Abstract
The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The time evolved block decimation (TEBD) algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.
Highlights
The study of classical dynamics in nonlinear media has proven to be a source of astonishing surprises over the last century
We further demonstrate that exact methods based on the algebraic Bethe ansatz [6] provide a framework to evaluate the time-dependent expectation value of the local magnetization Sjz(t) algebraically, which can be used to track those localized magnonlike wave packets
We considered quantum scattering of localized excitations, created from linear combinations of Bethe states with Gaussiandistributed momenta, constructing wave packets of n bound magnons
Summary
The study of classical dynamics in nonlinear media has proven to be a source of astonishing surprises over the last century. Been shown to be special, in the sense of being exactly solvable using the quantum version of the inverse scattering method [6] (one might say integrable, the quantum notion of integrability is not as well defined as its classical counterpart [7]) Fundamental representatives of this family are the Heisenberg spin chain, solved by Bethe using what is known as the Bethe ansatz [8], along with the Lieb-Liniger model of δ-interacting bosons on a line [9]. The Heisenberg chain supports distinct bound states of magnons, whose dynamics has been investigated theoretically [16] and has recently been observed experimentally [17] One could view such excitations as the quantum equivalents of classical solitons. The appendixes provide details involving scattering theory and details on obtaining the phase shift directly from the phase of the time-evolving wave function
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