Bound-state confinement after trap-expansion dynamics in integrable systems

Integrable systems possess stable families of quasiparticles, which are composite objects (bound states) of elementary excitations. Motivated by recent quantum computer experiments, we investigate bound-state transport in the spin- 1/2 anisotropic Heisenberg chain (XXZ chain). Specifically, we consider the sudden vacuum expansion of a finite region A prepared in a non-equilibrium state. In the hydrodynamic regime, if interactions are strong enough, bound states remain confined in the initial region. Bound-state confinement persists until the density of unbound excitations remains finite in the bulk of A. Since region A is finite, at asymptotically long times bound states are 'liberated' after the 'evaporation' of the unbound excitations. Fingerprints of confinement are visible in the space-time profiles of local spin-projection operators. To be specific, here we focus on the expansion of the p-N & eacute;el states, which are obtained by repetition of a unit cell with p up spins followed by p down spins. Upon increasing p, the bound-state content is enhanced. In the limit p ->infinity one obtains the domain-wall initial state. We show that for p < 4, only bound states with n > p are confined at large chain anisotropy. For p greater than or similar to 4, bound states with n = p are also confined, consistent with the absence of transport in the limit p ->infinity. The scenario of bound-state confinement leads to a hierarchy of timescales at which bound states of different sizes are liberated, which is also reflected in the dynamics of the von Neumann entropy.