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We investigate the real time propagation of local excitations in XXZ and in Hubbard chains, using Full Diagonalization and TEBD time evolution.
An initial string of N up-spins ("particles") in an empty environment produces N different linearly propagating excitations in each direction, consisting of from 1 to N bound particles, which are consecutively more entangled.
Their velocities depend on the anisotropy parameter Delta and can be calculated from the Bethe ansatz. The scattering of magnons from such bound states produces unexpected effects, including the transmutation of a particle into a hole excitation.
When the initial state is the ground state of an antiferromagnet at nonzero magnetization, similarly propagating bound states still occur, which are now repulsively bound, with different entanglement properties. We also investigate Bloch oscillations of bound states, which exhibit strong internal structure and a period doubling when Delta is increased. For Hubbard chains, we demonstrate Andreev reflection upon scattering from the boundary between two regions of different repulsion. |
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