Chiral Correlation Research Articles

DIFFERENTIAL EQUATIONS, DUALITY AND MODULAR INVARIANCE

We solve the problem of constructing all chiral genus-one correlation functions from chiral genus-zero correlation functions associated to a vertex operator algebra satisfying the following conditions: (i) V(n) = 0 for n < 0 and V(0) = ℂ1, (ii) every ℕ-gradable weak V-module is completely reducible and (iii) V is C2-cofinite. We establish the fundamental properties of these functions, including suitably formulated commutativity, associativity and modular invariance. The method we develop and use here is completely different from the one previously used by Zhu and others. In particular, we show that the q-traces of products of certain geometrically-modified intertwining operators satisfy modular invariant systems of differential equations which, for any fixed modular parameter, reduce to doubly-periodic systems with only regular singular points. Together with the results obtained by the author in the genus-zero case, the results of the present paper solves essentially the problem of constructing chiral genus-one weakly conformal field theories from the representations of a vertex operator algebra satisfying the conditions above.

Radiative corrections in weak semi-leptonic processes at low energy: a two-step matching determination*

We focus on the chiral Lagrangian couplings describing radiative corrections to weak semi-leptonic decays and relate them to the decay amplitude of a lepton, computed by Braaten and Li at one loop in the standard model. For this purpose, we follow a two-step procedure. A first matching, from the standard model to Fermi theory, yields a relevant set of counterterms. The latter are related to chiral couplings thanks to a second matching, from Fermi theory to the chiral Lagrangian, which is performed using the spurion method. We show that the chiral couplings of physical relevance obey integral representations in a closed form, expressed in terms of QCD chiral correlators and vertex functions. We deduce exact relations among the couplings, as well as numerical estimates which go beyond the usual $\log(M_Z/M_\rho)$ approximation.

Spin chirality on a two-dimensional frustrated lattice

The collective behaviour of interacting magnetic moments can be strongly influenced by the topology of the underlying lattice. In geometrically frustrated spin systems, interesting chiral correlations may develop that are related to the spin arrangement on triangular plaquettes. We report a study of the spin chirality on a two-dimensional geometrically frustrated lattice. Our new chemical synthesis methods allow us to produce large single-crystal samples of KFe3(OH)6(SO4)2, an ideal Kagomé lattice antiferromagnet. Combined thermodynamic and neutron scattering measurements reveal that the phase transition to the ordered ground-state is unusual. At low temperatures, application of a magnetic field induces a transition between states with different non-trivial spin-textures.

Atomic Correlation Between Adjacent Graphene Layers in Double-Wall Carbon Nanotubes

Atomic correlation between adjacent graphene layers was elucidated for double-wall carbon nanotubes (DWNTs) through a chiral index assignment of two nested nanotubes by high-resolution transmission electron microscopy. Our analysis provides a rather constant diameter difference close to 0.75 nm but no chiral angle correlation between the constituent nanotubes in the concentric DWNTs. The local atomic correlation as a commensurate graphene stacking was repeatedly found in eccentric DWNTs and circumscribed nanotubes, which should lead to elastic deformation and bundling of nanotubes.

Erratum: Realization of chiral symmetry in the domain model of QCD [Phys. Rev. D69, 074029 (2004)

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background domain-like gluon field. Quark fluctuations satisfy a chirality violating boundary conditions parametrized by a random chiral angle $\alpha_j$ on the $j-th$ domain. The free energy of an ensemble of $N\to\infty$ domains depends on $\{\alpha_j, j=1... N\}$ through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial U(1) degeneracy in the ground state, leaving only a residual axial Z(2) symmetry. This discrete symmetry and flavour $SU(N_f)_L\times SU(N_f)_R$ chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of Dirac operator. In order to illustrate the splitting between the $\eta'$ from octet pseudoscalar mesons realised in the domain model, we estimate the masses of light pseudoscalar and vector mesons.

Indication for a chiral phase in the molecular magnetic chain Gd(hfac)3NiTiPr by specific heat and $mu;+SR measurements

Specific heat and muon spin relaxation (μ + SR) measurements performed in the molecular magnetic chain Gd(hfac) 3 NiTiPr provide indication for the onset, at T 0 =2.08 K , of a phase with chiral order in the absence of long-range helical order. Specific heat data (probing the chirality–chirality correlation function) show a peak at T 0 that disappears upon application of a 5 T magnetic field, while μ + SR data (probing the spin–spin correlation function) do not present any anomaly at T 0 nor oscillations in the asymmetry curve below T 0 .

