Spectrum and Correlation Functions of a Quasi-One-Dimensional Quantum Ising Model

For a model of weakly coupled quantum Ising chains we outline the phase diagram and establish that well below the transition line the system has a remarkably one-dimensional spectrum. We study the dynamical magnetic susceptibility and find a very rich spectrum with several modes corresponding to a fundamental particle and its bound states. The approach is based on the Bethe ansatz and the random phase approximation applied to the interchain exchange.

Figure 1

Expected phase diagram of model (1). Estimates of $g_c$ and $T_c(g=0)$ are given by Eqs. (14, 10), respectively. In the vicinity of the $g=0$ point the physics is well described by model (5).

Figure 2

The three particle contribution to the dynamical susceptibility for a single chain.

Figure 3

A schematic diagram showing what happens to the coherent modes as a function of $g$. To the left of the figure, we have three coherent modes with very one-dimensional dispersions. As we move to the right, the transverse dispersion grows and the overall mass scale decreases until all modes collapse at criticality.