531 research outputs found
"Light-cone" dynamics after quantum quenches in spin chains
Signal propagation in the non equilibirum evolution after quantum quenches
has recently attracted much experimental and theoretical interest. A key
question arising in this context is what principles, and which of the
properties of the quench, determine the characteristic propagation velocity.
Here we investigate such issues for a class of quench protocols in one of the
central paradigms of interacting many-particle quantum systems, the spin-1/2
Heisenberg XXZ chain. We consider quenches from a variety of initial thermal
density matrices to the same final Hamiltonian using matrix product state
methods. The spreading velocities are observed to vary substantially with the
initial density matrix. However, we achieve a striking data collapse when the
spreading velocity is considered to be a function of the excess energy. Using
the fact that the XXZ chain is integrable, we present an explanation of the
observed velocities in terms of "excitations" in an appropriately defined
generalized Gibbs ensemble.Comment: 4+pages, 5 figures, supplementary materia
Finite-time quantum quenches in the XXZ Heisenberg chain
We study the time evolution of the two-point correlation functions in the XXZ
Heisenberg chain after a finite-time quantum quench in the anisotropy. We
compare results from numerical simulations to ones obtained in the Luttinger
model and find good agreement. We analyse the spreading of the correlations and
the associated light-cone features. We observe a delay in the appearance of the
light cone as compared to the sudden-quench setup, and link this delay to the
properties of the quench protocol
Higher-Order Hydrodynamics in 1D: a Promising Direction and a Null Result
We derive a Moyal dynamical equation that describes exact time evolution in
generic (inhomogeneous) noninteracting spin-chain models. Assuming
quasistationarity, we develop a hydrodynamic theory. The question at hand is
whether some large-time corrections are captured by higher-order hydrodynamics.
We consider in particular the dynamics after that two chains, prepared in
different conditions, are joined together. In these situations a light cone,
separating regions with macroscopically different properties, emerges from the
junction. In free fermionic systems some observables close to the light cone
follow a universal behavior, known as Tracy-Widom scaling. Universality means
weak dependence on the system's details, so this is the perfect setting where
hydrodynamics could emerge. For the transverse-field Ising chain and the XX
model, we show that hydrodynamics captures the scaling behavior close to the
light cone. On the other hand, our numerical analysis suggests that
hydrodynamics fails in more general models, whenever a condition is not
satisfied.Comment: 7+2 pages, 1+2 figure
Correlation spreading and properties of the quantum state in quench dynamics
The light cone spreading of correlations following a quantum quench is obtained from first principles. Fully taking into account quantum and interaction effects, the derivation shows how light cone dynamics does not require peculiar properties of the postquench state
A Nonequilibrium quantum phase transition in strongly coupled spin chains
We study spin transport in a boundary driven XXZ spin chain. Driving at the
chain boundaries is modeled by two additional spin chains prepared in
oppositely polarized states. Emergent behavior, both in the transient dynamics
and in the long-time quasi-steady state, is demonstrated. Time-dependent
matrix-product-state simulations of the system-bath state show ballistic spin
transport below the Heisenberg isotropic point. Indications of exponentially
vanishing transport are found above the Heisenberg point for low energy initial
states while the current decays asymptotically as a power law for high energy
states. Precisely at the critical point, non-ballistic transport is observed.
Finally, it is found that the sensitivity of the quasi-stationary state on the
initial state of the chain is a good witness of the different transport phases
Time-dependent Correlation Functions in Open Quadratic Fermionic Systems
We formulate and discuss explicit computation of dynamic correlation
functions in open quadradic fermionic systems which are driven and dissipated
by the Lindblad jump processes that are linear in canonical fermionic
operators. Dynamic correlators are interpreted in terms of local quantum quench
where the pre-quench state is the non-equilibrium steady state, i.e. a fixed
point of the Liouvillian. As an example we study the XY spin 1/2 chain and the
Kitaev Majorana chains with boundary Lindblad driving, whose dynamics exhibits
asymmetric (skewed) light cone behaviour. We also numerically treat the two
dimensional XY model and the XY spin chain with additional
Dzyaloshinskii-Moriya interactions. The latter exhibits a new non-equilibrium
phase transition which can be understood in terms of bifurcations of the
quasi-particle dispersion relation. Finally, considering in some detail the
periodic Kitaev chain (fermionic ring) with dissipation at a single (arbitrary)
site, we present analytical expressions for the first order corrections (in the
strength of dissipation) to the spectrum and the non-equilibrium steady state
(NESS) correlation functions.Comment: 25 pages, 10 figure
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