Infinite Infrared Regularization and a State Space for the Heisenberg Algebra

We present a method for the construction of a Krein space completion for spaces of test functions, equipped with an indefinite inner product induced by a kernel which is more singular than a distribution of finite order. This generalizes a regularization method for infrared singularities in quantum field theory, introduced by G. Morchio and F. Strocchi, to the case of singularites of infinite order. We give conditions for the possibility of this procedure in terms of local differential operators and the Gelfand- Shilov test function spaces, as well as an abstract sufficient condition. As a model case we construct a maximally positive definite state space for the Heisenberg algebra in the presence of an infinite infrared singularity.Comment: 18 pages, typos corrected, journal-ref added, reference adde

On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.Comment: 10 pages; to appear in Russian Journal of Mathematical Physics (memorial volume in honor of Vladimir Geyler). Results improved in this versio

CeRu4_4Sn6_6: heavy fermions emerging from a Kondo-insulating state

The combination of low-temperature specific-heat and nuclear-magnetic-resonance (NMR) measurements reveals important information of the ground-state properties of CeRu$_4$Sn$_6$, which has been proposed as a rare example of a tetragonal Kondo-insulator (KI). The NMR spin-latticerelaxation rate $1/T_1$ deviates from the Korringa law below 100 K signaling the onset of an energy gap $\Delta E_g1/k_B \simeq 30$K. This gap is stable against magnetic fields up to 10 T. Below 10 K, however, unusual low-energy excitations of in-gap states are observed, which depend strongly on the field H. The specific heat C detects these excitations in the form of an enhanced Sommerfeld coefficient $\gamma = C(T)/T$ : In zero field, $\gamma$ increases steeply below 5 K, reaching a maximum at 0.1 K, and then saturates at $\gamma = 0.6$ J/molK$^2$. This maximum is shifted to higher temperatures with increasing field suggesting a residual density of states at the Fermi level developing a spin gap $\Delta E_g2$. A simple model, based on two narrow quasiparticle bands located at the Fermi level - which cross the Fermi level in zero field at 0.022 states/meV f.u. - can account qualitatively as well as quantitatively for the measured observables. In particular, it is demonstrated that fitting our data of both specific heat and NMR to the model, incorporating a Ce magnetic moment of $\mu = \Delta E_g1/\mu_{0H} \simeq 1 \mu_B$, leads to the prediction of the field dependence of the gap. Our measurements rule out the presence of a quantum critical point as the origin for the enhanced $\gamma$ in CeRu$_4$Sn$_6$ and suggest that this arises rather from correlated, residual in-gap states at the Fermi level. This work provides a fundamental route for future investigations into the phenomenon of narrow-gap formation in the strongly correlated class of systemComment: 11 pages, 13 figure

Effect of external pressure on the magnetic properties of RRCoAsO (RR = La, Pr, Sm): a μ\muSR study

We report on a detailed investigation of the itinerant ferromagnets LaCoAsO, PrCoAsO and SmCoAsO performed by means of muon spin spectroscopy upon the application of external hydrostatic pressures $p$ up to $2.4$ GPa. These materials are shown to be magnetically hard in view of the weak dependence of both critical temperatures $T_{C}$ and internal fields at the muon site on $p$. In the cases $R$ = La and Sm, the behaviour of the internal field is substantially unaltered up to $p = 2.4$ GPa. A much richer phenomenology is detected in PrCoAsO instead, possibly associated with a strong $p$ dependence of the statistical population of the two different crystallographic sites for the muon. Surprisingly, results are notably different from what is observed in the case of the isostructural compounds $R$CoPO, where the full As/P substitution is already inducing a strong chemical pressure within the lattice but $p$ is still very effective in further affecting the magnetic properties.Comment: 8 pages, 9 figure

