Open Spin Chain Research Articles

Edge states in open antiferromagnetic Heisenberg chains.

In this letter we report our results in investigating edge effects of open antiferromagnetic Heisenberg spin chains with spin magnitudes $S=1/2, 1,3/2,2$ using the density-matrix renormalization group (DMRG) method initiated by White. For integer spin chains, we find that edge states with spin magnitude $S_{edge}=S/2$ exist, in agreement with Valence-Bond-Solid model picture. For half-integer spin chains, we find that no edge states exist for $S=1/2$ spin chain, but edge state exists in $S=3/2$ spin chain with $S_{edge}=1/2$, in agreement with previous conjecture by Ng. Strong finite size effects associated with spin dimmerization in half-integer spin chains will also be discussed.

Analytical Bethe ansatz for a A2n-1(2), Bn(1), Cn(1), Dn(1)quantum-algebra-invariant open spin chains

We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras A2n-1(2), Bn(1), Cn(1), Dn(1), and which have the quantum-algebra invariance Uq(Cn), Uq(Bn), Uq(Cn), Uq(Dn), respectively.

SPECTRUM OF THE TRANSFER MATRIX FOR THE Uq(Bn)-INVARIANT $A_{2n}^{(2)}$ OPEN SPIN CHAIN

We propose an expression for the eigenvalues of the transfer matrix for the Uq(Bn)-invariant open quantum spin chain associated with the fundamental representation of [Formula: see text] By assumption, the Bethe ansatz equations are “doubled” with respect to those of the corresponding closed chain with periodic boundary conditions. We verify that the transfer matrix eigenvalues have the correct analyticity properties and asymptotic behavior. We also briefly discuss the structure of the eigenstates of the transfer matrix.

Integrable open-boundary conditions for the Zn × Zn Belavin model

We use the unitarity and cross-unitarity properties of the Z n symmetric R-matrix to construct the transfer matrix t( u) for an N-site open spin chain. We prove that the t( u) constitute a one-parameter commutative family. By using a new family of solutions of the reflection equation, the Hamiltonian of the Belavin model with independent boundary conditions is obtained.

Generalized algebraic framework for open spin chains

An extension of the Sklyanin algebraic framework for construction of a commuting set of operators is presented. The conditions under which the operators can be interpreted as integrals of motion of an open spin chain with boundary conditions and nearest-neighbour interaction are investigated. An example based on the asymmetric six-vertex solutions of the YBE equation is given.

Bethe ansatz for an open Heisenberg spin chain with impurity

We have set up the algebraic Bethe ansatz equation for an open Heisenberg spin chain having an impurity of a different type of spin. The chain is considered to be open and hence the QISM approach as modified by Sklyanin is used to set up the equations for the Bethe ansatz.

On integrable quantum group invariant antiferromagnets

A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin's type K matrices are used to achieve this) and invariant under U ϵ (sl(2)) transformations in nilpotent irreps for ϵ 3 = 1. Some considerations on the centralizer of nilpotent representations and its representation theory are also presented.

Edge states in Schwinger-boson mean-field theory of low-dimensional quantum antiferromagnets.

The origin and properties of the S=1/2 end states in S=1 open spin chains is explained within the framework of Schwinger-boson mean-field theory. Moreover, we show that in two dimensions (square lattice), corresponding edge states exist with structures depending on spin magnitude S

Fusion procedure for open chains

The authors have generalized Sklyanin's approach of constructing open integrable quantum spin chains to the case of PT-invariant R matrices. They formulate a fusion procedure for such chains. In particular, they show that the fused transfer matrix can be expressed in terms of products of the original transfer matrix and products of certain quantum determinants which can be explicitly evaluated. Applications of these results include constructing open integrable higher-spin chains, as well as obtaining functional equations for transfer-matrix eigenvalues, which may be solved by an analytical Bethe ansatz.

Schwinger-boson mean-field theory for S=1 open spin chains.

The properties of S=1 open spin chains is studied using Schwinger-boson mean-field theory. It is found that localized S=1/2 states exist at the ends of chains and that the ground states of chains with even and odd number of sites are fundamentally different. Properties of the localized end states are discussed.

Analytical Bethe Ansatz for quantum-algebra-invariant spin chains

We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz (BA) method. In particular, we determine in this way the spectrum of the transfer matrices of the U q [su(2)]-invariant spin chains associated with A 1 (1) and A 2 (2) in the fundamental representation. The quantum-algebra invariance of these models plays an essential role in obtaining these results. The BA equations for these open chains are “doubled” with respect to the BA equations for the corresponding closed chains.

INTEGRABILITY OF OPEN SPIN CHAINS WITH QUANTUM ALGEBRA SYMMETRY

We construct an open quantum spin chain from the “twisted” [Formula: see text]R matrix in the fundamental representation which has the quantum algebra symmetry Uq[ su (2)]. This anisotropic spin-1 chain is different from the Uq[ su (2)]-invariant chain constructed from the “untwisted” [Formula: see text] spin-1 R matrix (namely, the spin-1 XXZ chain of Fateev-Zamolodchikov with boundary terms) but, nevertheless, is also completely integrable. We discuss the general case of an R matrix of the type g(k), where k∈{1, 2, 3}, and g is any simple Lie algebra.

Integrable open spin chains with nonsymmetric R-matrices

The authors extend Sklyanin's formalism for constructing integrable open spin chains to the case of 'non-symmetric' (PT-invariant) R-matrices. They use this formalism to show that the Hamiltonian of an integrable open chain is invariant under gauge transformations of the R-matrix.

Semiclassical theory of polarization and correlation in direct nuclear reactions: A. Y. Abul-Magd and M. El-Nadi, Physics Department, Faculty of Science, Cairo University, Giza, Cairo

The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow one to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl(2|1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their factorized form. The discussion corresponds to leading order of perturbation theory.