Magnon decay in gapped quantum spin systems

In the O(3) sigma-model description of gapped spin systems, S=1 magnons can only decay into three lower energy magnons. We argue that the symmetry of the quantum spin Hamiltonian often allows decay into two magnons, and compute this decay rate in model systems. Two magnon decay is present in Haldane gap S=1 spin chains, even though it cannot be induced by any allowed term written in powers and gradients of the sigma-model field. We compare our results with recent measurements of Stone et al. (cond-mat/0511266) on a two-dimensional spin system.Comment: 4 pages, 3 figure

Response functions of gapped spin systems in high magnetic field

We study the dynamical structure factor of gapped one-dimensional spin systems in the critical phase in high magnetic field. It is shown that the presence of a ``condensate'' in the ground state in the high-field phase leads to interesting signatures in the response functions.Comment: uses ptptex.sty (included), 10 pages, 3 figs, to appear in Prog. Theor. Phys. Suppl. (Proc. of the 16th Nishinomiya Yukawa Memorial Symposium

Nonlinear sigma model study of a frustrated spin ladder

A model of two-leg spin-S ladder with two additional frustrating diagonal exchange couplings J_{D}, J_{D}' is studied within the framework of the nonlinear sigma model approach. The phase diagram has a rich structure and contains 2S gapless phase boundaries which split off the boundary to the fully saturated ferromagnetic phase when J_{D} and J_{D}' become different. For the S=1/2 case, the phase boundaries are identified as separating two topologically distinct Haldane-type phases discussed recently by Kim et al. (cond-mat/9910023).Comment: revtex 4 pages, figures embedded (psfig

Current fidelity susceptibility and conductivity in one-dimensional lattice models with open and periodic boundary conditions

We study, both numerically and analytically, the finite size scaling of the fidelity susceptibility \chi_{J} with respect to the charge or spin current in one-dimensional lattice models, and relate it to the low-frequency behavior of the corresponding conductivity. It is shown that in gapless systems with open boundary conditions the leading dependence on the system size L stems from the singular part of the conductivity and is quadratic, with a universal form \chi_{J}= 7KL^2 \zeta(3)/2\pi^4 where K is the Luttinger liquid parameter. In contrast to that, for periodic boundary conditions the leading system size dependence is directly connected with the regular part of the conductivity (giving alternative possibility to study low frequency behavior of the regular part of conductivity) and is subquadratic, \chi_{J} \propto L^\gamma(K), (with a K dependent constant \gamma) in most situations linear, \gamma=1. For open boundary conditions, we also study another current-related quantity, the fidelity susceptibility to the lattice tilt \chi_{P} and show that it scales as the quartic power of the system size, \chi_{P}=31KL^4 \zeta(5)/8 u^2 \pi^6, where u is the sound velocity. We comment on the behavior of the current fidelity susceptibility in gapped phases, particularly in the topologically ordered Haldane state.Comment: 11 pages, 7 eps figure