LECTURES ON THE PHYSICS OF STRONGLY CORRELATED SYSTEMS XIII: Thirteenth Training Course in the Physics of Strongly Correlated Systems

Quantum Mechanics in Insulators
View Description Hide DescriptionAtomic physics is undergoing a large revival because of the possibility of trapping and cooling ions and atoms both for individual quantum control as well as collective quantum states, such as Bose‐Einstein condensates. The present lectures start from the ‘atomic’ physics of isolated atoms in semiconductors and insulators and proceed to coupling them together to yield magnets undergoing quantum phase transitions as well as displaying novel quantum states with no classical analogs. The lectures are based on: G.‐Y. Xu et al., Science 317, 1049–1052 (2007); G. Aeppli, P. Warburton, C. Renner, BT Technology Journal, 24, 163–169 (2006); H. M. Ronnow et al., Science 308, 392–395 (2005) and N. Q. Vinh et al., PNAS 105, 10649–10653 (2008).

Novel Quantum Condensates in Excitonic Matter
View Description Hide DescriptionThese lectures interleave discussion of a novel physical problem of a new kind of condensate with teaching of the fundamental theoretical tools of quantum condensed matter field theory. Polaritons and excitons are light mass composite bosons that can be made inside solids in a number of different ways. As bosonic particles, they are liable to make a phase coherent ground state—generically called a Bose‐Einstein condensate (BEC)—and these lectures present some models to describe that problem, as well as general approaches to the theory. The focus is very much to explain how mean‐field‐like approximations that are often presented heuristically can be derived in a systematic fashion by path integral methods. Going beyond the mean field theory then produces a systematic approach to calculation of the excitation energies, and the derivation of effective low energy theories that can be generalised to more complex dynamical and spatial situations than is practicable for the full theory, as well as to study statistical properties beyond the semi‐classical regime. in particular, for the polariton problem, it allows one to connect the regimes of equilibrium BEC and non‐equilibrium laser. The lectures are self‐sufficient, but not highly detailed. The methodological aspects are covered in standard quantum field theory texts and the presentation here is deliberately cursory: the approach will be closest to the book of Altland and Simons [1]. Since these lectures concern a particular type of condensate, reference should also be made to texts on BEC, for example by Pitaevskii and Stringari [2]. A recent theoretically focussed review of polariton systems is [3] covers many of the technical issues associated with the polariton problem in greater depth and provides many further references.

Introduction to unconventional superconductivity in non‐centrosymmetric metals
View Description Hide DescriptionThese lecture notes are an extension of my previous notes [1] presented in this lecture series and are concerned with the recently emerging research field of unconventional superconductivity in non‐centrosymmetric metals. Inversion symmetry together with time reversal symmetry represent key symmetries for the formation of Cooper pairs in superconductors and allows to distinguish between even‐parity spin‐singlet and odd‐parity spin‐triplet pairing. The absence of at least one of two symmetries leads to the spin‐splitting of the electronic states, through Zeeman fields (loss of time reversal symmetry) and through antisymmetric spin‐orbit coupling (loss of inversion symmetry), which has a strong influence on the Cooper pairing states possible. Anderson’s theorems show the basic symmetry requirements for the Cooper pair formation. The meaning of these theorems can be demonstrated in a perturbative analysis of the superconducting instability. The structure of the pairing states are derived for systems without inversion and time reversal symmetry, and are shown to be non‐unitary. In the case of non‐centrosymmetric materials the pairing interaction displays interesting spin‐orbit coupling‐induced features which are analyzed within a toy model for the superconductivity in one of the non‐centrosymmetric heavy Fermion superconductors, in order to give a catalogue of possible pairing states in this material. A further important point is the essentially universal behavior of the spin susceptibility in the superconducting phase of a non‐centrosymmetric materials. This behavior is spectacularly manifested in the upper critical field of and Magneto‐electric effects represent one of the most extraordinary parts in the phenomenology of non‐centrosymmetric superconductors. Two examples of magneto‐electric behaviors are discussed: (1) the helical phase in the mixed superconducting state and (2) relation between supercurrent and the spin magnetization. Eventually also the possibility of surface Andreev bound states is discussed and it is shown that such states can carry spin currents.

Quantum Monte Carlo Simulations
View Description Hide DescriptionIn these lecture notes we present an introduction to modern quantum Monte Carlo methods for strongly correlated quantum lattice models. After an introduction to classical Monte Carlo methods we will present the loop algorithm, directed loop algorithm, worm algorithm, Wang‐Landau sampling for quantum systems, and continuous‐time algorithms for quantum impurity problems.

Quasi‐particles dynamics in underdoped Bi2212 under strong optical perturbation
View Description Hide DescriptionIn this work an optical pump‐probe set‐up is used to study the photo‐induced non‐equilibrium dynamics of a superconducting underdoped Bi2212 single crystal in a strong excitation regime The use of a tunable repetition rate 120 fs pulsed laser source allows us to avoid significant average heating of the sample and to optimize the signal‐to‐noise ratio in the detection of the transient reflectivity variation. A discontinuity of the transient reflectivity is observed at high excitation intensities Numerical simulations of the heat diffusion problem indicate that, in this regime, the local temperature of the sample is lower than confirming the impulsive nature of this phenomenon. The quasi‐particles (QP) dynamics in the strongly perturbed superconducting state is analysed within the framework of the Rotwarf‐Taylor model. The picture emerging from the data is consistent with a dynamics governed by high‐frequency phonon (HFP) population, which causes a “bottleneck” effect in the QP recombination.

