We define quantum determinants in matrix algebras related to pairs of compatible braidings. establish relations between these and the so-called column row determinants, which are often used theory integrable systems. also generalize spin systems using generalized Yangians demonstrate that such not uniquely determined by “quantum coordinate ring” basic space $$V$$ . For example, plane” $$xy=qyx$...

Path integral techniques for the density matrix of a one-dimensional statistical system near a boundary previously employed in black-hole physics are applied to providing a new interpretation of the density matrix renormalization group: its efficacy is due to the concentration of quantum states near the boundary. There has recently been a revival of interest in the study of statistical properti...

We present a new integrable extension of the a = −2, N = 2 SKdV hierarchy, with the ”small” N = 4 superconformal algebra (SCA) as the second hamiltonian structure. As distinct from the previously known N = 4 supersymmetric KdV hierarchy associated with the same N = 4 SCA, the new system respects only N = 2 rigid supersymmetry. We give for it both matrix and scalar Lax formulations and consider ...

This brief review deals with prepotentials inspired by N = 1 SUSY considerations due to Cachazo, Intrilligator, Vafa. These prepotentials associated with matrix models following Dijkgraaf and Vafa should be considered as given on an enlarged moduli space that includes Whitham times (couplings of the superpotential). This moduli space is nothing but the whole moduli space of (decorated) hyperell...

In this paper we consider the matrix lattice equation Un,t(Un+1−Un−1)=g(n)I, in both its autonomous (g(n)=2) and nonautonomous (g(n)=2n−1) forms. We show that each of these two equations are integrable. addition, explore construction Miura maps which relate equations, via intermediate to analogs Volterra but dependent variables. For last systems, cases where variables belong certain special cla...

Based on two higher-dimensional extensions of Lie algebras, three kinds of specific Lie algebras are introduced. Upon constructing proper loop algebras, six isospectral matrix spectral problems are presented and they yield nonlinear integrable couplings of the AblowitzKaup-Newell-Segur hierarchy, the Broer-Kaup hierarchy and the Kaup-Newell hierarchy. Especially, the reduced cases of the result...

In this paper we study the boundary effects for off-critical integrable field theories which have close analogs with integrable lattice models. Our models are the SU(2)k ⊗ SU(2)l/SU(2)k+l coset conformal field theories perturbed by integrable boundary and bulk operators. The boundary interactions are encoded into the boundary reflection matrix. Using the TBA method, we verify the flows of the c...