76 research outputs found
Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
We propose a method for controllable generation of non-local entangled pairs
using spinor atoms loaded in an optical superlattice. Our scheme iteratively
increases the distance between entangled atoms by controlling the coupling
between the double wells. When implemented in a finite linear chain of 2N
atoms, it creates a triplet valence bond state with large persistency of
entanglement (of the order of N). We also study the non-equilibrium dynamics of
the one-dimensional ferromagnetic Heisenberg Hamiltonian and show that the time
evolution of a state of decoupled triplets on each double well leads to the
formation of a highly entangled state where short-distance antiferromagnetic
correlations coexist with longer-distance ferromagnetic ones. We present
methods for detection and characterization of the various dynamically generated
states. These ideas are a step forward towards the use of atoms trapped by
light as quantum information processors and quantum simulators.Comment: 13 pages, 10 figures, references adde
On the determinant representations of Gaudin models' scalar products and form factors
We propose alternative determinant representations of certain form factors
and scalar products of states in rational Gaudin models realized in terms of
compact spins. We use alternative pseudo-vacuums to write overlaps in terms of
partition functions with domain wall boundary conditions. Contrarily to
Slavnovs determinant formulas, this construction does not require that any of
the involved states be solutions to the Bethe equations; a fact that could
prove useful in certain non-equilibrium problems. Moreover, by using an
atypical determinant representation of the partition functions, we propose
expressions for the local spin raising and lowering operators form factors
which only depend on the eigenvalues of the conserved charges. These
eigenvalues define eigenstates via solutions of a system of quadratic equations
instead of the usual Bethe equations. Consequently, the current work allows
important simplifications to numerical procedures addressing decoherence in
Gaudin models.Comment: 15 pages, 0 figures, Published versio
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
Quantum quench dynamics of the sine-Gordon model in some solvable limits
In connection with the the thermalization problem in isolated quantum
systems, we investigate the dynamics following a quantum quench of the
sine-Gordon model in the Luther-Emery and the semiclassical limits. We consider
the quench from the gapped to the gapless phase as well as reversed one. By
obtaining analytic expressions for the one and two-point correlation functions
of the order parameter operator at zero-temperature, the manifestations of
integrability in the absence of thermalization in the sine-Gordon model are
studied. It is thus shown that correlations in the long time regime after the
quench are well described by a generalized Gibbs ensemble. We also consider the
case where the system is initially in contact with a reservoir at finite
temperature. The possible relevance of our results to current and future
experiments with ultracold atomic systems is also critically considered.Comment: 21 pages, no figures. To appear in New J. Phys
Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
We study the time evolution of quantum one-dimensional gapless systems
evolving from initial states with a domain-wall. We generalize the
path-integral imaginary time approach that together with boundary conformal
field theory allows to derive the time and space dependence of general
correlation functions. The latter are explicitly obtained for the Ising
universality class, and the typical behavior of one- and two-point functions is
derived for the general case. Possible connections with the stochastic Loewner
evolution are discussed and explicit results for one-point time dependent
averages are obtained for generic \kappa for boundary conditions corresponding
to SLE. We use this set of results to predict the time evolution of the
entanglement entropy and obtain the universal constant shift due to the
presence of a domain wall in the initial state.Comment: 27 pages, 10 figure
Quantum quenches from integrability: the fermionic pairing model
Understanding the non-equilibrium dynamics of extended quantum systems after
the trigger of a sudden, global perturbation (quench) represents a daunting
challenge, especially in the presence of interactions. The main difficulties
stem from both the vanishing time scale of the quench event, which can thus
create arbitrarily high energy modes, and its non-local nature, which curtails
the utility of local excitation bases. We here show that nonperturbative
methods based on integrability can prove sufficiently powerful to completely
characterize quantum quenches: we illustrate this using a model of fermions
with pairing interactions (Richardson's model). The effects of simple (and
multiple) quenches on the dynamics of various important observables are
discussed. Many of the features we find are expected to be universal to all
kinds of quench situations in atomic physics and condensed matter.Comment: 10 pages, 7 figure
Dephasing-induced diffusive transport in anisotropic Heisenberg model
We study transport properties of anisotropic Heisenberg model in a disordered
magnetic field experiencing dephasing due to external degrees of freedom. In
the absence of dephasing the model can display, depending on parameter values,
the whole range of possible transport regimes: ideal ballistic conduction,
diffusive, or ideal insulating behavior. We show that the presence of dephasing
induces normal diffusive transport in a wide range of parameters. We also
analyze the dependence of spin conductivity on the dephasing strength. In
addition, by analyzing the decay of spin-spin correlation function we discover
a presence of long-range order for finite chain sizes. All our results for a
one-dimensional spin chain at infinite temperature can be equivalently
rephrased for strongly-interacting disordered spinless fermions.Comment: 15 pages, 9 PS figure
Many-body Landau-Zener dynamics in coupled 1D Bose liquids
The Landau-Zener model of a quantum mechanical two-level system driven with a
linearly time dependent detuning has served over decades as a textbook paradigm
of quantum dynamics. In their seminal work [L. D. Landau, Physik. Z. Sowjet. 2,
46 (1932); C. Zener, Proc. Royal Soc. London 137, 696 (1932)], Landau and Zener
derived a non-perturbative prediction for the transition probability between
two states, which often serves as a reference point for the analysis of more
complex systems. A particularly intriguing question is whether that framework
can be extended to describe many-body quantum dynamics. Here we report an
experimental and theoretical study of a system of ultracold atoms, offering a
direct many-body generalization of the Landau-Zener problem. In a system of
pairwise tunnel-coupled 1D Bose liquids we show how tuning the correlations of
the 1D gases, the tunnel coupling between the tubes and the inter-tube
interactions strongly modify the original Landau-Zener picture. The results are
explained using a mean-field description of the inter-tube condensate
wave-function, coupled to the low-energy phonons of the 1D Bose liquid.Comment: 13 pages, 10 figures
Light-cone-like spreading of correlations in a quantum many-body system
How fast can correlations spread in a quantum many-body system? Based on the
seminal work by Lieb and Robinson, it has recently been shown that several
interacting many-body systems exhibit an effective light cone that bounds the
propagation speed of correlations. The existence of such a "speed of light" has
profound implications for condensed matter physics and quantum information, but
has never been observed experimentally. Here we report on the time-resolved
detection of propagating correlations in an interacting quantum many-body
system. By quenching a one-dimensional quantum gas in an optical lattice, we
reveal how quasiparticle pairs transport correlations with a finite velocity
across the system, resulting in an effective light cone for the quantum
dynamics. Our results open important perspectives for understanding relaxation
of closed quantum systems far from equilibrium as well as for engineering
efficient quantum channels necessary for fast quantum computations.Comment: 7 pages, 5 figures, 2 table
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
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