Benoit Estienne, Blagoje Oblak, JeanMarie Stéphan
SciPost Phys. 11, 016 (2021) ·
published 20 July 2021

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The gapless modes on the edge of fourdimensional (4D) quantum Hall droplets are known to be anisotropic: they only propagate in one direction, foliating the 3D boundary into independent 1D conduction channels. This foliation is extremely sensitive to the confining potential and generically yields chaotic flows. Here we study the quantum correlations and entanglement of such edge modes in 4D droplets confined by harmonic traps, whose boundary is a squashed threesphere. Commensurable trapping frequencies lead to periodic trajectories of electronic guiding centers; the corresponding edge modes propagate independently along $S^1$ fibers, forming a bundle of 1D conformal field theories over a 2D base space. By contrast, incommensurable frequencies produce quasiperiodic, ergodic trajectories, each of which covers its invariant torus
densely; the corresponding correlation function of edge modes has fractal features. This wealth of behaviors highlights the sharp differences between 4D Hall droplets and their 2D peers; it also exhibits the dependence of 4D edge modes on the choice of trap, suggesting the existence of observable bifurcations due to droplet deformations.
SciPost Phys. 11, 015 (2021) ·
published 16 July 2021

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Fixed points in three dimensions described by conformal field theories with
$MN_{m,n}= O(m)^n\rtimes S_n$ global symmetry have extensive applications in
critical phenomena. Associated experimental data for $m=n=2$ suggest the
existence of two nontrivial fixed points, while the $\varepsilon$ expansion
predicts only one, resulting in a puzzling state of affairs. A recent numerical
conformal bootstrap study has found two kinks for small values of the
parameters $m$ and $n$, with critical exponents in good agreement with
experimental determinations in the $m=n=2$ case. In this paper we investigate
the fate of the corresponding fixed points as we vary the parameters $m$ and
$n$. We find that one family of kinks approaches a perturbative limit as $m$
increases, and using large spin perturbation theory we construct a large $m$
expansion that fits well with the numerical data. This new expansion, akin to
the large $N$ expansion of critical $O(N)$ models, is compatible with the fixed
point found in the $\varepsilon$ expansion. For the other family of kinks, we
find that it persists only for $n=2$, where for large $m$ it approaches a
nonperturbative limit with $\Delta_\phi\approx 0.75$. We investigate the
spectrum in the case $MN_{100,2}$ and find consistency with expectations from
the lightcone bootstrap.
Noah F. Berthusen, Yuriy Sizyuk, Mathias S. Scheurer, Peter P. Orth
SciPost Phys. 11, 011 (2021) ·
published 14 July 2021

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We present a deep machine learning algorithm to extract crystal field (CF)
Stevens parameters from thermodynamic data of rareearth magnetic materials.
The algorithm employs a twodimensional convolutional neural network (CNN) that
is trained on magnetization, magnetic susceptibility and specific heat data
that is calculated theoretically within the singleion approximation and
further processed using a standard wavelet transformation. We apply the method
to crystal fields of cubic, hexagonal and tetragonal symmetry and for both
integer and halfinteger total angular momentum values $J$ of the ground state
multiplet. We evaluate its performance on both theoretically generated
synthetic and previously published experimental data on CeAgSb$_2$, PrAgSb$_2$
and PrMg$_2$Cu$_9$, and find that it can reliably and accurately extract the CF
parameters for all site symmetries and values of $J$ considered. This
demonstrates that CNNs provide an unbiased approach to extracting CF parameters
that avoids tedious multiparameter fitting procedures.
SciPost Phys. 11, 009 (2021) ·
published 13 July 2021

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In chiral magnets a magnetic helix forms where the magnetization winds around a propagation vector $\boldsymbol{q}$.
We show theoretically that a magnetic field $\boldsymbol{B}_\perp(t) \perp \boldsymbol{q}$, which is spatially homogeneous but oscillating in time, induces a net rotation of the texture around $\boldsymbol{q}$. This rotation is reminiscent of the motion of an Archimedean screw and is equivalent
to a translation with velocity $v_{screw}$ parallel to $\boldsymbol{q}$. Due to the coupling to a Goldstone mode, this nonlinear effect arises for arbitrarily
weak $\boldsymbol{B}_\perp(t) $ with $v_{screw} \propto {\boldsymbol{B}_\perp}^2$ as long as pinning by disorder is absent. The effect is resonantly enhanced when internal modes of the helix are excited and the sign of $v_{screw}$ can be controlled either by changing the frequency or the polarization of $\boldsymbol{B}_\perp(t)$.
The Archimedean screw can be used to transport spin and charge and thus the screwing motion is predicted to induce a voltage parallel to $\boldsymbol{q}$.
Using a combination of numerics and Floquet spin wave theory, we show that the helix becomes unstable upon increasing $\boldsymbol{B}_\perp$ forming a `time quasicrystal' which oscillates in space and time for moderately strong drive.
SciPost Phys. 11, 003 (2021) ·
published 9 July 2021

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Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of nonHermitian noninteracting fermionic systems. We limit our attention to nonHermitian systems with a complete set of biorthonormal eigenvectors and an entirely real energy spectrum.
The original system has a reduced density matrix $\rho_\mathrm{o}$ and the real space is partitioned via a projecting operator $\mathcal{R}_{\mathrm o}$. After dualization, we obtain a
new reduced density matrix $\rho_{\mathrm{d}}$ and a new real space projector $\mathcal{R}_{\mathrm d}$. Remarkably, entanglement spectrum and entanglement entropy keep invariant. Inspired by the duality, we
defined two types of nonHermitian models, upon $\mathcal R_{\mathrm{o}}$ is given.
In typeI exemplified by the ``nonreciprocal model'', there exists
at least one duality such that $\rho_{\mathrm{d}}$ is Hermitian. In other
words, entanglement information of typeI nonHermitian models with a given $\mathcal{R}_{\mathrm{o}}$ is entirely controlled by Hermitian models
with $\mathcal{R}_{\mathrm{d}}$. As a result, we are
allowed to apply known results of Hermitian systems to efficiently obtain
entanglement properties of typeI models. On the other hand,
the duals of typeII models, exemplified by ``nonHermitian
SuSchriefferHeeger model'', are always nonHermitian. For the practical purpose, the
duality provides a potentially \textit{efficient} computation route to entanglement of
nonHermitian systems. Via connecting different models, the duality also sheds lights on either trivial or nontrivial role of
nonHermiticity played in quantum entanglement, paving the way to potentially systematic
classification and characterization of nonHermitian systems from the
entanglement perspective.