Classical and nonclassical randomness in quantum measurements

The space of positive operator-valued measures on the Borel sets of a compact (or even locally compact) Hausdorff space with values in the algebra of linear operators acting on a d-dimensional Hilbert space is studied from the perspectives of classical and non-classical convexity through a transform $\Gamma$ that associates any positive operator-valued measure with a certain completely positive linear map of the homogeneous C*-algebra $C(X)\otimes B(H)$ into $B(H)$. This association is achieved by using an operator-valued integral in which non-classical random variables (that is, operator-valued functions) are integrated with respect to positive operator-valued measures and which has the feature that the integral of a random quantum effect is itself a quantum effect. A left inverse $\Omega$ for $\Gamma$ yields an integral representation, along the lines of the classical Riesz Representation Theorem for certain linear functionals on $C(X)$, of certain (but not all) unital completely positive linear maps $\phi:C(X)\otimes B(H) \rightarrow B(H)$. The extremal and C*-extremal points of the space of POVMS are determined.Comment: to appear in Journal of Mathematical Physic

Nambu-Goldstone Mechanism in Real-Time Thermal Field Theory

In a one-generation fermion condensate scheme of electroweak symmetry breaking, it is proven based on Schwinger-Dyson equation in the real-time thermal field theory in the fermion bubble diagram approximation that, at finite temperature $T$ below the symmetry restoration temperature $T_c$, a massive Higgs boson and three massless Nambu-Goldstone bosons could emerge from the spontaneous breaking of electroweak group $SU_L(2)\times U_Y(1) \to U_Q(1)$ if the two fermion flavors in the one generation are mass-degenerate, thus Goldstone Theorem is rigorously valid in this case. However, if the two fermion flavors have unequal masses, owing to "thermal flactuation", the Goldstone Theorem will be true only approximately for a very large momentum cut-off $\Lambda$ in zero temperature fermion loop or for low energy scales. All possible pinch singularities are proven to cancel each other, as is expected in a real-time thermal field theory.Comment: 11 pages, revtex, no figure, Phys. Rev. D, to appea

Kondo Problem and Related One-Dimensional Quantum Systems: Bethe Ansatz Solution and Boundary Conformal Field Theory

We review some exact results on Kondo impurity systems derived from Bethe-ansatz solutions and boundary conformal field theory with particular emphasis on universal aspects of the phenomenon. The finite-size spectra characterizing the low-energy fixed point are computed from the Bethe-ansatz solutions of various models related to the Kondo problem. Using the finite-size scaling argument, we investigate their exact critical properties. We also discuss that a universal relation between the Kondo effect and the impurity effect in one-dimensional quantum systems usefully expedites our understanding of these different phenomena.Comment: 6 pages, no figure

Exact Critical Properties of the Multi-Component Interacting Fermion Model with Boundaries

Exact critical properties of the one-dimensional SU($N$) interacting fermion model with open boundaries are studied by using the Bethe ansatz method. We derive the surface critical exponents of various correlation functions using boundary conformal field theory. They are classified into two types, i.e. the exponents for the chiral SU($N$) Tomonaga-Luttinger liquid and those related to the orthogonality catastrophe. We discuss a possible application of the results to the photoemission (absorption) in the edge state of the fractional quantum Hall effect.Comment: 17 pages, RevTe

Boundary susceptibility in the spin-1/2 chain: Curie like behavior without magnetic impurities

We investigate the low-temperature thermodynamics of the spin-1/2 Heisenberg chain with open ends. On the basis of boundary conformal field theory arguments and numerical density matrix renormalization group calculations, it is established that in the isotropic case the impurity susceptibility exhibits a Curie-like divergent behavior as the temperature decreases, even in the absence of magnetic impurities. A similar singular temperature dependence is also found in the boundary contributions of the specific heat coefficient. In the anisotropic case, for $1/2<\Delta<1$, these boundary quantities still show singular temperature dependence obeying a power law with an anomalous dimension. Experimental consequences will be discussed.Comment: 5 pages, 1 figure, final versio

Zeta functions, renormalization group equations, and the effective action

We demonstrate how to extract all the one-loop renormalization group equations for arbitrary quantum field theories from knowledge of an appropriate Seeley--DeWitt coefficient. By formally solving the renormalization group equations to one loop, we renormalization group improve the classical action, and use this to derive the leading-logarithms in the one-loop effective action for arbitrary quantum field theories.Comment: 4 pages, ReV-TeX 3.

Exact finite-size spectrum for the multi-channel Kondo model and Kac-Moody fusion rules

The finite-size spectrum for the multi-channel Kondo model is derived analytically from the exact solution, by mapping the nontrivial Z$_{n}$ part of the Kondo scattering into that for the RSOS model coupled with the impurity. The analysis is performed for the case of $n-2S=1$, where $n$ is the number of channel and $S$ is the impurity spin. The result obtained is in accordance with the Kac-Moody fusion hypothesis proposed by Affleck and Ludwig.Comment: RevTex, 4 page

Effects of anisotropic spin-exchange interactions in spin ladders

We investigate the effects of the Dzialoshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions on various thermodynamic and magnetic properties of a spin 1/2 ladder. Using the Majorana fermion representation, we derive the spectrum of low energy excitations for a pure DM interaction and in presence of a superimposed KSEA interaction. We calculate the various correlation functions for both cases and discuss how they are modified with respect to the case of an isotropic ladder. We also discuss the electron spin resonance (ESR) spectrum of the system and show that it is strongly influenced by the orientation of the magnetic field with respect to the Dzialoshinskii-Moriya vector. Implications of our calculations for NMR and ESR experiments on ladder systems are discussed.Comment: 14 pages, 4 eps figures, corrected calculation of NMR rate (v3

Geometrical frustration induced (semi-)metal to insulator transition

We study the low-energy properties of the geometrically frustrated Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice on the basis of the renormalization group method and mean field analysis. It is found that in the half-filling case, a (semi-)metal to insulator transition (MIT) occurs. Also, in the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The results are applied to the description of the MIT observed in the pyrochlore system ${\rm Tl_2Ru_2O_7}$.Comment: 4 pages, 5 figure