These lectures, prepared for Higher Structures in China III, held in Changchun, Aug 2012, describe a relationship between two forms of categorification of algebras by giving a combinatorial model for Khovanov’s categorification of the Heisenberg algebra in a 2-category of spans of groupoids. This is joint work with Jamie Vicary. The goal here is to describe two notions of “categorifying an alge...

We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact results. In a complementary approach we generalize previous work[1, 2] and present a new description of these and other processes and the related quantum chains ...

We find using Monte Carlo simulations of the 2D square lattice nearest neighbour quantum Heisenberg anti-ferromagnet that the high energy peak locations at (π,0) and (π/2,π/2) differ by about 6%, (π/2,π/2) being the highest. This is a deviation from linear spin wave theory which predicts equal magnon energies at these points. It is also found that the peak at (π,0) is broader than the peak at (...

This paper is a short review of recent results on interface states in the Falicov-Kimball model and the ferromagnetic XXZ Heisenberg model. More specifically, we discuss the following topics: 1) The existence of interfaces in quantum lattice models that can be considered as perturbations of classical models. 2) The rigidity of the 111 interface in the three-dimensional FalicovKimball model at s...

We consider the statics and dynamics of distinguishable spin-1/2 systems on an arbitrary graph G with N vertices. In particular, we consider systems of quantum spins evolving according to one of two hamiltonians: (i) the XY hamiltonian HXY , which contains an XY interaction for every pair of spins connected by an edge in G; and (ii) the Heisenberg hamiltonian HHeis, which contains a Heisenberg ...

We study the entanglement in the quantum Heisenberg XY model in which the so-called W entangled states can be generated for 3 or 4 qubits. By the concept of concurrence, we study the entanglement in the time evolution of the XY model. We investigate the thermal entanglement in the two-qubit isotropic XY model with a magnetic field and in the anisotropic XY model, and find that the thermal entan...

We employ nonperturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. A precision estimate of the universal critical equation of state for the three–dimensional O(4) Heisenberg model is presented. We explicitly connect the...

As shown in former papers, the nonadiabatic Heisenberg model presents a mechanism of Cooper pair formation generated by the strongly correlated atomic-like motion of the electrons in narrow, roughly half-filled “superconducting bands” of special symmetry. The formation of Cooper pairs is not only the result of an attractive electron–electron interaction but is additionally the outcome of quantu...

Polarized neutron study of the spin dynamics for a Heisenberg antiferromagnet with easy-axis anisotropy, CsNiCl3, clearly demonstrates the almost isotropic character of the system. The study also revealed a difference between the observed and the calculated spin wave dispersion using the classical spin wave theory for T << 4.8 K and T > 4.8 K. This may be interpreted as a quantum effect on the ...

A class of quantum chains possessing a family of local conserved charges with a Catalan tree pattern is studied. Recently, we have identified such a structure in the integrable SU(N)-invariant chains. In the present work we find sufficient conditions for the existence of a family of charges with this structure in terms of the underlying algebra. Two additional systems with a Catalan tree struct...