3 research outputs found
Reflection of a Lieb-Liniger wave packet from the hard-wall potential
Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the
hard-wall potential is studied. We demonstrate that a time-dependent wave
function, which describes quantum dynamics of a Lieb-Liniger wave packet
comprised of N particles, can be found by solving an -dimensional Fourier
transform; this follows from the symmetry properties of the many-body
eigenstates in the presence of the hard-wall potential. The presented formalism
is employed to numerically calculate reflection of a few-body wave packet from
the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde
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