48 research outputs found
Relaxation in the XX quantum chain
We present the results obtained on the magnetisation relaxation properties of
an XX quantum chain in a transverse magnetic field. We first consider an
initial thermal kink-like state where half of the chain is initially
thermalized at a very high temperature while the remaining half, called
the system, is put at a lower temperature . From this initial state, we
derive analytically the Green function associated to the dynamical behaviour of
the transverse magnetisation. Depending on the strength of the magnetic field
and on the temperature of the system, different regimes are obtained for the
magnetic relaxation. In particular, with an initial droplet-like state, that is
a cold subsystem of finite size in contact at both ends with an infinite
temperature environnement, we derive analytically the behaviour of the
time-dependent system magnetisation
Long-Time Tails and Anomalous Slowing Down in the Relaxation of Spatially Inhomogeneous Excitations in Quantum Spin Chains
Exact analytic calculations in spin-1/2 XY chains, show the presence of
long-time tails in the asymptotic dynamics of spatially inhomogeneous
excitations. The decay of inhomogeneities, for , is given in the
form of a power law where the relaxation time
and the exponent depend on the wave vector ,
characterizing the spatial modulation of the initial excitation. We consider
several variants of the XY model (dimerized, with staggered magnetic field,
with bond alternation, and with isotropic and uniform interactions), that are
grouped into two families, whether the energy spectrum has a gap or not. Once
the initial condition is given, the non-equilibrium problem for the
magnetization is solved in closed form, without any other assumption. The
long-time behavior for can be obtained systematically in a form
of an asymptotic series through the stationary phase method. We found that
gapped models show critical behavior with respect to , in the sense that
there exist critical values , where the relaxation time
diverges and the exponent changes discontinuously. At those points, a
slowing down of the relaxation process is induced, similarly to phenomena
occurring near phase transitions. Long-lived excitations are identified as
incommensurate spin density waves that emerge in systems undergoing the Peierls
transition. In contrast, gapless models do not present the above anomalies as a
function of the wave vector .Comment: 25 pages, 2 postscript figures. Manuscript submitted to Physical
Review
Real-time dynamics in spin-1/2 chains with adaptive time-dependent DMRG
We investigate the influence of different interaction strengths and
dimerizations on the magnetization transport in antiferromagnetic spin-1/2
XXZ-chains. We focus on the real-time evolution of the inhomogeneous initial
state with all spins pointing up along the z axis in the left half and down in
the right half of the chain, using the adaptive time-dependent density-matrix
renormalization group (adaptive t-DMRG). We find on time-scales accessible to
us ballistic magnetization transport for small Sz-Sz-interaction and arbitrary
dimerization, but almost no transport for stronger Sz-Sz-interaction, with a
sharp crossover at Jz=1. At Jz=1 results indicate superdiffusive transport.
Additionally, we perform a detailed analysis of the error made by the adaptive
time-dependent DMRG using the fact that the evolution in the XX-model is known
exactly. We find that the error at small times is dominated by the error made
by the Trotter decomposition, whereas for longer times the DMRG truncation
error becomes the most important, with a very sharp crossover at some "runaway"
time.Comment: 13 pages, 20 figure