3,944 research outputs found
Quantum dynamics in transverse-field Ising models from classical networks
The efficient representation of quantum many-body states with classical
resources is a key challenge in quantum many-body theory. In this work we
analytically construct classical networks for the description of the quantum
dynamics in transverse-field Ising models that can be solved efficiently using
Monte Carlo techniques. Our perturbative construction encodes time-evolved
quantum states of spin-1/2 systems in a network of classical spins with local
couplings and can be directly generalized to other spin systems and higher
spins. Using this construction we compute the transient dynamics in one, two,
and three dimensions including local observables, entanglement production, and
Loschmidt amplitudes using Monte Carlo algorithms and demonstrate the accuracy
of this approach by comparisons to exact results. We include a mapping to
equivalent artificial neural networks, which were recently introduced to
provide a universal structure for classical network wave functions
Effective time reversal and echo dynamics in the transverse field Ising model
The question of thermalisation in closed quantum many-body systems has
received a lot of attention in the past few years. An intimately related
question is whether a closed quantum system shows irreversible dynamics.
However, irreversibility and what we actually mean by this in a quantum
many-body system with unitary dynamics has been explored very little. In this
work we investigate the dynamics of the Ising model in a transverse magnetic
field involving an imperfect effective time reversal. We propose a definition
of irreversibility based on the echo peak decay of observables. Inducing the
effective time reversal by different protocols we find algebraic decay of the
echo peak heights or an ever persisting echo peak indicating that the dynamics
in this model is well reversible
Phase Diagram of Bosons in Two-Color Superlattices from Experimental Parameters
We study the zero-temperature phase diagram of a gas of bosonic 87-Rb atoms
in two-color superlattice potentials starting directly from the experimental
parameters, such as wavelengths and intensities of the two lasers generating
the superlattice. In a first step, we map the experimental setup to a
Bose-Hubbard Hamiltonian with site-dependent parameters through explicit
band-structure calculations. In the second step, we solve the many-body problem
using the density-matrix renormalization group (DMRG) approach and compute
observables such as energy gap, condensate fraction, maximum number
fluctuations and visibility of interference fringes. We study the phase diagram
as function of the laser intensities s_2 and s_1 as control parameters and show
that all relevant quantum phases, i.e. superfluid, Mott-insulator, and quasi
Bose-glass phase, and the transitions between them can be investigated through
a variation of these intensities alone.Comment: 4 pages, 3 figure
Quantum many-body dynamics in two dimensions with artificial neural networks
The efficient numerical simulation of nonequilibrium real-time evolution in
isolated quantum matter constitutes a key challenge for current computational
methods. This holds in particular in the regime of two spatial dimensions,
whose experimental exploration is currently pursued with strong efforts in
quantum simulators. In this work we present a versatile and efficient machine
learning inspired approach based on a recently introduced artificial neural
network encoding of quantum many-body wave functions. We identify and resolve
some key challenges for the simulation of time evolution, which previously
imposed significant limitations on the accurate description of large systems
and long-time dynamics. As a concrete example, we study the dynamics of the
paradigmatic two-dimensional transverse field Ising model, as recently also
realized experimentally in systems of Rydberg atoms. Calculating the
nonequilibrium real-time evolution across a broad range of parameters, we, for
instance, observe collapse and revival oscillations of ferromagnetic order and
demonstrate that the reached time scales are comparable to or exceed the
capabilities of state-of-the-art tensor network methods.Comment: 6+10 pages, 2+9 figure
Ultracold Bose gases in time-dependent 1D superlattices: response and quasimomentum structure
The response of ultracold atomic Bose gases in time-dependent optical
lattices is discussed based on direct simulations of the time-evolution of the
many-body state in the framework of the Bose-Hubbard model. We focus on
small-amplitude modulations of the lattice potential as implemented in several
recent experiment and study different observables in the region of the first
resonance in the Mott-insulator phase. In addition to the energy transfer we
investigate the quasimomentum structure of the system which is accessible via
the matter-wave interference pattern after a prompt release. We identify
characteristic correlations between the excitation frequency and the
quasimomentum distribution and study their structure in the presence of a
superlattice potential.Comment: 4 pages, 4 figure
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