Optical Excitations in Insulating Plaquette Networks: Discussion Based on a One Dimensional Mott Insulator
View Description Hide DescriptionInsulating cuprates become insulator thanks to the strong Coulomb repulsion at Cu d orbitals. They have charge gap between filled oxygen 2p and empty Cu 3d states categorized as charge transfer insulators. Although only Cu 3d and O 2p states are involved in low energy optical transitions, optical excitation spectra of insulating cuprates show rich structures depending on the form of networks. One dimensional chain systems with corner‐sharing plaquettes and edge‐sharing plaquettes provide basic characters of these transitions. Comparison of available spectra of two dimensional cuprates with one dimensional chain compound suggests that excitonic effect is important in planes.

On the multipolar ordered phase of
View Description Hide DescriptionIn 1953, the first measurements of the low‐temperature specific heat on neptunium dioxide showed a clear phase transition at 25 K. Half a century later this phase transition is still of major interest because intensive research has shown that it is driven by the ordering of high‐order magnetic multipoles. Multipole densities (deviations from spherical symmetry) also appear in research areas as diverse as nuclear deformations and molecular interactions; applied to atomic charge and magnetization density they have been invoked to explain several unusual phase transitions, but their experimental identification is extremely complex. which has the simple cubic fluorite structure, is now regarded as one of the clearest examples of this unusual ordering and, following theoretical work based on resonant X‐ray scattering measurements, the latest neutron experiments have added crucial experimental evidence to this long‐running saga. In this article, I briefly review our most recent results on this topic, culminating in how a clear signature of the primary order parameter has finally been unveiled.

From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
View Description Hide DescriptionUsing a loop‐cluster algorithm we investigate the spin Heisenberg antiferromagnet on a square lattice with exchange coupling J and a four‐spin interaction of strength Q. We confirm the existence of a phase transition separating antiferromagnetism at from a valence bond solid (VBS) state at Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as we find evidence for a weak first order phase transition. We also present a detailed study of the antiferromagnetic phase. For the staggered magnetization, the spin stiffness, and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low‐energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at and we show that long but finite antiferromagnetic correlations are still present.

Optical Properties of Crystal Water in Single Crystals
View Description Hide DescriptionSpectral structure in the absorption spectra of Crystals (Magnesium sulfite hexahydrate, symmetry group ) can be observed in the near IR spectral range (900–1200 nm). The water molecules in the crystal lattice stipulated this structure. The investigations show that the structure anisotropy of the crystal causes the appearing of optical anisotropy of the crystal water spectra. The anisotropy manifests itself by the differences of the absorption coefficients measured with linear polarized light (c̄ is the crystal optical axis). The induced anisotropy can be presented by the spectra of the linear dichroism. The influence of Ni impurity on the spectra of the crystal water in the crystals of has been proved experimentally. The details in the absorption spectra of the crystal water in have been analysed by λ—modulation method.

Strong electron correlation in impurity models: singlet and triplet multiple scatterings
View Description Hide DescriptionWe study the strong‐coupling regime of the single impurity Anderson model. We calculate the two‐particle vertex and the spectral function using a resummation of the diagrammatic expansion in the interaction strength. The earlier developed parquet resummation is extended to include all three representations of Bethe‐Salpeter equations. In an applied magnetic field we find two exponentially small Kondo scales (temperatures), one for transverse and one for longitudinal spin fluctuations. As expected, the Kondo peak splits in a weak magnetic field.

Spin, Orbital, and Spin‐Orbital Polarons in Transition Metal Oxides
View Description Hide DescriptionI give a brief overview of a polaron formation in three distinct transition metal oxides: (i) spin polaron when a hole is added to the antiferromagnetic (AF) ordered plane in (ii) orbital polaron when a hole is added to the alternating orbital (AO) ordered plane in and (iii) spin‐orbital polaron when a hole is added to the AF and AO ordered plane in Comparison of the distinct features of the above polarons can shed some light on the basic differences between the experimental phase diagrams of the lightly doped transition metal oxides and

Low‐energy spin fluctuations in the metallic spinel compound
View Description Hide DescriptionIn the family of transition metal oxides the spinel compound is a rare metallic system showing heavy fermion behavior. In particular, an anomalously large specific heat coefficient and strongly enhanced magnetic susceptibility were detected in the low temperature limit, Recently we have proposed a model which allowed us to relate such an anomalous behavior of to the proximity of the underlying 3d‐electron system to a magnetic instability at The emergence of a rather peculiar paramagnetic ground state with largely degenerate lowenergy “critical” antiferromagnetic fluctuations in is the combined effect of strong electron correlations and the geometrical frustration of V‐ion pyrochlore lattice forming the metallic system in this compound. A self‐consistent renormalization theory was developed to describe effects of strong coupling between spin fluctuation modes and their evolution with varying temperature and external pressure. The theory was shown to provide a firm basis for understanding many peculiar properties of spin dynamics obtained in the inelastic neutron scattering and NMR measurements on