Dynamics of the transverse Ising model with next-nearest-neighbor interactions

Abstract

We study the effects of next-nearest-neighbor (NNN) interactions on the dynamics of the one-dimensional spin-1/2 transverse Ising model in the high-temperature limit. We use exact diagonalization to obtain the time-dependent transverse correlation function and the corresponding spectral density for a tagged spin. Our results for chains of 13 spins with periodic boundary conditions produce results which are valid in the infinite-size limit. In general we find that the NNN coupling produces slower dynamics accompanied by an enhancement of the central mode behavior. Even in the case of a strong transverse field, if the NNN coupling is sufficiently large, then there is a crossover from collective mode to central mode behavior. We also obtain several recurrants for the continued fraction representation of the relaxation function.

Recent Advances in the Calculation of Dynamical Correlation Functions

“…Consider the transverse Ising model with an additional axial nextnearest-neighbor interaction (transverse ANNNI model) [17]. The Hamiltonian for a chain with L spins can be written as:…”

“…45, the competing interaction between the ferromagnetic and antiferromagnetic terms induces frustration in the magnetic ordering. This will give rise to a much richer variety of phases when either the transverse magnetic field or the spin-spin interations are varied, such as ferromagnetic or antiferromagnetic phases, disordered or paramagnetic phases, and floating phases [17]. Such variety of phases in the ground-state could carry over their effects into the dynamics at the high temperature limit, like the known transverse Ising model.…”

“…On the other hand, exact diagonalization methods have also been used in several areas of physics [13][14][15][16][17]. In this method one numerically determines the eigenvalues and eigenfunctions of a given Hamiltonian of a finite system to find the dynamical correlations of interest.…”

A Diatomic Chain with A Mass Impurity

“…Most of the early work used the normal coordinates method [1][2][3][4]. Since earlier 1980s, the recurrence relations method [5][6][7][8] is used in the study of various areas in physics [9][10][11][12][13] as well as in different models of oscillator chains [14][15][16][17][18][19][20][21][22].…”

Local Dynamics in an Infinite Harmonic Chain

“…For reviews, see [3][4][5][6][7]. For a partial list of recent papers, see [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”