A new class ${\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix

Details A new class ${\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix A new class ${\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix

2006-07-17

arxiv.org/abs/math/0607379v3

J. Math. Phys. 47, 123301 (2006)

Mathematics

Quantum Algebra

27 pages

Scientific paper

Statistical models corresponding to a new class of braid matrices ($\hat{o}_N; N\geq 3$) presented in a previous paper are studied. Indices labeling states spanning the $N^r$ dimensional base space of $T^{(r)}(\theta)$, the $r$-th order transfer matrix are so chosen that the operators $W$ (the sum of the state labels) and (CP) (the circular permutation of state labels) commute with $T^{(r)}(\theta)$. This drastically simplifies the construction of eigenstates, reducing it to solutions of relatively small number of simultaneous linear equations. Roots of unity play a crucial role. Thus for diagonalizing the 81 dimensional space for N=3, $r=4$, one has to solve a maximal set of 5 linear equations. A supplementary symmetry relates invariant subspaces pairwise ($W=(r,Nr)$ and so on) so that only one of each pair needs study. The case N=3 is studied fully for $r=(1,2,3,4)$. Basic aspects for all $(N,r)$ are discussed. Full exploitation of such symmetries lead to a formalism quite different from, possibly generalized, algebraic Bethe ansatz. Chain Hamiltonians are studied. The specific types of spin flips they induce and propagate are pointed out. The inverse Cayley transform of the YB matrix giving the potential leading to factorizable $S$-matrix is constructed explicitly for N=3 as also the full set of $\hat{R}tt$ relations. Perspectives are discussed in a final section.

Affiliated with

Also associated with

No associations

Rating

A new class ${\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A new class ${\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new class ${\hat o}_N$ of statistical models: Transfer matrix eigenstates, chain Hamiltonians, factorizable $S$-matrix will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-506909