118 research outputs found
Tensor networks for Lattice Gauge Theories and Atomic Quantum Simulation
We show that gauge invariant quantum link models, Abelian and non-Abelian,
can be exactly described in terms of tensor networks states. Quantum link
models represent an ideal bridge between high-energy to cold atom physics, as
they can be used in cold-atoms in optical lattices to study lattice gauge
theories. In this framework, we characterize the phase diagram of a (1+1)-d
quantum link version of the Schwinger model in an external classical background
electric field: the quantum phase transition from a charge and parity ordered
phase with non-zero electric flux to a disordered one with a net zero electric
flux configuration is described by the Ising universality class.Comment: 9 pages, 9 figures. Published versio
Real-time Dynamics in U(1) Lattice Gauge Theories with Tensor Networks
Tensor network algorithms provide a suitable route for tackling real-time
dependent problems in lattice gauge theories, enabling the investigation of
out-of-equilibrium dynamics. We analyze a U(1) lattice gauge theory in (1+1)
dimensions in the presence of dynamical matter for different mass and electric
field couplings, a theory akin to quantum-electrodynamics in one-dimension,
which displays string-breaking: the confining string between charges can
spontaneously break during quench experiments, giving rise to charge-anticharge
pairs according to the Schwinger mechanism. We study the real-time spreading of
excitations in the system by means of electric field and particle fluctuations:
we determine a dynamical state diagram for string breaking and quantitatively
evaluate the time-scales for mass production. We also show that the time
evolution of the quantum correlations can be detected via bipartite von Neumann
entropies, thus demonstrating that the Schwinger mechanism is tightly linked to
entanglement spreading. To present the variety of possible applications of this
simulation platform, we show how one could follow the real-time scattering
processes between mesons and the creation of entanglement during scattering
processes. Finally, we test the quality of quantum simulations of these
dynamics, quantifying the role of possible imperfections in cold atoms, trapped
ions, and superconducting circuit systems. Our results demonstrate how
entanglement properties can be used to deepen our understanding of basic
phenomena in the real-time dynamics of gauge theories such as string breaking
and collisions.Comment: 15 pages, 25 figures. Published versio
Unitary -designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies
We present a general framework for the generation of random unitaries based
on random quenches in atomic Hubbard and spin models, forming approximate
unitary -designs, and their application to the measurement of R\'enyi
entropies. We generalize our protocol presented in [Elben2017:
arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and
spin lattice models. We further present an in-depth numerical and analytical
study of experimental imperfections, including the effect of decoherence and
statistical errors, and discuss connections of our approach with many-body
quantum chaos.Comment: This is a new and extended version of the Supplementary material
presented in arXiv:1709.05060v1, rewritten as a companion paper. Version
accepted to Phys. Rev. A. Minus sign corrected in Eq (5
Trimer liquids and crystals of polar molecules in coupled wires
We investigate the pairing and crystalline instabilities of bosonic and
fermionic polar molecules confined to a ladder geometry. By means of analytical
and quasi-exact numerical techniques, we show that gases of composite molecular
dimers as well as trimers can be stabilized as a function of the density
difference between the wires. A shallow optical lattice can pin both liquids,
realizing crystals of composite bosons or fermions. We show that these exotic
quantum phases should be realizable under current experimental conditions in
finite-size confining potentials.Comment: 5 pages, 3 figures plus additional material; Accepted for publication
in Phys. Rev. Let
Majorana Quasi-Particles Protected by Angular Momentum Conservation
We show how angular momentum conservation can stabilise a symmetry-protected
quasi-topological phase of matter supporting Majorana quasi-particles as edge
modes in one-dimensional cold atom gases. We investigate a number-conserving
four-species Hubbard model in the presence of spin-orbit coupling. The latter
reduces the global spin symmetry to an angular momentum parity symmetry, which
provides an extremely robust protection mechanism that does not rely on any
coupling to additional reservoirs. The emergence of Majorana edge modes is
elucidated using field theory techniques, and corroborated by
density-matrix-renormalization-group simulations. Our results pave the way
toward the observation of Majorana edge modes with alkaline-earth-like fermions
in optical lattices, where all basic ingredients for our recipe - spin-orbit
coupling and strong inter-orbital interactions - have been experimentally
realized over the last two years.Comment: 12 pages (6 + 6 supplementary material
Atomic Quantum Simulation of U(N) and SU(N) Non-Abelian Lattice Gauge Theories
Using ultracold alkaline-earth atoms in optical lattices, we construct a
quantum simulator for U(N) and SU(N) lattice gauge theories with fermionic
matter based on quantum link models. These systems share qualitative features
with QCD, including chiral symmetry breaking and restoration at non-zero
temperature or baryon density. Unlike classical simulations, a quantum
simulator does not suffer from sign problems and can address the corresponding
chiral dynamics in real time.Comment: 12 pages, 5 figures. Main text plus one basic introduction to the
topic and one supplementary material on implementation. Final versio
SO(3) "Nuclear Physics" with ultracold Gases
An ab initio calculation of nuclear physics from Quantum Chromodynamics
(QCD), the fundamental SU(3) gauge theory of the strong interaction, remains an
outstanding challenge. Here, we discuss the emergence of key elements of
nuclear physics using an SO(3) lattice gauge theory as a toy model for QCD. We
show that this model is accessible to state-of-the-art quantum simulation
experiments with ultracold atoms in an optical lattice. First, we demonstrate
that our model shares characteristic many-body features with QCD, such as the
spontaneous breakdown of chiral symmetry, its restoration at finite baryon
density, as well as the existence of few-body bound states. Then we show that
in the one-dimensional case, the dynamics in the gauge invariant sector can be
encoded as a spin S=3/2 Heisenberg model, i.e., as quantum magnetism, which has
a natural realization with bosonic mixtures in optical lattices, and thus sheds
light on the connection between non-Abelian gauge theories and quantum
magnetism.Comment: 34 pages, 9 figure
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