3 research outputs found
The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with
toroidal boundary conditions and an even number of sites provide a projection
mechanism yielding the spectra of models with a central charge c<1 including
the unitary and non-unitary minimal series. Taking into account the
half-integer angular momentum sectors - which correspond to chains with an odd
number of sites - in many cases leads to new spinor operators appearing in the
projected systems. These new sectors in the XXZ chain correspond to a new type
of frustration lines in the projected minimal models. The corresponding new
boundary conditions in the Hamiltonian limit are investigated for the Ising
model and the 3-state Potts model and are shown to be related to duality
transformations which are an additional symmetry at their self-dual critical
point. By different ways of projecting systems we find models with the same
central charge sharing the same operator content and modular invariant
partition function which however differ in the distribution of operators into
sectors and hence in the physical meaning of the operators involved. Related to
the projection mechanism in the continuum there are remarkable symmetry
properties of the finite XXZ chain. The observed degeneracies in the energy and
momentum spectra are shown to be the consequence of intertwining relations
involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published
back in 1993. It has been made available here because there has been recent
interest in conformal twisted boundary conditions. The "duality-twisted"
boundary conditions discussed in this paper are particular examples of such
boundary conditions for quantum spin chains, so there might be some renewed
interest in these result
A sufficient criterion for integrability of stochastic many-body dynamics and quantum spin chains
We propose a dynamical matrix product ansatz describing the stochastic
dynamics of two species of particles with excluded-volume interaction and the
quantum mechanics of the associated quantum spin chains respectively. Analyzing
consistency of the time-dependent algebra which is obtained from the action of
the corresponding Markov generator, we obtain sufficient conditions on the
hopping rates for identifing the integrable models. From the dynamical algebra
we construct the quadratic algebra of Zamolodchikov type, associativity of
which is a Yang Baxter equation. The Bethe ansatz equations for the spectra are
obtained directly from the dynamical matrix product ansatz.Comment: 19 pages Late
Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
Recent work on stochastic interacting particle systems with two particle
species (or single-species systems with kinematic constraints) has demonstrated
the existence of spontaneous symmetry breaking, long-range order and phase
coexistence in nonequilibrium steady states, even if translational invariance
is not broken by defects or open boundaries. If both particle species are
conserved, the temporal behaviour is largely unexplored, but first results of
current work on the transition from the microscopic to the macroscopic scale
yield exact coupled nonlinear hydrodynamic equations and indicate the emergence
of novel types of shock waves which are collective excitations stabilized by
the flow of microscopic fluctuations. We review the basic stationary and
dynamic properties of these systems, highlighting the role of conservation laws
and kinetic constraints for the hydrodynamic behaviour, the microscopic origin
of domain wall (shock) stability and the coarsening dynamics of domains during
phase separation.Comment: 72 pages, 6 figures, 201 references (topical review for J. Phys. A:
Math. Gen.