Discrete-time quantum walks, quantum generalizations of classical random walks, provide a framework for quantum information processing, quantum algorithms, and quantum simulation of condensed-matter systems. The key property of quantum walks, which lies at the heart of their quantum information applications, is the possibility for a parametric quantum speedup in propagation compared to classical random walks. In this work we study propagation of quantum walks on percolation-generated two-dimensional random lattices. In large-scale simulations of topological and trivial split-step walks, we identify distinct prediffusive and diffusive behaviors at different timescales. Importantly, we show that even arbitrarily weak concentrations of randomly removed lattice sites give rise to a complete breakdown of the superdiffusive quantum speedup, reducing the motion to ordinary diffusion. By increasing the randomness, quantum walks eventually stop spreading due to Anderson localization. Near the localization threshold, we find that the quantum walks become subdiffusive. The fragility of quantum speedup implies dramatic limitations for quantum information applications of quantum walks on random geometries and graphs.

Recently, unconventional materials (or obstructed atomic insulators) have attracted much attention owing to the unconventional feature of mismatch between Wannier centers and atomic positions. In this paper, we demonstrate that the trigonal selenium and tellurium host an unconventional nature in both electronic and phonon spectra. In electronic band structures, the band representation (BR) decomposition for occupied bands has to contain the essential BR of $A@3b$, and the real-space invariant is ${\delta }_1@3b=-1$. The $\pi$ Zak phase suggests that the one-dimensional Se/Te chain is a chiral Su-Schrieffer-Heeger chain. The effective magnetism can be induced by $p$ states at ends. More importantly, a large shift current is obtained in the Se quantum well. In addition, in phonon spectra, three sets of phonon bands are well separated and assigned to $B@3b, B@3a$, and $A@3b$ BRs, respectively. Thus, the obstructed phonon states are predicted on the (0001) surface. As the prototypes of unconventional materials in both electronic and phonon spectra, our findings could create much interest in the study of obstructed surface electronic and phonon states in these novel materials.

The in-plane (thermal) Hall effect is an unconventional transverse response when the applied magnetic field is in the (heat) current plane. In contrast to the normal Hall effect, the in-plane Hall effect requires the absence of certain crystal symmetries, and possibly manifests a nontrivial topology of quantum materials. An accurate estimation of the intrinsic in-plane (thermal) Hall conductivity is crucial to identify the underlying mechanisms as in the case of the Kitaev spin-liquid candidate $\alpha \text{−}{\mathrm{RuCl}}_3$. Here, we give the symmetry conditions for the in-plane Hall effect and discuss the implications that may impede the experimental evaluation of the in-plane Hall conductivity within the single-device measurement. First, the lack of symmetry in crystals can create merohedral twin domains that cancel the total Hall signal. Second, even in a twin-free crystal, the intrinsic response is potentially contaminated by the out-of-plane conduction in three-dimensional systems, which is systematically unavoidable in the in-plane Hall systems. Third, even in a quasi-two-dimensional system, the conversion of (thermal) resistivity $\widehat{\rho }$ ($\widehat{\lambda }$) to (thermal) conductivity $\widehat{\sigma }$ ($\widehat{\kappa }$) requires protocols beyond the widely-used simplified formula ${\sigma }_{xy}={\rho }_{yx}/({\rho }_{xx}^2+{\rho }_{yx}^2)$ (${\kappa }_{xy}={\lambda }_{yx}/({\lambda }_{xx}^2+{\lambda }_{yx}^2)$) due to the lack of in-plane-rotational symmetry. In principle, two independent sample devices are necessary to accurately estimate the ${\sigma }_{xy}$ (${\kappa }_{xy}$). As a case study, we discuss the half-integer quantization of the in-plane thermal Hall effect in the spin-disordered state of $\alpha \text{−}{\mathrm{RuCl}}_3$. For an accurate measurement of the thermal Hall effect, it is necessary to avoid crystals with the merohedral twins contributing oppositely to ${\kappa }_{xy}$, while the out-of-plane transport may have a negligible effect. To deal with the field-induced rotational-symmetry breaking, we propose two symmetry-based protocols, improved single-device and two-device methods. The considerations in the paper are generally applicable to a broad class of materials and provide a useful starting point for understanding the unconventional aspects of the in-plane Hall effect.

The type-II Weyl semimetal (WSM) $\beta \text{-W}{\mathrm{P}}_2$ was recently demonstrated as a supreme quantum material with various interestingtransport properties. Toward deciphering these peculiar transport phenomena for future topological device applications, it is highly necessary to understand the dynamical process of phonon scatterings under nonequilibrium conditions. By performing temperature-dependent coherent phonon spectroscopy in $\beta \text{-W}{\mathrm{P}}_2$, we provide here direct experimental evidence that phonons decaying into electron-hole pairs overwhelm the anharmonic phonon-phonon scattering process. Remarkably, the dominating phonon-electron coupling in $\beta \text{-W}{\mathrm{P}}_2$ is further supported by observations of the transient Fano resonance. First-principles calculations suggest that the anomalous phonon decaying results from the acoustic bunching and the limited phonon density of states in $\beta \text{-W}{\mathrm{P}}_2$. Our real-time observations provide dynamical insight into quasiparticle scatterings that are of vital importance for fundamental transport properties in $\beta \text{-W}{\mathrm{P}}_2$.

