Particle-hole symmetry and the nu=5/2 quantum Hall state

We discuss the implications of approximate particle-hole symmetry in a half-filled Landau level in which a paired quantum Hall state forms. We note that the Pfaffian state is not particle-hole symmetric. Therefore, in the limit of vanishing Landau-level mixing, in which particle-hole transformation is an exact symmetry, the Pfaffian spontaneously breaks this symmetry. There is a particle-hole conjugate state, which we call the anti-Pfaffian, which is degenerate with the Pfaffian in this limit. We observe that strong Landau-level mixing should favor the Pfaffian, but it is an open problem which state is favored for the moderate Landau-level mixing which is present in experiments. We discuss the bulk and edge physics of the anti-Pfaffian. We analyze a simplified model in which transitions between analogs of the two states can be studied in detail. Finally, we discuss experimental implications.     

Particle-hole symmetry and the effect of disorder on the Mott-Hubbard insulator

The understanding of the interplay of electron correlations and randomness in solids is enhanced by demonstrating that particle-hole ( p-h) symmetry plays a crucial role in determining the effects of disorder on the transport and thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that the low-temperature conductivity decreases with increasing disorder when p-h symmetry is preserved, and shows the opposite behavior, i.e., conductivity increases with increasing disorder, when p-h symmetry is broken. The Mott insulating gap is insensitive to weak disorder when there is p-h symmetry, whereas in its absence the gap diminishes with increasing disorder.     

Stable Pfaffian state in bilayer graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.     

Particle-hole state densities for calculation of the multi-step compound emission

Analytical formulae have been derived for the density of particle-hole states having all particles bound. Such states are involved in the statistical multi-step compound MSC emission. Results of calculations are compared with predictions of other theoretical approaches.     

A Chern-Simons effective field theory for the Pfaffian quantum Hall state

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at v = 1 is an SU(2)₂ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chem-Simons theory with coupling constant k = 2. The effective field theories for other Pfaffian states, such as the fermionic one at v = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.     

Pfaffian bundles and the Ising model

An infinite volume Pfaffian formalism is developed for the Ising model.Research supported in part by NSF grant DMS-8421289     

On the symmetry of the seminal Horodecki state

It is shown that the seminal Horodecki 2-qutrit state belongs to the class of states displaying symmetry governed by a commutative subgroup of the unitary group U(3). Taking a conjugate subgroup one obtains another classes of symmetric states and one finds equivalent representations of the Horodecki state. These results are generalized to d⊗d systems.     

Pfaffian identities and Virasoro operators

Letters in Mathematical Physics - A formula for Schur Q-functions is presented which describes the action of the Virasoro operators. For a strict partition $$\lambda =(\lambda _1,\lambda _2,\ldots...     

Equation of state and symmetry energy within the stability valley

We apply the direct variational method to derive the equation of state for finite nuclei within the stability valley. The extended Thomas-Fermi approximation for the energy functional with Skyrme forces is used. Applying the leptodermous expansion for the profile nucleon densities, we have studied the neutron coat and the isospin symmetry energy for neutron-rich nuclei. Using the equation of state for the pressure, we derive the region of spinodal instability of finite nuclei and its dependence on the mass number, the asymmetry parameter and the Skyrme force parameters. We suggest the procedure of derivation of the isospin symmetry energy from the analysis of the isospin shift of the chemical potential = - beyond the beta-stability line. We show that both the structure of the neutron coat and the position of the drip line depend significantly on the Skyrme force parameters.     

Particle-hole mixing driven by the superconducting fluctuations

Development of the STM and ARPES spectroscopy enabled to reach the resolution sufficient for probing the particle-hole entanglement in superconducting materials, even above the critical temperature T_c. On a quantitative level one can characterize such entanglement in terms of the Bogoliubov angle which determines to what extent the particles and holes constitute the effective quasiparticles. In classical superconductors, where the phase transition is related to formation of the Cooper pairs almost simultaneously accompanied by onset of their long-range phase coherence, the Bogoliubov angle is slanted (due to finite particle-hole mixing) all the way up to T_c. In the high temperature superconductors and in superfluid ultracold fermion atoms near the Feshbach resonance the situation is different because the preformed pairs can exist above T_c albeit loosing coherence due to the strong quantum fluctuations. We discuss a generic temperature dependence of the Bogoliubov angle in such pseudogap state indicating a novel, non-BCS behavior. For analysis we use the two-component model describing the pairs coexisting with single fermions and study selfconsistently their feedback effects by the similarity transformation originating from the renormalization group approach.     

The Pfaffian line bundle

We analyze the holomorphic Pfaffian line bundle defined over an infinite dimensional isotropic Grassmannian manifold. Using the infinite dimensional relative Pfaffian, we produce a Fock space structure on the space of holomorphic sections of the dual of this bundle. On this Fock space, an explicit and rigorous construction of the spin representations of the loop groupsLO _n is given. We also discuss and prove some facts about the connection between the Pfaffian line bundle over the Grassmannian and the Pfaffian line bundle of a Dirac operator.Supported by a National Science Foundation Graduate Fellowship     

Particle-hole excitations in nucleus-nucleus collisions

Nucleus-nucleus collisions lead to nuclear excitations which can be expressed in terms of particles and holes. An empirical formula is presented to calculate this initially degree of freedom. The formula is tested against data and found to have a large range of validity with respect to projectile masses and bombarding energies.     

Particle-hole transformations and sum rules for the Hubbard model

By applying the partial particle-hole and the particle-hole unitary transformations to the Hubbard model, we establish several new sum rules for the Hubbard model defined on a bipartite lattice.     

Particle-hole amplitudes in spherical nuclei

Equations and relations are discussed which allow to calculate particle-hole amplitudes of excited states of spherical nuclei. In particular we investigate the case where the Bethe-Salpeter equation must be solved in both particle-hole channels.     

Particle-hole calculation of the isobaric analog and isovector monopole resonances

The correlated proton-particle—neutron-hole spectrum is calculated for N > Z nuclei using a Skyrme type interaction and the response function method. The basis of the calculation is a complete one-particle—one-hole space with the continuum included. As a result the distribution of the isovector monopole strength in the analog nucleus is obtained. This distribution has a narrow peak which corresponds to the isobaric analog resonance and at higher energies a broad peak which is the isovector monopole resonance. The coupling between these two states is inherent in the calculation.