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

*Vietri sul Mare (Salerno) Italy*

*October 3 - 14, 2011*

*Participant Seminar
Abstracts*

**
Mr.
Marcin
Abram
**

Condensed Matter Theory and Nanophysics Department, Marian Smoluchowski Institute of Physics, Jagiellonian University, Kraków, Poland

**
Statistically-consistent Gutzwiller Approach (SGA) for t-J-U model**

**Abstract:**
A Statistically-consistent Gutzwiller Approximation (SGA), which has been developed very recently in our group by J. Jędrak, J. Kaczmarczyk and J. Spałek [arXiv:1008.0021v2] is introduced and compared with the well-known Gutzwiller Approximation (GA). Application to the Hubbard and t-J-U models is discussed in detail. For the t-J-U model a coexistence of antiferromagnetism (AF) and superconductivity (SC) is examined.

**
Mr.
Ádám
Bácsi
**

Department of Physics, Budapest University of Technology and Economics, Budapest, Hungary

**
Mean-field quantum phase transition in graphene and in general gapless systems**

**Abstract:**
In the seminar I will study the quantum critical properties of antiferromagnetism in graphene at zero temperature within mean-field (MF) theory. The resulting exponents differ from the conventional MF exponents describing finite temperature transitions. I will show that this description can be generalized for general gapless systems in which the density of states has power-law dependence, i.e., g(e)~e^r, r>-1. For r>2, the conventional MF exponents are recovered, while for -1<r<2, the exponents vary significantly with r. This extends the MF universality class of quantum-critical phase transitions, covering a much broader region of values of critical exponents than that of the conventional Landau theory. (The seminar is based on Phys. Rev. B 82, 153406 (2010).)

**
Mr.
Edmund
Bennett
**

School of Physics & Astronomy, University of St. Andrews, St. Andrews, Scotland

**
Depicting spin with Majorana fermions**

**Abstract:**
My research considers the analysis of quantum critical points 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 [2]. Furthermore, the representation of valence bond type operators and spin operators is equally simple in this formalism. I shall demonstrate a mean-field theory developed in terms of “valence bond” operators made from of Majorana fermions. These mean-field equations are then Fourier transformed, giving us access to the partition function for these systems. Methods of this type will hopefully demonstrate that Majorana fermions are a novel and powerful method of depicting spin in condensed matter systems.
[1] W. Mao, P. Coleman, C. Hooley & D. Langreth; PRL, 91, 20, p. 2072031-2072034; 2003
[2] Quantum Field Theory in Condensed Matter Physics, 2nd Edition, Alexei M. Tsvelik, CUP; 1996

**
Dr.
Gianluca
Bertaina
**

Institute of Theoretical Physics, EPFL, Lausanne, Switzerland

**
BCS-BEC crossover in two dimensions and the role of polarons and molecules: a Quantum Monte Carlo study**

**Abstract:**
We investigate the crossover from Bardeen-Cooper-Schrieffer (BCS) superfluidity to Bose-Einstein condensation (BEC) in a two-dimensional Fermi gas at $T=0$ using the fixed-node diffusion Monte Carlo method. We calculate the equation of state and the gap parameter as a function of the interaction strength, observing large deviations compared to mean-field predictions. In the BEC regime our results show the important role of dimer-dimer and atom-dimer interaction effects that are completely neglected in the mean-field picture. We also consider the highly polarized gas and the competition between a polaronic and a molecular picture.

**
Mr.
Wojciech
Brzezicki
**

Marian Smoluchowski Institute of Physics, Jagiellonian University, Krakow, Poland

