the honeycomb lattice has many interesting properties. In usual square-lattice systems, any nonzero interaction energy U between the electrons drives a Mott metal-insulator and paramagnetic-antiferromagnetic phase
transitions. In the honeycomb lattice, it is necessary a finite energy Uc to drive both transitions. Moreover it is interesting to study such systems with a disorder term. Anderson showed that below a critical density any system with disorder could not possess conductivity. The approach used in this work is the Hubbard-Anderson model, where we can define different onsite energies chosen randomically within a symmetric range. This configures a
disorder term and it can be measured by the magnitude of the range. To perform the simulations we employ the determinant quantum monte carlo
(DQMC) method. In this work, the aim is to study how magnetic correlations are affected by disorder at near half-filling.
We will present results for spin correlations as a function of temperature, lattice size and correlation strength U for different degrees of disorder.

**
Dr.
Gang
Li
**

Institute of Theoretical Physics and Astrophysics, University of Wuerzburg, Germany

**
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**Abstract:**
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**
Miss
Aroon
O'Brien
**

Max Planck Institute for the Physics of Complex Systems, Dresden, Germany

**
Charge fractionalization in a model of spinless fermions on a kagome lattice**

**Abstract:**
The study of the magnetic properties of geometrically frustrated spin systems is an area of intense interest. However, the charge degrees of freedom of such structures are less understood. Previous work on checkboard lattice models has revealed the existence of fractional charges [1]. These charges were later shown to be confined [2].
We study a model of spinless fermions on finite kagome clusters, which gives rise to charge fractionalization in a similar manner. The 2D nature of the kagome lattice raises the question as to whether the fractional charges have anyonic statistics. Furthermore, kagome lattice models have established and emerging analogies in experiment [3].
In our model, the fractional charge excitations occur at 1/3 filling. We present an investigation of the statistics and dynamics of these fractional charges through an analysis of the dynamical properties of hardcore bosonic and spinless fermionic spectral functions. Furthermore we discuss a complementary dimer model analysis.
[1] P.Fulde, K. Pence, N. Shannon, Ann. Phys., V11, 892 (2002)
[2] F. Pollmann. and P. Fulde, Europhys. Lett., v75, 133 (2006)
[3] arXiv: 0906.3042v1 [cond-mat.quant-gas] 16 Jun 2009

**
Miss
Dorota
Rudzinska
**

Institute of Physics, University of Technology, Wroclaw, Poland

**
Broader view on superconducting phase in presence of a momentum-dependent impurity scattering potential.**

**Abstract:**
Controlled impurity doping is an useful tool in the identification of a symmetry of a superconducting ground state. We intensively studied behavior of order parameter (OP) and local density of states (LDOS) in s-wave superconductors in vicinity of scattering center [1-7] and analized these quantities from two points of view. Namely in real and complementary in reciprocal space. The k-space image carries interesting information about feature of the system like in case of LDOS [8,9]. Followed this trace we also investigate Fourier transform of order parameter. Our calculation are done in linear approximation and more extended form in T-matrix approximation but only for 'on-site' potential.
1.A.L. Fetter, Phys. Rev. 140, A1921 (1965).
2.T. Xiang, J.M. Wheatley, Phys. Rev. B 51, 11721 (1995).
3.G. Litak, Physica B 359-361, 566 (2005).
4.A. Ghosal, M.Randeria, N. Trivedi, Phys. Rev. Lett. 81, 3940 (1998).
5.G. Harań, PRB 65, 216501 (2002)
6.A. Maciąg, P. Pisarski, G. Harań, Physica C 387, 73 (2003)
7.D. Rudzińska, P. Pisarski, G. Harań Acta Phys. Pol. A 114, 149 (2008).
8.L. Capriotti, D.J. Scalapino, R.D Sedgewick, Phys. Rev. B. 68, 014508 (2003).
9.P.Pisarski,G.Harań, Phys. Status Solidi B 242, 426 (2005).

