Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory

We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2N+kappa as N-->infinity, where kappa and kappa are determined explicitly. In an important class of systems, kappa is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for kappa therefore provides an explicit formula for the central charge.     

Adsorption on the carbon nanotubes

Adsorption on single walled carbon nanotubes (SWCNTs) is a subject of growing experimental and theoretical interest. The possible adsorbed patterns of atoms and molecules on the single-walled carbon nanotubes vary with the diameters and chirality of the tubes due to the confinement. The curvature of the carbon nanotube surface enlarges the distance of the adsorbate atoms and thus enhances the stability of high coverage structures of adsorbate. There exist two novel high-coverage stable structures of potassium adsorbed on SWCNTs, which are not stable on graphite. The electronic properties of SWCNTs can be modified by adsorbate atoms and metal-semiconductor and semiconductor-semi-conductor transitions can be achieved by the doping of alkali atoms.     

Addition energies of fullerenes and carbon nanotubes as quantum dots: the role of symmetry

Using density-functional theory calculations, we investigate the addition energy (AE) of quantum dots formed of fullerenes or closed single-wall carbon nanotubes. We focus on the connection between symmetry and oscillations in the AE spectrum. In the highly symmetric fullerenes the oscillation period is large because of the large level degeneracy and Hund's rule. For long nanotubes, the AE oscillation is fourfold. Adding defects destroys the spatial symmetry of the tubes, leaving only spin degeneracy; correspondingly, the fourfold behavior is destroyed, leaving an even/odd behavior which is quite robust. We use our symmetry results to explain recent experiments.     

Dual symmetry in classical and quantum spin theory

Apropos the continuing discussion of the observability of the magnetic charge (the Dirac monopole [1]), there is interest in investigating the dual symmetry of the spin equations of motion in classical and quantum theory. It is known that in dual symmetry theory the presence of a magnetic charge is a simple consequence of the dual invariance of the equations of electrodynamics [2], The matter of the observability of a magnetic charge is not tackled there, and becomes only experimentally verifiable [2, p. 64].Translated from Izvestiya Vysshikh Uchebnkh, Zavedenii, Fizika, No. 7, pp. 56–59, July, 1932.     

Hidden quantum group symmetry and integrable perturbations of conformal field theories

The hidden quantum group symmetry in the quantum Sine-Gordon model is found. This symmetry provides the possibility to restrict the operator algebra of the model to subalgebras. It is shown that these subalgebras are massive deformations of minimal conformal field theories.Supported in part by the Department of Energy under Grant DE-FG02-88ER25065     

单壁碳纳米管中的金属-半导体转变与对称性

报道了最近作者对受压扶手椅形单壁碳纳米管中的金属-半导体转变机理的理论研究。这种转变在两种因素的共同作用下得以发生，即外加压力造成碳纳米管镜像对称破缺，以及被压碳纳米管两侧原子发生成键相互作用．作者还进一步揭示了发生这种转变的普遍机制：只要将单壁碳纳米管中两套原来等价的子晶格变得可以区分(对称性破缺)，在费米能附近就会产生能隙．     

Neutrinos,axions and conformal symmetry

We demonstrate that radiative breaking of conformal symmetry (and simultaneously electroweak symmetry) in the standard model with right-chiral neutrinos and a minimally enlarged scalar sector induces spontaneous breaking of lepton number symmetry, which naturally gives rise to an axion-like particle with some unusual features. The couplings of this ‘axion’ to standard model particles, in particular photons and gluons, are entirely determined (and computable) via the conformal anomaly, and their smallness turns out to be directly related to the smallness of the masses of the light neutrinos.     

Generalized spin and pseudo-spin symmetry: Relativistic extension of supersymmetric quantum mechanics

We consider the Dirac equation in 1+1$1+1$ space–time dimension with vector, scalar and pseudo-scalar coupling. In the traditional spin (or pseudo-spin) symmetry, the difference between (or sum of) the scalar and vector potentials is a constant. Here, however, we introduce an alternative symmetry where the scalar or pseudo-scalar potential is proportional to the vector potential. This leads to a model with significant extensions to supersymmetric quantum mechanics. We present a formal solution of the problem but give explicit analytic results for specific examples.     

Mass-generation,symmetry breaking and conformal invariance

We present a principle of mass-generation in which conformal invariance is only spontaneously broken. Some examples are given and we speculate about the relation to the Higgs-Kibble mechanism and the renormalizability of such models.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Defects, quasibound states, and quantum conductance in metallic carbon nanotubes

The effects of impurities and local structural defects on the conductance of metallic carbon nanotubes are calculated using an ab initio pseudopotential method within the Landauer formalism. Substitutionally doped boron or nitrogen produces quasibound impurity states of a definite parity and reduces the conductance by a quantum unit (2e(2)/h) via resonant backscattering. These resonant states show strong similarity to acceptor or donor states in semiconductors. The Stone-Wales defect also produces quasibound states and exhibits quantized conductance reduction. In the case of a vacancy, the conductance shows a much more complex behavior than the prediction from the widely used pi-electron tight-binding model.     