Realization of chiral symmetry in the domain model of QCD

The domain model for the QCD vacuum has previously been developed and shown to exhibit confinement of quarks, a strong correlation of the local chirality of quark modes, and a duality of the background domainlike gluon field. Quark fluctuations satisfy a chirality violating boundary condition parametrized by a random chiral angle ${\ensuremath{\alpha}}_{j}$ on the jth domain. The free energy of an ensemble of $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ domains depends on ${{\ensuremath{\alpha}}_{j},j=1,\dots{},N}$ through the logarithm of the quark determinant. Its parity odd part is given by the axial anomaly. The anomaly contribution to the free energy suppresses continuous axial $U(1)$ degeneracy in the ground state, leaving only a residual axial $Z(2)$ symmetry. This discrete symmetry and the flavor ${SU(N}_{f}{)}_{L}\ifmmode\times\else\texttimes\fi{}{SU(N}_{f}{)}_{R}$ chiral symmetry in turn are spontaneously broken with a quark condensate arising due to the asymmetry of the spectrum of the Dirac operator. In order to illustrate the splitting between the ${\ensuremath{\eta}}^{\ensuremath{'}}$ from octet pseudoscalar mesons realized in the domain model, we estimate the masses of the light pseudoscalar and vector mesons.

Chirald+issuperconducting state in the two-dimensionalt−t′Hubbard model

Applying the recently developed variational approach to Kohn-Luttinger superconductivity to the $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model in two dimensions, we have found, for sizeable next-nearest-neighbor hopping, an electron-density-controlled quantum phase transition between a d-wave superconducting state close to half filling and an s-wave superconductor at lower electron density. The transition occurs via an intermediate time-reversal breaking $d+is$ superconducting phase, which is characterized by nonvanishing chirality and density-current correlation. Our results suggest the possibility of a bulk time-reversal symmetry breaking state in overdoped cuprates.

UA(1) and spontaneous chiral symmetry breaking within a confining model of the QCD vacuum

A model for the QCD vacuum based on domain-like background gluon fields has previously been developed and demonstrated to exhibit confinement of quarks and strong correlation of the local chirality of quark modes and duality of the background gluon field. On the boundary of the j-th domain, quark fluctuations satisfy chirality violating boundary conditions parametrized by a chiral angle $\alpha_j$ which is treated as a collective variable. The dependence of the free energy of an ensemble of $N\to\infty$ domains on $\{\alpha_j, j=1... N\}$ is studied. For one massless flavour there are only two degenerate minima ($\alpha_j=0,\pi$ $\forall j$) due to the contribution of the anomaly to the free energy, which suppresses the continuous U(1) degeneracy. The residual discrete symmetry is spontaneously broken with a quark condensate of $-(238 {\rm{MeV}})^3.$ For $N_f$ massless flavours a continuous $SU(N_f)_L\times SU(N_f)_R$ degeneracy appears, while the $U_A(1)$ direction remains suppressed.

Indication for a chiral phase in the molecular magnetic chain Gd(hfac)3NiTiPr by specific heat and μ+SR measurements

Abstract Specific heat and muon spin relaxation (μ+SR) measurements performed in the molecular magnetic chain Gd(hfac)3NiTiPr provide indication for the onset, at T 0 =2.08 K , of a phase with chiral order in the absence of long-range helical order. Specific heat data (probing the chirality–chirality correlation function) show a peak at T0 that disappears upon application of a 5 T magnetic field, while μ+SR data (probing the spin–spin correlation function) do not present any anomaly at T0 nor oscillations in the asymmetry curve below T0.

Comments on gluino condensates in Script N = 1/2 SYM theory

Using Ward identities of N=1/2 supersymmetric Yang-Mills theory, we show that while the partition function and antichiral gluino condensates remain invariant under the $C$ deformation, chiral gluino correlators can get contributions from all gauge fields with instanton numbers $k\leq 1$. In particular, a Ward identity of the $U(1)_R$ symmetry allows us to determine the explicit dependence of chiral gluino correlators on the deformation parameter.

A Monte Carlo study of the chiral columnar organizations of dissymmetric discotic mesogens

We study the relation between the chirality of a discotic mesogen and that of the chiral columnar aggregates that they can spontaneously form by self-assembly. We discuss first the different types of chiral columns that can be in principle obtained. We introduce then a simple two-site Gay–Berne dissymmetric molecular model where chirality can be easily varied and perform extensive NPT Monte Carlo simulations of samples of these particles for different chiralities. At low temperatures we find nematic discotic and columnar mesophases formed by overall chiral columns and we analyze the results in terms of suitably defined observables and chiral correlation functions. We find that, at least for our model system, the columnar chirality is not originating from a regular helical or spiral arrangement of particles but it is mainly due to one-particle high-chirality defects separated by low-chirality domains.

Ordering of the Heisenberg spin glass in two dimensions

The spin and the chirality orderings of the Heisenberg spin glass in two dimensions with the nearest-neighbor Gaussian coupling are investigated by equilibrium Monte Carlo simulations. Particular attention is paid to the behavior of the spin and the chirality correlation lengths. In order to observe the true asymptotic behavior, fairly large system size L\gsim 20 (L the linear dimension of the system) appears to be necessary. It is found that both the spin and the chirality order only at zero temperature. At high temperatures, the chiral correlation length stays shorter than spin correlation length, whereas at lower temperatures below the crossover temperature T_\times, the chiral correlation length exceeds the spin correlation length. The spin and the chirality correlation-length exponents are estimated above T_\times to be \nu_SG=0.9+-0.2 and \nu_CG=2.1+-0.3, respectively. These values are close to the previous estimates on the basis of the domain-wall-energy calculation. Discussion is given about the asymptotic critical behavior realized below T_\times.

