Interplay between field-induced and frustration-induced quantum criticalities in the frustrated two-leg Heisenberg ladder

The antiferromagnetic Heisenberg two-leg ladder in the presence of frustration and an external magnetic field is a system that is characterized by two sorts of quantum criticalities, not only one. One criticality is the consequence of intrinsic frustration, and the other one is a result of the external magnetic field. So the behaviour of each of them in the presence of the other deserves to be studied. Using the Jordan–Wigner transformation in dimensions higher than one and the bond-mean-field theory we examine the interplay between the field-induced and frustration-induced quantum criticalities in this system. The present work could constitute a prototype for those systems showing multiple, perhaps sometimes competing, quantum criticalities. We calculate several physical quantities such as magnetization and spin susceptibility as functions of field and temperature.PACS Nos.: 75.10.Jm 73.43.Nq 75.10.Pq 75.10.Dg

Quantum and classical criticalities in the frustrated two-leg Heisenberg ladder

This paper is about the frustration-induced criticality in the antiferromagnetic Heisenberg model on the two-leg ladder with exchange interactions along the chains, rungs, and diagonals, and also about the effect of thermal fluctuations on this criticality. The method used is the bond-mean-field theory, which is based on the Jordan–Wigner transformation in dimensions higher than one. In this paper, we will summarize the main results presented in a talk, and report on new results about the couplings and temperature dependences of the spin susceptibility.PACS Nos.: 75.10.Jm, 75.10.Dg, 75.50.Ee

Density matrix renormalization group studies on the stability of quasi-1-D undoped and doped polymer ferromagnets

We study the ferromagnetic ground state of the theoretical model proposed for quasi-one-dimensional organic polymer ferromagnets by using the density matrix renormalization group method. We find that the chain–radical interaction, the on-site electron–electron repulsion, and the electron–phonon coupling play important roles in the stability of the ferromagnetic state, whether in doped systems or not. We are convinced that when the system is doped by one electron, a polaron appears, diminishing the stability of the high-spin state.PACS No.: 75.10.Jm

Article

A method for calculating complete secular polynomials is discussedthat is based on the evaluation of matrix elementsof a specific Hamiltonian.Several Hamiltonians are presented and described in detail as well astheir physical significance. It is shown that theycan be transformed into an equivalent form in termsof raising and lowering operators, and the third componentof the spin operator. A basis set is definedand the action of a specific Hamiltonian on thebasis set is described in detail. Several Hamiltoniansare given explicitly and in matrix form. Results in terms of secularpolynomials for an anisotropic Hamiltonian with one anisotropyparameter and a Hamiltonian with two anisotropy parameters forseveral values of N are reported. These polynomialsthat have not appeared before are given in terms of both theenergy and anisotropy variables.PACS Nos.: 05.50+q, 75.10Dg, and 75.10 Jm