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W. M. Koo

Publications and source records attributed to W. M. Koo.

6 recordsLinked to original sources
arXiv1996

Boundary Yang-Baxter equation in the RSOS/SOS representation

We construct and solve the boundary Yang-Baxter equation in the RSOS/SOS representation. We find two classes of trigonometric solutions; diagonal and non-diagonal. As a lattice model, these two classes of solutions correspond to RSOS/SOS models with fixed and free boundary spins respectively. Applied to (1+1)-dimenional quantum field theory, these solutions give the boundary scattering amplitudes of the particles. For the diagonal solution, we propose an algebraic Bethe ansatz method to diagonalize the SOS-type transfer matrix with boundary and obtain the Bethe ansatz equations.

hep-th↗
arXiv1995

Oriented Polymers: A Transfer Matrix Calculation

Based on transfer matrix techniques and finite size scaling, we study the oriented polymer (self-avoiding walk) with nearest neighbor interaction. In the repulsive regime, various critical exponents are computed and compared with exact values predicted recently. The polymer is also found to undergo a spiral transition for sufficiently strong attractive interaction. The fractal dimension of the polymer is computed in the repulsive, attractive regimes and at the spiral transition point. The later is found to be different from that at the collapse transition of ordinary self-avoiding walk.

cond-mat↗
arXiv1995

$gl(n|m)$ color Calogero-Sutherland models and Super Yangian Algebra

A supersymmetric extension of the color Calogero-Sutherland model is considered based on the Yangian $Y(gl(n|m))$. The algebraic structure of the model is discussed in some details. We show that the commuting conserved quantities can be generated from the super-quantum determinant, thus establishing the integrability of the model. In addition, rational limit of the model is studied where the Yangian symmetry degenerates into a super loop algebra.

hep-th↗
arXiv1993

Representations of the Virasoro algebra from lattice models

We investigate in details how the Virasoro algebra appears in the scaling limit of the simplest lattice models of XXZ or RSOS type. Our approach is straightforward but to our knowledge had never been tried so far. We simply formulate a conjecture for the lattice stress-energy tensor motivated by the exact derivation of lattice global Ward identities. We then check that the proper algebraic relations are obeyed in the scaling limit. The latter is under reasonable control thanks to the Bethe-ansatz solution. The results, which are mostly numerical for technical reasons, are remarkably precise. They are also corroborated by exact pieces of information from various sources, in particular Temperley-Lieb algebra representation theory. Most features of the Virasoro algebra (like central term, null vectors, metric properties...) can thus be observed using the lattice models. This seems of general interest for lattice field theory, and also more specifically for finding relations between conformal invariance and lattice integrability, since basis for the irreducible representations of the Virasoro algebra should now follow (at least in principle) from Bethe-ansatz computations.

hep-th↗
arXiv1993

Fused Potts Models

Generalizing the mapping between the Potts model with nearest neighbor interaction and six vertex model, we build a family of "fused Potts models" related to the spin $k/2$ ${\rm U}_{q}{\rm su}(2)$ invariant vertex model and quantum spin chain. These Potts model have still variables taking values $1,\ldots,Q$ ($\sqrt{Q}=q+q^{-1}$) but they have a set of complicated multi spin interactions. The general technique to compute these interactions, the resulting lattice geometry, symmetries, and the detailed examples of $k=2,3$ are given. For $Q>4$ spontaneous magnetizations are computed on the integrable first order phase transition line, generalizing Baxter's results for $k=1$. For $Q\leq 4$, we discuss the full phase diagram of the spin one ($k=2$) anisotropic and ${\rm U}_{q}{\rm su}(2)$ invariant quantum spin chain (it reduces in the limit $Q=4$ ($q=1$) to the much studied phase diagram of the isotropic spin one quantum chain). Several critical lines and massless phases are exhibited. The appropriate generalization of the Valence Bond State method of Affleck et al. is worked out.

hep-th↗