G. L. Rossini

THE ζ FUNCTION ANSWER TO PARITY VIOLATION IN THREE-DIMENSIONAL GAUGE THEORIES

We study parity violation in (2+1)-dimensional gauge theories coupled to massive fermions. Using the ζ function regularization approach we evaluate the ground state fermion current in an arbitrary gauge field background, showing that it gets two different contributions which violate parity invariance and induce a Chern–Simons term in the gauge field effective action. One is related to the well-known classical parity breaking produced by a fermion mass term in three dimensions; the other, already present for massless fermions, is related to peculiarities of gauge-invariant regularization in odd-dimensional spaces.

Gauge invariance and finite temperature effective actions of Chern-Simons gauge theories with fermions

Abstract We discuss the behavior of theories of fermions coupled to Chern-Simons gauge fields with a non-abelian gauge group in three dimensions and at finite temperature. Using non-perturbative arguments and gauge invariance, and in contradiction with perturbative results, we show that the coefficient of the Chern-Simons term of the effective actions for the gauge fields at finite temperature can be at most an integer function of the temperature. This is in a sense a generalized no-renormalization theorem. We also discuss the case of abelian theories and give indications that a similar condition should hold there too. We discuss consequences of our results to the thermodynamics of anyon superfluids and fractional quantum Hall systems.

Theory of spin-Peierls transition beyond the adiabatic approximation

We develop a theory of the spin-Peierls transition taking into account the three dimensional character of the phonon field. Our approach does not rely on the adiabatic or mean-field treatment for the phonons. It is instead based in the exact integration of the phonon field, the exact long wavelength solution of the one-chain spin problem, and then a mean-field approximation for the interchain interaction. We show that the spin gap and the critical temperature are strongly reduced due to the finite frequency effects of the phonon coupling transverse to the magnetic chains. We show that the long standing discussion on absence of a soft mode in some compounds can be naturally resolved within our theory. We claim that our results should be applicable to the inorganic spin-Peierls compound

Anisotropic frustrated Heisenberg model on the honeycomb lattice

\mathrm{Cu}\mathrm{Ge}{\mathrm{O}}_{3}

NON-ABELIAN FRACTIONAL QUANTUM HALL STATES AND CHIRAL COSET CONFORMAL FIELD THEORIES

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ON THE PATH INTEGRAL REPRESENTATION FOR SPIN SYSTEMS

We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size periodic lattices.

Spinons as Composite Fermions

We propose an effective Lagrangian for the low energy theory of the Pfaffian states of the fractional quantum Hall effect in the bulk in terms of non-Abelian Chern-Simons (CS) actions. Our approach exploits the connection between the topological Chern-Simons theory and chiral conformal field theories. This construction can be used to describe a large class of non-Abelian FQH states.

FERMIONIC COSET MODELS AS TOPOLOGICAL MODELS

We propose a classical constrained Hamiltonian theory for the spin. After the Dirac treatment we show that due to the existence of second-class constraints the Dirac brackets of the proposed theory represent the commutation relations for the spin. We show that the corresponding partition function, obtained via the Fadeev - Senjanovic procedure, coincides with that obtained using coherent states. We also evaluate this partition function for the case of a single spin in a magnetic field.

Quantum phases of a frustrated four-leg spin tube

We show that gauge invariant composites in the fermionic realization of SU(N)1 conformal field theory explicitly exhibit the holomorphic factorization of the corresponding WZW primaries. In the SU(2)1 case we show that the holomorphic sector realizes the spinon Y(sl2) algebra, thus allowing the classification of the chiral Fock space in terms of semionic quasiparticle excitations created by the composite fermions.

Resonances in a dilute gas of magnons and metamagnetism of isotropic frustrated ferromagnetic spin chains

By considering the fermionic realization of