**
ENTANGLED SPIN-ORBITAL PHASES IN THE d9 MODELS**

**Abstract:**
The phase diagram of the spin-orbital (SO) Kugel-Khomskii (d9) model posed a challenging theoretical problem [1], yet it is still unknown. Here we investigate the phase diagrams of the d9 model,depending on Hund's exchange J_h and the e_g orbital splitting E_z, for a bilayer and a monolayer square lattice using Bethe-Peierls-Weiss methodwith exact diagonalization of a cubic or square cluster coupled to its neighbors in ab planes by the mean-field (MF) terms. The cluster MF method confirms existence of singlet phases similar to those obtained by variational wave functions [2], and enables finite SO order parameter independent of spin and orbital ordering. For a bilayer we obtain phases with interlayer spin singlets stabilized by holes in 3z^2-r^2 orbitals and with alternating plaquette valence-bond (PVB) as well as two new phases with SO entanglement, in addition to the antiferromagnetic (G-AF, A-AF) and ferromagnetic (FM) order. For a monolayer we obtained at temperature T=0: (i) the PVB phase, (ii) two AF phases with either 3z^2-r^2 or x^2-y^2 orbitals occupied, and (iii) a FM phase. However, after including thermal fluctuations (T>0) we found the same entangled SO phases as for a bilayer at T=0. This shows that both quantum and thermal fluctuations can stabilize phases with exotic SO order while the classical spin order is destroyed.
[1] L. F. Feiner, A. M. Ole\'s, and J. Zaanen,
Phys. Rev. Lett. \textbf{78}, 2799 (1997).
[2] A. M. Ole\'s, Acta Phys. Polon. A \textbf{115}, 36 (2009).

**
Mr.
Jonathan
Buhmann
**

Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

**
Normal state charge transport of overdoped cuprates**

**Abstract:**
Fermi Surface Dependence of Normal State Charge Transport of Overdoped Cuprates
Jonathan Buhmann, Matthias Ossadnik, T.M. Rice and Manfred Sigrist
Institute for Theoretical Physics, ETH Zürich
We study charge transport properties in the normal state of heavily overdoped high-temperature superconducting cuprates. We analyze the effect of strongly anisotropic quasiparticle scattering on transport life times within a semiclassical approach based on the Boltzmann transport theory. The scattering rates are determined by a renormalization group calculation to one loop corrections to the quasiparticle self energy. We solve the linearized Boltzmann equation numerically including the full angular and radial dependence of the distribution function. The dependence of the transport life times and the resulting resistivity on the geometry of the Fermi surface and temperature is discussed.
This study is motivated by the correlation between charge transport and superconductivity for Tl_{2}Ba_{2}CuO_{6+x} reported by Abdel-Jawad et at. [1] and the non-perturbative linear temperature dependence of the anisotropic part of the quasiparticle life times found within a functional renormalization group study [2]. In addition, N. Hussey et al. [3] have experimentally probed the resistivity in La_{2-x}Sr_{x}CuO_{4} for several doping levels and found anomalous scaling behavior which we aim to discuss within our theoretical study.
[1] M. Abdel-Jawad et al.; Nature Physics 2, 821 (2006)
[2] M. Ossadnik et al.; Phys. Rev. Lett. 101 256405, (2008)
[3] R.A. Cooper et al.; Science 323 603-607, (2009)

**
Mr.
Matteo
Capati
**

Department of Physics, Università Sapienza di Roma , Italy

**
Nematic phase without Heisenberg physics in FeAs planes**

**Abstract:**
We use Monte Carlo simulations and analytical arguments to analyze a frustrated Ising model with nearest neighbour antiferromagnetic coupling and next nearest neighbour coupling.
The model is inspired on the physics of pnictide superconductors and to some extent we argue that it can be more representative of this physics than the Heisenberg counterpart.
Parameters are chosen such that the ground state is a columnar or striped state, as observed experimentally, but is close to the transition to the simple Neel ordered antiferromagnetic state.
We find that a nematic phase is induced by finite size effects and argue that this explains experiments in imperfect samples which find a more robust nematic state as the quality of the
sample decreases. Including the effect of a weak coupling with the lattice we find that a structural transition occurs associated with a nematic phase, with a magnetic transition occurring at
a lower temperature. These two transitions merge into a single structural and magnetic transition with a stronger first-order character for larger spin-lattice couplings.
These two situations are in agreement with the different phenomenologies found in different families of pnictides.

