Benoit Estienne, Blagoje Oblak, Jean-Marie Stéphan
SciPost Phys. 11, 016 (2021) ·
published 20 July 2021
|
· pdf
The gapless modes on the edge of four-dimensional (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 three-sphere. 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 quasi-periodic, 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
|
· pdf
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 non-trivial 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 non-perturbative 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
|
· pdf
We present a deep machine learning algorithm to extract crystal field (CF) Stevens parameters from thermodynamic data of rare-earth magnetic materials. The algorithm employs a two-dimensional convolutional neural network (CNN) that is trained on magnetization, magnetic susceptibility and specific heat data that is calculated theoretically within the single-ion 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 half-integer 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 multi-parameter fitting procedures.
SciPost Phys. 11, 009 (2021) ·
published 13 July 2021
|
· pdf
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 non-linear 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
|
· pdf
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 non-Hermitian non-interacting fermionic systems. We limit our attention to non-Hermitian 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 non-Hermitian models, upon $\mathcal R_{\mathrm{o}}$ is given. In type-I exemplified by the ``non-reciprocal model'', there exists at least one duality such that $\rho_{\mathrm{d}}$ is Hermitian. In other words, entanglement information of type-I non-Hermitian 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 type-I models. On the other hand, the duals of type-II models, exemplified by ``non-Hermitian Su-Schrieffer-Heeger model'', are always non-Hermitian. For the practical purpose, the duality provides a potentially \textit{efficient} computation route to entanglement of non-Hermitian systems. Via connecting different models, the duality also sheds lights on either trivial or nontrivial role of non-Hermiticity played in quantum entanglement, paving the way to potentially systematic classification and characterization of non-Hermitian systems from the entanglement perspective.