Spin Gap in the Single Spin-1/2 Chain Cuprate Sr1.9_{1.9}Ca0.1_{0.1}CuO3_3

We report $^{63}$Cu nuclear magnetic resonance and muon spin rotation measurements on the S=1/2 antiferromagnetic Heisenberg spin chain compound Sr$_{1.9}$Ca$_{0.1}$CuO$_3$. An exponentially decreasing spin-lattice relaxation rate 1/T$_1$ indicates the opening of a spin gap. This behavior is very similar to what has been observed for the cognate zigzag spin chain compound Sr$_{0.9}$Ca$_{0.1}$CuO$_2$, and confirms that the occurrence of a spin gap upon Ca doping is independent of the interchain exchange coupling $J'$. Our results therefore generally prove the appearance of a spin gap in an antiferromagnetic Heisenberg spin chain induced by a local bond disorder of the intrachain exchange coupling $J$. A low temperature upturn of 1/T$_1$ evidences growing magnetic correlations. However, zero field muon spin rotation measurements down to 1.5 K confirm the absence of magnetic order in this compound which is most likely suppressed by the opening of the spin gap.Comment: 5 pages, 4 figure

Parametrizations of density matrices

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and Conclusion section added, references adde

CeRuPO: A rare example of a Ferromagnetic Kondo lattice

We have determined the physical ground state properties of the compounds CeRuPO and CeOsPO by means of magnetic susceptibility chi(T), specific heat C(T), electrical resistivity rho(T), and thermopower S(T) measurements. chi(T) reveals a trivalent 4f1 cerium state in both compounds. For CeRuPO a pronounced decrease of rho(T) below 50K indicates the onset of coherent Kondo scattering which is confirmed by enhanced S(T). The temperature and magnetic field dependence of chi(T) and C(T) evidence ferromagnetic (FM) order at TC=15K. Thus, CeRuPO seems to be one of the rare example of a FM Kondo lattice. In contrast, CeOsPO shows antiferromagnetic order at TN=4.4K despite only minor changes in lattice parameters and electronic configuration. Additional 31P NMR results support these scenarios. LSDA+U calculations evidence a quasi two dimensional electronic band structure, reflecting a strong covalent bonding within the CeO and RuP layers and a weak ionic like bonding between the layers.Comment: accepted in Phys. Rev. B, high quality figures: http://www.cpfs.mpg.de/~krellner

Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

CeFePO: A Heavy Fermion Metal with Ferromagnetic Correlations

The ground state properties of CeFePO, a homologue of the new high temperature superconductors RFePnO(1-x)Fx, were studied by means of susceptibility, specific heat, resistivity, and NMR measurements on polycrystals. All the results demonstrate that this compound is a magnetically non-ordered heavy Fermion metal with a Kondo temperature TK~10K, a Sommerfeld coefficient gamma=700mJ/molK2 and a mass enhancement factor of the order of 200. The absence of a Fe-contribution to the effective moment at high temperatures indicates that the magnetism in CeFePO is completely dominated by the effect of Ce. Thus the strong electronic correlation effects originate from the Ce-4f electrons rather than from the Fe-3d electrons. An enhanced Sommerfeld-Wilson ratio R=5.5 as well as a Korringa product S0/T1TK2~0.065 well below 1 indicate the presence of ferromagnetic correlations. Therefore, CeFePO appears to be on the non-magnetic side of a ferromagnetic instability.Comment: 5 pages, 4 figure

Common effect of chemical and external pressures on the magnetic properties of RECoPO (RE = La, Pr)

We report a detailed investigation of RECoPO (RE = La, Pr) and LaCoAsO materials performed by means of muon spin spectroscopy. Zero-field measurements show that the electrons localized on the Pr$^{3+}$ ions do not play any role in the static magnetic properties of the compounds. Magnetism at the local level is indeed fully dominated by the weakly-itinerant ferromagnetism from the Co sublattice only. The increase of the chemical pressure triggered by the different ionic radii of La$^{3+}$ and Pr$^{3+}$, on the other hand, plays a crucial role in enhancing the value of the magnetic critical temperature and can be mimicked by the application of external hydrostatic pressure up to 24 kbar. A sharp discontinuity in the local magnetic field at the muon site in LaCoPO at around 5 kbar suggests a sizeable modification in the band structure of the material upon increasing pressure. This scenario is qualitatively supported by \emph{ab-initio} density-functional theory calculations.Comment: 13 pages, 10 figure