Generalization of the shell model and correlation effects in strongly correlated oxides

Direct analytical and numerical calculation show that the two-electron atomic configuration can be unstable with respect to a static or dynamic displacement of the electron shells. This enables us to develop a so-called nonrigid shell model for a partial account of the intra-atomic electron correlations. In frames of the model a correlated state of two-electron molecular configuration is described by a set of symmetrized shell displacements similarly to the well-known shell model developed for a description of the lattice dynamics. The former relate to the latter as the optical phonon modes relate to the acoustical one. The effect under consideration is expected to be of particular importance for anionic ${2p}^{6}$ background in oxides. The nonrigid anionic background forms an unconventional magnetoelectric system characterized by a set of independent orbital order parameters and competition of paramagnetic and diamagnetic responses. The model allows an introduction of the pseudospin formalism and effective ``spin Hamiltonian'' for a description of the short- and long-range ordering of nonrigid atomic backgrounds in crystals. We predict a number of unconventional correlation effects including: (i) a formation of polaronlike holes and charge-transfer excitons; (ii) the mechanism of the self-trapping for holes and/or charge-transfer excitons; (iii) a purely electronic (pseudo)Jahn-Teller effect due to a coupling between valent hole and a nonrigid anionic background; (iv) a combined (pseudo)Jahn-Teller effect provided by a joint account both of the electron shell displacements and conventional nuclear ones; (v) an appearance of the soliton chiral correlation states; (vi) unconventional magnetic response; (vii) unconventional hyperfine coupling.

Magnetic wall from chiral phase transition and CMBR correlations

Possible cosmic microwave background radiation (CMBR) correlations are estimated for a model in which a Hubble-size magnetic wall is formed during the QCD chiral phase transition. Measurable polarization correlations are found for l values greater than about 1000. It is also found that metric perturbations from the wall could give rise to observable CMBR correlations for large l.

Spin-chirality duality in a spin ladder with four-spin cyclic exchange.

Effect of four-spin cyclic exchange on magnetism is studied in the two-leg S=1/2 ladder. We develop an exact spin-chirality duality transformation, under which the system is self-dual when the four-spin exchange J4 is half of the two-spin exchange. Using the density-matrix renormalization-group method and the duality relation, we find that the four-spin exchange makes the vector-chirality correlation dominant. A "chirality short-range resonating-valence-bond" phase is identified for the first time at large J4.

The general correlation function in the Schwinger model on a torus

In the framework of the Euclidean path integral approach we derive the exact formula for the general N-point chiral densities correlator in the Schwinger model on a torus

Critical behavior of the frustrated antiferromagnetic six-state clock model on a triangular lattice.

We study the antiferromagnetic six-state clock model with nearest neighbor interactions on a triangular lattice with extensive Monte Carlo simulations. We find clear indications of two phase transitions at two different temperatures: Below T(I) a chirality order sets in and by a thorough finite-size-scaling analysis of the specific heat and the chirality correlation length we show that this transition is in the Ising universality class (with a nonvanishing chirality order parameter below T(I)). At T(KT) (<T(I)) the spin-spin correlation length as well as the spin susceptibility diverges according to a Kosterlitz-Thouless (KT) form and spin correlations decay algebraically below T(KT). We compare our results to recent x-ray diffraction experiments on the orientational ordering of CF3Br monolayers physisorbed on graphite. We argue that the six-state clock model describes the universal feature of the phase transition in the experimental system and that the orientational ordering belongs to the KT universality class.

Chiral fluctuations in achiral clusters and liquids via molecular dynamics simulations

A chiral correlation function described previously [R. A. Harris, J. Chem. Phys. 115, 10577 (2001)] is employed here to detect chiral fluctuations in achiral systems. For the sake of illustration, classical constant volume and energy molecular dynamics simulations were employed in order to generate trajectories for each of the following systems: clusters of 4 to 119 water molecules in vacuum, a cluster of 6 water molecules in liquid carbon tetrachloride, the neat carbon tetrachloride liquid, and water itself. The power spectrum of the normalized chiral correlation function also has been calculated for each of these systems. The simulation results suggest that the chiral fluctuations, through their correlations, could give statistically significant signals from about 1 GHz for the liquids, to 10–100 GHz for either the solvated or the intermediate clusters, to 500 GHz–1 THz for the smallest clusters.

The chiral densities correlator in the Schwinger model on a torus

In the framework of the Euclidean path integral approach we derive the exact formula for the general N-point chiral densities correlator in the Schwinger model on a torus.