**
Mr.
Marcin
Wysokiński
**

Department of Physics,Jagiellonian University, Kraków, Poland

**
Magnetization curve of liquid helium 3 within statistically-consistent mean-field approach to Hubbard model: comparison with experiment**

**Abstract:**
We study theoretically the Hubbard model in order to calculate magnetization in high magnetic field and apply the results to the liquid helium 3 close to the solidification and at low temperature. For this, we employ the Gutzwiller's mean-field approach with additional statistical consistency conditions [1] on correlated fermion system and in the case of an almost half-filled band. It is in a semiquantitative agreement with the experimentally measured magnetization curve [2]. We study our model for selected types of lattices: simple cubic, face-centered cubic, and triangular. The last case models behavior of solid helium 3 deposited on graphite [3].
[1] J. Jędrak, J. Kaczmarczyk, and J. Spałek, arXiv:1008.0021v1 [cond-mat.str-el]
[2] S. Wiegers, P. Wolf, and L. Puech, Phys. Rev. Lett. 66, 2895–2898 (1991)
[3] H. Nema, A. Yamaguchi, T. Hayakawa, and H. Ishimoto, Phys. Rev. Lett. 102, 075301 (2009)

**
Dr.
Aldo
Isidori
**

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

**
Quantum criticality of dipolar spin chains**

**Abstract:**
I will show that a one-dimensional chain of Heisenberg spins, interacting with long-range dipolar forces in a magnetic field perpendicular to the chain, exhibits a quantum critical point belonging to the two-dimensional Ising universality class. Within linear spin-wave theory (corresponding to the Gaussian approximation in field theory) the long-wavelength magnon dispersion is characterized by a logarithmic singularity in the magnon velocity for vanishing momenta, due to the peculiar behavior of dipole-dipole interactions in one-dimension. However, in the vicinity of the critical point this logarithmically divergent term is renormalized to zero by the effects of quantum fluctuations, signaling the reemergence of scale invariance, in accordance with the Ising critical scenario. The quantum critical regime, where linear spin-wave theory becomes infrared divergent, is studied using the non-perturbative density-matrix and functional renormalization group methods. On the disordered side of the transition the Ginzburg regime, where non-Gaussian fluctuations play an important role, is found to be rather broad.

**
Mr.
Andreas
Kreisel
**

Institut für Theoretische Physik, Goethe Universität Frankfurt, Germany

**
Elastic constants and ultrasonic attenuation in the cone state of the frustrated antiferromagnet Cs$_2$CuCl$_4$**

**Abstract:**
In an external magnetic field perpendicular to the plane of the layers, the quasi two-dimensional frustrated antiferromagnet Cs$_2$CuCl$_4$ exhibits a magnetically ordered ``cone state'' at low temperatures. In this state the component of the magnetic moments in field direction is finite, while their projection onto the plane of the layers forms a spiral. We present both theoretical and experimental results for the magnetic-field dependence of the elastic constants and the ultrasonic attenuation rate in the cone state. Our theoretical analysis is based on the usual spin-wave expansion around the classical ground state of a Heisenberg model on an anisotropic triangular lattice with Dzyaloshinskii--Moriya interactions. Magnon-phonon interactions are modeled by expanding the exchange interactions up to second order in powers of the phonon coordinates. As long as the external magnetic field is not too close to the critical field where the cone state becomes unstable, we obtain reasonable agreement between theory and experiment, suggesting that at least in this regime magnons behave as well-defined quasiparticles.We also show that the assumption of well-defined magnons implies that at long wavelengths the ultrasonic attenuation rate in the cone state of Cs$_2$CuCl$_4$ is proportional to the fourth power of the phonon momentum.

**
Mr.
Pasquale
Marra
**

IFW Dresden, Germany

**
Fingerprints of Orbital Physics in Magnetic RIXS**

**Abstract:**
Resonant Inelastic X-ray Scattering (RIXS) has become nowadays one of the main experimental techniques to investigate elementary excitations in strongly correlated materials, and above all, cuprates. We describe a simple way to analytically calculate the scattering intensities in the case of copper L edge in the single ion picture. We use this result to obtain the scattering intensities of spin waves in systems with different orbital ground states. It occurs that even in this case, RIXS intensities behave differently depending on the type of orbital order.

