Showing papers by "Pierre Mathieu published in 1994"
TL;DR: In this article, a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model is presented, with the use of the boost operator, and a simple description of conserved charges is found in terms of a Catalan tree.
Abstract: We present a detailed analysis of the structure of the conservation laws in quantum integrable chains of the XYZ-type and in the Hubbard model. With the use of the boost operator, we establish the general form of the XYZ conserved charges in terms of simple polynomials in spin variables and derive recursion relations for the relative coefficients of these polynomials. For two submodels of the XYZ chain - namely the XXX and XY cases, all the charges can be calculated in closed form. For the XXX case, a simple description of conserved charges is found in terms of a Catalan tree. This construction is generalized for the su(M) invariant integrable chain. We also indicate that a quantum recursive (ladder) operator can be traced back to the presence of a hamiltonian mastersymmetry of degree one in the classical continuous version of the model. We show that in the quantum continuous limits of the XYZ model, the ladder property of the boost operator disappears. For the Hubbard model we demonstrate the non-existence of a ladder operator. Nevertheless, the general structure of the conserved charges is indicated, and the expression for the terms linear in the model's free parameter for all charges is derived in closed form.
83 citations
TL;DR: In this article, an explicit expression for all the quantum integrals of motion for the isotropic Heisenberg s = 1/2 spin chain is presented, expressed in terms of a sum over simple polynomials in spin variables.
Abstract: An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg s=1/2 spin chain is presented. The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct and independent of the transfer matrix formalism. Continuum limits of these integrals in both ferromagnetic and antiferromagnetic sectors are briefly discussed.
60 citations
TL;DR: An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg $s=1/2$ spin chain is presented in this paper.The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables.
Abstract: An explicit expression for all the quantum integrals of motion for the isotropic Heisenberg $s=1/2$ spin chain is presented.
The conserved quantities are expressed in terms of a sum over simple polynomials in spin variables. This construction is direct and independent of the transfer matrix formalism. Continuum limits of these integrals in both ferrromagnetic and antiferromagnetic sectors are briefly discussed.
8 citations
TL;DR: A hybrid system of stimulated Raman scattering and optical parametric amplification pumped by a single 1.06-µm Nd:YAG laser source provides a simple system that could provide a high pulse energy output at a repetition rate of greater than 10 Hz.
Abstract: A high-energy eye safe laser source at 1.54 µm is demonstrated experimentally by using a hybrid system of stimulated Raman scattering and optical parametric amplification pumped by a single 1.06-µm Nd:YAG laser source. This system overcomes some of the technical problems that occur in conventional eye safe lasers, such as optical breakdown and thermal blooming in the Raman laser, and thermal conduction problems in the erbium-doped glass solid-state laser that limit the repetition rate when high-energy output is sought. Thus this hybrid design provides a simple system that could provide a high pulse energy output (> 50 mJ) at a repetition rate of greater than 10 Hz.
4 citations