**
Mr.
Philipp
Wissgott
**

Solid State Physics, UT Vienna, Austria

**
Thermopower of Na0.7CoO2 studied by LDA+DMFT**

**Abstract:**
Recently, cobaltates NaxCoO2 have attracted much interest due to their high thermopower and for the appearance of superconductivity in the H_2O intercalated compounds. This talk describes a combined Local Density Approximation(LDA) and Dynamical Mean Field Theory (DMFT) study to investigate the strength of correlation effects in the representative compound Na$0.7CoO2.
The bandstructure shows mostly a1g characteristics around the Fermi edge. Therefore, an effective one band model is considered, where a single-band tight-binding fit has been applied to the LDA bandstructure.
To account for the stoichiometric factor xNa=0.7, we extend the existing DMFT code to include disorder by means of the Coherent Potential Approximation. Computational results can be separated in sodium and vacancy contributions, which allows for a detailed correlation analysis.
From the DMFT self energy, the thermopower for various temperatures is computed by Linear Response Theory and compared with experiment.

**
Mr.
Andrej
Schwabe
**

Physics Department, University of Hamburg, Germany

**
Interacting Spin Waves in the Ferromagnetic Kondo Lattice Model**

**Abstract:**
We present an approach for the ferromagnetic, three-dimensional, translational symmetric Kondo lattice model which allows to derive both magnon energies and linewidths (lifetimes) and study the properties of the ferromagnetic phase.
Our approach consists of mapping the Kondo lattice model onto an effective Heisenberg model by the help of the "modified RKKY interaction" and the "interpolating self-energy approach". The Heisenberg model is approximatively solved by applying the Dyson-Maleev transformation and using the "spectral density approach" with a broadened magnon spectral density.

**
Dr.
Bretislav
Sopik
**

Institute of Physics, Academy of Sciences, Prague, Czech Republic

**
Conserving T-matrix theory of superconductivity**

**Abstract:**
A selfconsistent T-matrix theory of many-Fermion systems is proposed. In the normal state the theory agrees with the Galitskii-Feynmann approximation, in the superconducting state it has the form of the renormalized Kadanoff-Martin approximation. The two-particle propagator satisfies the Baym-Kadanoff symmetry condition which guarantees that the theory conserves the number of particles, momentum and energy. The theory is developed for retarded interactions leading to the Eliashberg theory in the approximation of a single pairing channel.
Let us note, we hope to have finished a numerical discussion of T-matrix behaviour close to Tc using proposed theory during the end of summer.

**
Miss
Hanna
Terletska
**

Florida State University, National High Magnetic Field Laboratory, Tallahassee, USA

**
Fingerprints of intrinsic phase separation**

**Abstract:**
We theoretically study the properties of a recently observed [1] inhomogeneous phase preceding the metal-insulator transition in a magnetically-doped two-dimensional electron gas (2DEG). We show that, due to competition between (ferromagnetic) double-exchange and (anti-ferromagnetic) super-exchange, at very low carrier density such a system is unstable toward intrinsic phase separation (PS). Here, ferromagnetic carrier-rich (metallic) ``droplets'' emerge within a magnetically disordered carrier-poor (insulating) matrix. Our calculations indicate that this regime should display very unusual transport, featuring colossal magneto-resistance with exceptionally weak density dependence - in striking agreement with experiments [1] on CdMnTe quantum wells. Such exotic transport properties - we argue - should be considered as ``fingerprints'' for intrinsic phase separation, a behavior very different from situations where phase coexistence is driven by disorder due to extrinsic impurities or defects.
[1] J. Jaroszynski et.al, Phys. Rev. B 76, 045322 (2007).

**
Dr.
Luca
Tocchio
**

Institute for Theoretical Physics, University of Frankfurt , Germany

**
Spin-liquid and magnetic phases in the anisotropic triangular lattice: the case of organic charge-transfer salts**

**Abstract:**
The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different
hopping amplitudes t and t', is relevant to describe the low-energy physics of k-(ET)2X, a family of
organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques,
on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems.
The results show that there is no magnetic order for reasonably large values of the electron-electron
interaction U and frustrating ratio t′/t = 0.85, suitable to describe the non-magnetic compound with
X=Cu2(CN)3. On the contrary, Néel order takes place for weaker frustrations, i.e., t′/t = 0.4÷0.6,
suitable for other compounds.