**
Mr.
Kazutaka
Nishiguchi
**

Department of Physics, University of Tokyo, Tokyo, Japan

**
Theoretical study of superconductivity in multi-layered cuprates**

**Abstract:**
Since Kamerlingh Onnes discovered the superconducting phase transition in Hg 100 years ago, followed by Bednorz and Müller who have opened a new avenue for the high-Tc superconductivity in cuprates in 1986, superconductivity has been one of the main topics in condensed-matter physics. Multi-layered cuprates, typically HgBa2Ca_{n-1}Cu_nO_{2+2n+δ} and Bi_2Sr_2Ca_{n-1}Cu_nO_{4+2n+δ}, have the highest-Tc to date, on which my talk will be focused. There are n-layers of Cu0_2 planes in a unit cell, which determines the electron structure of the compound. One of the key questions is that Tc systematically varies with the number of CuO_2 planes. Namely, Tc increases as we go from n=1 to n=3, with the tri-layered Hg-series with n=3 being the highest Tc superconductor (Tc=135K) at ambient pressure, while Tc starts to decrease for n≧4. The reason for this behavior is still not fully understood.
We have studied the superconductivity in the multi-layered cuprates by solving the Eliashberg equation for the multi-orbital Hubbard model with the random-phase approximation (RPA) and with the fluctuation-exchange approximation (FLEX). The hopping parameters are obtained by downfolding from the first principles calculations based on density functional theory (DFT) for the Hg-series cuprates HgBa_2Ca_{n-1}Cu_nO_{2+2n+δ} (n=1, 2, 3). We then discuss on possible factors that may determine Tc in multi-layered cuprates for different numbers of CuO_2 planes such as inter-layer single electron hopping and inter-layer Cooper pair hopping.

**
Mr.
Martin
Nuss
**

Institute of Theoretical and Computational Physics, Graz University of Technology, Graz, Austria

**
Quantum Impurity Models in and out of equilibrium studied by means of Variational Cluster Perturbation Theory**

**Abstract:**
We study the single impurity Anderson model by means of variational cluster perturbation theory (VCA). Results for dynamic correlation functions and static expectation values in all parameter regimes are shown to be in good agreement with renormalization group, quantum Monte Carlo and analytic results. We address the question whether the elusive low energy properties of the model are properly reproduced within the framework of VCA. Based on the good results in equilibrium we extend the formalism, using Keldysh Green’s function, to the non-equilibrium situation and study the long time / steady state behavior. The method is shown to be a flexible tool in treating many-impurity models in any configuration and dimension in the strong-, weak- and intermediate coupling region.

**
Mr.
Vladislav
Pokorný
**

Institute of Physics of the Academy of Sciences, Czech Republic

**
Electrical conductivity of the strongly disordered Anderson model**

**Abstract:**
We propose a renormalization scheme of the Kubo formula for the electrical conductivity
using the asymptotic limit to high spatial dimensions. We utilize the dominance of a pole
due to maximally crossed diagrams in the electron-hole irreducible vertex to an approximate
diagonalization of the Bethe-Salpeter equation for the two-particle Green function and
a non-perturbative representation of the electrical conductivity. The latter is then
obtained without the necessity of separate evaluation of the mean-field (Drude) term
and vertex corrections. The electrical conductivity calculated in this way remains non-negative
also in the strongly disordered regime where the localization effects become significant
and the negative vertex corrections in the standard Kubo formula overweight the positive Drude term.

**
Dr.
Simone
Taioli
**

Interdisciplinary Laboratory for Computational Science, Fondazione Bruno Kessler and University of Trento, Trento, Italy

**
Is contact potential the hallmark of the fermion-fermion interaction?**

**Abstract:**
We develop a theoretical method to describe contact interaction in mean-field
theories of many-fermion systems, using the low-energy T-matrix of the pair
potential to rigorously define the effective radius of the interaction. One of
the main consequences of our approach is the possibility to investigate
finite-density effects, which are outside the range of validity of
approximations based on delta-like potentials. We apply our method to the
calculation of density dependent properties of an ultracold gas of 6Li
atoms at unitarity, whose two-body interaction potential is calculated using
ab-initio quantum chemistry methods. We find that density effects will
be significant in ultracold gases with densities one order of magnitude higher
than those attained in current experiments.