In the present paper we revisit the so-called Haldane limit, i.e. a particular continuum limit, which leads from a spin chain to a sigma model. We use the coherent state formulation of the path integral to reduce the problem to a semiclassical one, which leads us to the observation that the Haldane limit is closely related to a Lagrangian embedding into the classical phase space of the spin cha...

We consider a special correlation function in the isotropic spin-1 2 Heisenberg antiferromagnet. It is the probability of nding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two diierent representations for this correlation function. Both of them are exact at any distance, but one becomes more eeective for the description of long distance behaviour, t...

By using the density matrix renormalization group method, we investigate groundand excited-state properties of the eg-orbital degenerate Hubbard model at quarter filling for two kinds of lattices, zigzag chain and ladder. In the zigzag chain, the system is effectively regarded as a decoupled double chain of the S=1/2 antiferromagnetic Heisenberg model, and the spin gap is approximately zero, si...

In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin s XXZ model of a finite size and the q-Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz equations give rise to the polynomial solutions of a second order q-difference equation in terms of Askey-Wilson operator. The more general form of Bethe Ansatz e...

Recently certain identities for solutions of the Bethe equations in the six-vertex model were obtained in [FM]. In the note we give an elementary proof of similar identities for the case of the inhomogeneous arbitrary spin XXX or XXZ model. Though the corresponding calculations can be done in the elliptic case too, almost without modification , in that case the resulting identites have rather t...

It is observed that when the conformational properties of DNA molecule are mapped onto an antiferromagnetic spin system we can realize the specific properties of the rod-like-chain (RLC) model where the analytically continued partition function corresponds to the symmetric top Hamiltonian. The relevant path integral represents a charge particle in the field of a non-quantized monopole which sug...

We analyze the fast-moving string in the magnetic Melvin field background and find that the associated effective Lagrangian of string sigma model describes the spin chain model with external magnetic field. The spin vector in the spin chain has been properly deformed and is living on the deformed two-sphere or deformed two-dimensional hyperboloid, depending on the direction around which the str...

Using the Algebraic Bethe Ansatz we consider the correlation functions of the integrable higher spin chains. We apply a method recently developed for the spin 12 Heisenberg chain, based on the solution of the quantum inverse problem. We construct a representation for the correlation functions on a finite chain for arbitrary spin. Then we show how the string solutions of the Bethe equations can ...

Lin, Ching-Yang, and Miyamoto, Hiroaki—An estimated search and matching model of the Japanese labor market This paper studies how well a simple search and matching model can describe aggregate Japanese labor market dynamics in a full information setting. We develop a discrete-time search and matching model with a convex vacancy posting cost and three shocks: productivity, separation, and markup...