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Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium
Recent experimental achievements in controlling ultracold gases in optical
lattices open a new perspective on quantum many-body physics. In these
experimental setups it is possible to study coherent time evolution of isolated
quantum systems. These dynamics reveal new physics beyond the low-energy
properties usually relevant in solid-state many-body systems. In this paper we
study the time evolution of antiferromagnetic order in the Heisenberg chain
after a sudden change of the anisotropy parameter, using various numerical and
analytical methods. As a generic result we find that the order parameter, which
can show oscillatory or non-oscillatory dynamics, decays exponentially except
for the effectively non-interacting case of the XX limit. For weakly ordered
initial states we also find evidence for an algebraic correction to the
exponential law. The study is based on numerical simulations using a numerical
matrix product method for infinite system sizes (iMPS), for which we provide a
detailed description and an error analysis. Additionally, we investigate in
detail the exactly solvable XX limit. These results are compared to
approximative analytical approaches including an effective description by the
XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories.
This reveals which aspects of non-equilibrium dynamics can as in equilibrium be
described by low-energy theories and which are the novel phenomena specific to
quantum quench dynamics. The relevance of the energetically high part of the
spectrum is illustrated by means of a full numerical diagonalization of the
Hamiltonian.Comment: 28 page
Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
We present a modification of Matrix Product State time evolution to simulate
the propagation of signal fronts on infinite one-dimensional systems. We
restrict the calculation to a window moving along with a signal, which by the
Lieb-Robinson bound is contained within a light cone. Signal fronts can be
studied unperturbed and with high precision for much longer times than on
finite systems. Entanglement inside the window is naturally small, greatly
lowering computational effort. We investigate the time evolution of the
transverse field Ising (TFI) model and of the S=1/2 XXZ antiferromagnet in
their symmetry broken phases after several different local quantum quenches.
In both models, we observe distinct magnetization plateaus at the signal
front for very large times, resembling those previously observed for the
particle density of tight binding (TB) fermions. We show that the normalized
difference to the magnetization of the ground state exhibits similar scaling
behaviour as the density of TB fermions. In the XXZ model there is an
additional internal structure of the signal front due to pairing, and wider
plateaus with tight binding scaling exponents for the normalized excess
magnetization. We also observe parameter dependent interaction effects between
individual plateaus, resulting in a slight spatial compression of the plateau
widths.
In the TFI model, we additionally find that for an initial Jordan-Wigner
domain wall state, the complete time evolution of the normalized excess
longitudinal magnetization agrees exactly with the particle density of TB
fermions.Comment: 10 pages with 5 figures. Appendix with 23 pages, 13 figures and 4
tables. Largely extended and improved versio
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