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Propagation of Bound States in Heisenberg XXZ Chains

Hans Gerd Evertz, Martin Ganahl, Elias Rabel

Published Jan 1, 2010• 0 citations
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We consider the nonequilibrium evolution in the spin-1/2 XXZ Heisenberg chain for fixed magnetization after a local quantum quench. This model is equivalent to interacting spinless fermions. Initially an infinite magnetic field is applied to n consecutive sites and the ground state is calculated. At time t=0 the field is switched off and the time evolution of observables such as the z component of spin is computed using the time evolving block decimation algorithm. We find that the observables exhibit strong signatures of linearly propagating spinon and bound state excitations. These persist even when integrability-breaking perturbations are included. Since bound states ("strings") are notoriously difficult to observe using conventional probes such as inelastic neutron scattering, we conclude that local quantum quenches are an ideal setting for studying their properties. We comment on implications of our results for cold atom experiments.
We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle (``spinon'') excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.