SciPost Phys. 10, 049 (2021) ·
published 25 February 2021
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In this work, we study non-equilibrium dynamics in Floquet conformal field
theories (CFTs) in 1+1D, in which the driving Hamiltonian involves the
energy-momentum density spatially modulated by an arbitrary smooth function.
This generalizes earlier work which was restricted to the sine-square deformed
type of Floquet Hamiltonians, operating within a $\mathfrak{sl}_2$ sub-algebra.
Here we show remarkably that the problem remains soluble in this generalized
case which involves the full Virasoro algebra, based on a geometrical approach.
It is found that the phase diagram is determined by the stroboscopic
trajectories of operator evolution. The presence/absence of spatial fixed
points in the operator evolution indicates that the driven CFT is in a
heating/non-heating phase, in which the entanglement entropy grows/oscillates
in time. Additionally, the heating regime is further subdivided into a
multitude of phases, with different entanglement patterns and spatial
distribution of energy-momentum density, which are characterized by the number
of spatial fixed points. Phase transitions between these different heating
phases can be achieved simply by changing the duration of application of the
driving Hamiltonian. We demonstrate the general features with concrete CFT
examples and compare the results to lattice calculations and find remarkable
agreement.
SciPost Phys. 10, 045 (2021) ·
published 22 February 2021
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We describe an efficient numerical method for simulating the dynamics and
steady states of collective spin systems in the presence of dephasing and
decay. The method is based on the Schwinger boson representation of spin
operators and uses an extension of the truncated Wigner approximation to map
the exact open system dynamics onto stochastic differential equations for the
corresponding phase space distribution. This approach is most effective in the
limit of very large spin quantum numbers, where exact numerical simulations and
other approximation methods are no longer applicable. We benchmark this
numerical technique for known superradiant decay and spin-squeezing processes
and illustrate its application for the simulation of non-equilibrium phase
transitions in dissipative spin lattice models.
SciPost Phys. 10, 044 (2021) ·
published 22 February 2021
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We numerically study the possibility of many-body localization transition in
a disordered quantum dimer model on the honeycomb lattice. By using the
peculiar constraints of this model and state-of-the-art exact diagonalization
and time evolution methods, we probe both eigenstates and dynamical properties
and conclude on the existence of a localization transition, on the available
time and length scales (system sizes of up to N=108 sites). We critically
discuss these results and their implications.
SciPost Phys. 10, 040 (2021) ·
published 17 February 2021
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Several tensor networks are built of isometric tensors, i.e. tensors satisfying $W^\dagger W = \mathrm{I}$. Prominent examples include matrix product states (MPS) in canonical form, the multiscale entanglement renormalization ansatz (MERA), and quantum circuits in general, such as those needed in state preparation and quantum variational eigensolvers. We show how gradient-based optimization methods on Riemannian manifolds can be used to optimize tensor networks of isometries to represent e.g. ground states of 1D quantum Hamiltonians. We discuss the geometry of Grassmann and Stiefel manifolds, the Riemannian manifolds of isometric tensors, and review how state-of-the-art optimization methods like nonlinear conjugate gradient and quasi-Newton algorithms can be implemented in this context. We apply these methods in the context of infinite MPS and MERA, and show benchmark results in which they outperform the best previously-known optimization methods, which are tailor-made for those specific variational classes. We also provide open-source implementations of our algorithms.
SciPost Phys. 10, 031 (2021) ·
published 10 February 2021
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In the last decades, the blossoming of experimental breakthroughs in the
domain of electron energy loss spectroscopy (EELS) has triggered a variety of
theoretical developments. Those have to deal with completely different
situations, from atomically resolved phonon mapping to electron circular
dichroism passing by surface plasmon mapping. All of them rely on very
different physical approximations and have not yet been reconciled, despite
early attempts to do so. As an effort in that direction, we report on the
development of a scalar relativistic quantum electrodynamic (QED) approach of
the inelastic scattering of fast electrons. This theory can be adapted to
describe all modern EELS experiments, and under the relevant approximations,
can be reduced to any of the last EELS theories. In that aim, we present in
this paper the state of the art and the basics of scalar relativistic QED
relevant to the electron inelastic scattering. We then give a clear relation
between the two once antagonist descriptions of the EELS, the retarded green
Dyadic, usually applied to describe photonic excitations and the quasi-static
mixed dynamic form factor (MDFF), more adapted to describe core electronic
excitations of material. We then use this theory to establish two important
EELS-related equations. The first one relates the spatially resolved EELS to
the imaginary part of the photon propagator and the incoming and outgoing
electron beam wavefunction, synthesizing the most common theories developed for
analyzing spatially resolved EELS experiments. The second one shows that the
evolution of the electron beam density matrix is proportional to the mutual
coherence tensor, proving that quite universally, the electromagnetic
correlations in the target are imprinted in the coherence properties of the
probing electron beam.
SciPost Phys. 10, 025 (2021) ·
published 3 February 2021
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We employ the Gross-Pitaevskii equation to study acoustic emission generated
in a uniform Bose gas by a static impurity. The impurity excites a sound-wave
packet, which propagates through the gas. We calculate the shape of this wave
packet in the limit of long wave lengths, and argue that it is possible to
extract properties of the impurity by observing this shape. We illustrate here
this possibility for a Bose gas with a trapped impurity atom -- an example of a
relevant experimental setup. Presented results are general for all
one-dimensional systems described by the nonlinear Schr\"odinger equation and
can also be used in nonatomic systems, e.g., to analyze light propagation in
nonlinear optical media. Finally, we calculate the shape of the sound-wave
packet for a three-dimensional Bose gas assuming a spherically symmetric
perturbation.