Electronic structure and quantum transport in carbon nanotubes

Received: 3 April 1998     

Adsorption of nonpolar benzene derivatives on single-walled carbon nanotubes

The adsorption of benzene, toluene, and chlorobenzene on single-walled carbon nanotubes (SWCNTs) with and without acid oxidation was conducted to investigate the influences of derivative groups on benzene rings and functional groups from SWCNTs on adsorption by SWCNTs. The SWCNTs of high purity were chosen and moderate acid oxidation was performed so that the surface physical properties remained unchanged after acid oxidation and the influences of acid oxidation on adsorption were only contributed from the modification of the surface chemistry of SWCNTs. The oxygen-containing surface groups introduced by acid oxidation obstructed the interactions between functional groups of nonpolar benzene derivatives and C-rings of SWCNTs significantly. The dispersive interaction between the partially positive H⁺ of the methyl group and the oxygen-containing surface groups slightly increased the adsorption of toluene on oxidized SWCNTs at high solution pH. The thermodynamic of adsorption was also studied at different temperatures.     

Electron spin resonance and quantum critical phenomena in VOx multiwall nanotubes

Basing on the high frequency (60 GHz) electron spin resonance study of the VO_x multiwall nanotubes (VO_x ‐NTs) carried out in the temperature range 4.2–200 K we report: (i) the first direct experimental evidence of the presence of the antiferromagnetic dimers in VO_x ‐NTs and (ii) the observation of an anomalous low temperature growth of the magnetic susceptibility for quasi‐free spins, which obey the power law χ (T)～1/T ^α with the exponent α ≈ 0.6 in a wide temperature range 4.2–50 K. We argue that the observed departures from the Curie–Weiss behaviour manifest the onset of the quantum critical regime and formation of the Griffiths phase as a magnetic ground state of these spin species. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Adsorption and desorption of an O2 molecule on carbon nanotubes

Adsorption and desorption of an oxygen molecule on carbon nanotubes are investigated using density functional calculations. Several precursor states exist at the edge of armchair nanotubes, whereas an exothermic adsorption takes place at the edge of zigzag nanotubes. We also estimate desorption barriers of a CO molecule from nanotubes as well as fullerenes and amorphous phases. Our calculations suggest that carbon nanotubes can survive selectively during the oxidative etching process with a precise control of annealing temperature, in good agreement with experimental results of purification process of carbon nanotubes.     

Adsorption of hydrogen on normal and pentaheptite single wall carbon nanotubes

Density functional calculations of the physisorption of molecular hydrogen and the dissociative atomic chemisorption on the external surface of hexagonal and pentaheptite carbon nanotubes, have been carried out. Physisorption binding energies are near 100 meV/molecule and are similar on metallic and semiconducting nanotubes. Full coverage of the nanotube with one molecule per graphitic hexagon decreases the binding energy per molecule. Chemisorption binding energies per H atom are larger on pentaheptites than on hexagonal carbon nanotubes. The molecular physisorption and dissociative chemisorption states on pentaheptites have very similar total energies (some chemisorbed states are even slightly more stable than the physisorbed states), while on hexagonal carbon nanotubes molecular physisorption is more stable than dissociative chemisorption. However, a substantial energy barrier has to be overcome to go from physisorption to dissociative chemisorption in both types of nanotubes.     

Adsorption of the insensitive explosive TATB on single-walled carbon nanotubes

The non-covalent adsorption of the insensitive explosive TATB (1,3,5-triamino-2,4,6-trinitrobenzene) on the sidewalls of single-walled carbon nanotubes (CNTs) has been calculated using an ONIOM approach. It was found that TATB deformed remarkably when attached non-covalently on the surface of CNTs, especially on the inner wall of the nanotubes. The diameter of the nanotube determined the degree of distortion of the inner-adsorbed TATB, but had little effect on the deformation of the outer-attached TATB. The non-covalent combination of TATB with the nanotube is an exothermic process due to the negative adsorption energy. TATB adsorption on the inner wall of nanotubes was energetically more favorable than that on the outer wall of the nanotubes. In both cases, the adsorption became more stable with increasing diameter of the nanotube. Our theoretical results can be used as a guideline for the design of energetic nanocomposites based on CNTs and aromatic nitro-explosives.