Numerical simulations of quantum spin models are crucial for a profound understanding of many-body phenomena in a variety of research areas in physics. An outstanding problem is the availability of methods to tackle systems that violate area laws of entanglement entropy. Such scenarios cover a wide range of compelling physical situations including disordered quantum spin systems among others. In this paper, we employ a numerical technique referred to as multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) to evaluate the ground state of several disordered spin models. ML-MCTDH has previously been used to study problems of high-dimensional quantum dynamics in molecular and ultracold physics but is here applied to study spin systems. We exploit the inherent flexibility of the method to present results in one and two spatial dimensions and treat challenging setups that incorporate long-range interactions as well as disorder. Our results suggest that the hierarchical multilayering inherent to ML-MCTDH allows to tackle a wide range of quantum many-body problems such as spin dynamics of varying dimensionality.

We unveil a duality that extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond ($2+1$)D. Thus, a quantum system in arbitrary dimensions can experience a modification of its statistical properties if coupled to a certain gauge field. For instance, a bosonic quantum fluid can feature composite fermionic (or anyonic) excitations when coupled to a statistical gauge field. We compute the explicit form of the aforementioned synthetic gauge fields in $\text{D}\le 3+1$. We introduce a bosonic liquid and its composite dual in ($1+1$)D as proof of principle. We recover well-known results, resolve old controversies, and suggest a microscopic mechanism for the emergence of such a gauge field. We also outline potential directions for experimental realizations in ultracold atom platforms.

We report the development of a combined machine learning and high-throughput density functional theory (DFT) framework to accelerate the search for new ferroelectric materials. The framework can predict potential ferroelectric compounds using only elemental composition as input. A series of machine-learning algorithms initially predict the possible stable and insulating stoichiometries with polar crystal structures, necessary for ferroelectricity, within a given chemical composition space. A classification model then predicts the point groups of these stoichiometries. A subsequent series of high-throughput DFT calculations finds the lowest-energy crystal structure within the point group. As a final step, nonpolar parent structures are identified using group theory considerations, and the values of the spontaneous polarization are calculated using DFT. By predicting the crystal structures and the polarization values, this method provides a powerful tool to explore new ferroelectric materials beyond those in existing databases.

Two-dimensional (2D) Dirac materials are electronically and structurally very sensitive to proximity effects. We demonstrate, however, the opposite effect: that the deposition of a monolayer 2D material could exercise a substantial influence on the substrate electronic structure. Here we investigate TiC(111) and show that a graphene overlayer produces a proximity effect, changing the Fermi surface topology of the TiC from six electron pockets to one hole pocket on the depth of several atomic layers inside the substrate. In addition, the graphene electronic structure undergoes an extreme modification as well. While the Dirac cone remains gapless, it experiences an energy shift of 1.0 eV beyond what was recently achieved for the Lifshitz transition of overdoped graphene. Due to this shift, the antibonding ${\pi }^{*}$ band at the $\overline{\mathrm{M}}$ point becomes occupied and observable by photoemission.

Electrostatic charges placed near the interface between ordinary and topological insulators induce magnetic fields through the so-called topological magnetoelectric effect. Here we present a numerical implementation of the associated Maxwell equations. The resulting model is simple, fast, and quantitatively as accurate as the image charge method but with the advantage of providing easy access to elaborate geometries when pursuing specific effects. The model is used to study how magnetoelectric fields are influenced by the dimensions and the shape of the most common semiconductor nanostructures: quantum wells, quantum wires, quantum dots, and quantum rings. Pointlike charges give rise to magnetic fields of the order of mT, whose sign and spatial orientation are governed by the geometry of the nanostructure and the location of the charge. The results are rationalized in terms of the Hall currents induced on the surface, which constitute a simple yet valid framework for the deterministic design of magnetoelectric fields.

In amorphous solids, there exists a universal phenomenon of vibrational anomaly, i.e., an excess of vibrational modes over the Debye level in the low-terahertz-frequency regime, which is termed a boson peak. Although the origin of the boson peak has been studied extensively for decades, quantitative prediction of its intensity remains elusive. In this paper, we try to quantify the intensity of the boson peak via an interpretable machine-learning strategy based on a dataset consisting of >1600 glass samples prepared with cooling rates spanning four orders of magnitude. We have attempted to extract information from a pure static structure and vibrational localization through four different feature inputs, among which the partial pair distribution function (PDF) yields the best predictive performance. It is found that the first several neighbor shells corresponding to a characteristic subnanometer length scale are important for capturing the structural genes of the boson peak in amorphous solids, regardless of the size of the glasses. Moreover, a higher boson peak relates to a more disordered atomic arrangement with lower peaks and shallower basins in the PDF. The obtained knowledge sheds light on rationalization of the boson peak in amorphous solids from pure structural information.

Square-root topology describes models whose topological properties can be revealed upon squaring the Hamiltonian, which produces their respective parent topological insulators. This concept has recently been generalized to $2^n$-root topology, characterizing models where $n$ squaring operations must be applied to the Hamiltonian to arrive at the topological source of the model. In this paper, we analyze the Hofstadter regime of quasi-one-dimensional and two-dimensional $2^n$-root models, the latter of which has the square lattice (SL) (known for the Hofstadter Butterfly) as the source model. We show that upon increasing the root-degree of the model, there appear multiple magnetic flux insensitive flat bands, and we analytically determine corresponding eigenstates. These can be recast as compact localized states (CLSs) occupying a finite region of the lattice. For a finite flux, these CLSs correspond to different harmonics contained within the same Aharonov-Bohm cage. Furthermore, as the root-degree increases, a kaleidoscope of butterflies is seen to appear in the Hofstadter diagram, with each butterfly constituting a topologically equivalent replica of the original one of the SL. As such, the index $n$, which uniquely identifies the root-degree of the model, can be seen as an additional fractal dimension of the $2^n$-root model present in its Hofstadter diagram. We discuss how these dynamics could be realized in experiments with ultracold atoms, and measured by Bragg spectroscopy or through observing dynamics of initially localized atoms in a quantum gas microscope.