Symmetries play a paramount role in many aspects of topological physics. A particularly illuminating example is the Su-Schrieffer-Heeger (SSH) chain, whose reflection and chiral symmetry endow the quantization of the Zak phase and winding number, subsequently guaranteeing the existence of topological edge states. Here, we harness recent graph-theoretical results to construct families of setups whose unit cells feature neither of these symmetries, but instead a so-called latent or hidden reflection symmetry. This causes the isospectral reduction—akin to an effective Hamiltonian—of the resulting lattice to resemble an SSH model. These latent SSH models exhibit features such as multiple topological transitions, edge states, a quantized Zak phase, and, counterintuitively, immunity to orientational disorder. We confirm our findings through electric circuit experiments, where the topological edge states can be directly observed. Serving as a first proof of principle, our paper demonstrates the wealth and generality of a stroboscopic point of view, taking advantage of hidden properties such as symmetries.

Weyl semimetals are predicted to host signature magneto-optical properties sourced by their peculiar Landau-level structure, including the chiral level. Analytical studies are often leaving out the Hall component of the conductivity due to its complicated nature, and even though the chiral anomaly requires Weyl nodes to come in charge-conjugate pairs, toy models hosting only one node are considered almost exclusively; numerical studies including several Weyl nodes are, on the other hand, often limited to high-field quantum limits or dc studies. Here, we present a twofold purpose study, where we (a) analytically derive a closed-form expression also for the Hall conductivity of a generic Weyl semimetal using linear response theory and (b) apply this general framework to evaluate the transverse conductivity components for Weyl systems with two nodes. We study how various model parameters, including the tilt, momentum separation, and energy location of the nodes, as well as the chemical potential, affect the magneto-optical conductivity, and complement these studies by deriving an analytical expression for the dc Hall conductivity, which is also evaluated in various systems. Including a chiral pair of nodes results in two important differences compared to earlier studies: the contribution from the chiral level is equal in size but opposite at the two nodes, making the net contribution disappear, and the energy scales at which intraband transitions occur is smeared out and approaches that of interband transitions, strengthening the hypothesis that intraband transitions mask signature optical features in materials. This general formalism can be applied to a large family of generic Weyl semimetals, and comprise an important piece towards unravelling the source of the mismatch between theoretical predictions and experimental observations in candidate materials.

The fractional quantum Hall (FQH) effect gives rise to abundant topological phases, presenting an ultimate platform for studying the transport of edge states. Generic FQH edge contains multiple edge modes, commonly including the counterpropagating ones. A question of the influence of Anderson localization on transport through such edges arises. Recent experimental advances in engineering novel devices with interfaces of different FQH states enable transport measurements of FQH edges and edge junctions also featuring counterpropagating modes. These developments provide an additional strong motivation for the theoretical study of the effects of localization on generic edge states. We develop a general framework for analyzing transport in various regimes that also naturally includes localization. Using a reduced field theory of the edge after localization, we derive a general formula for the conductance. We apply this framework to analyze various experimentally relevant geometries of FQH edges and edge junctions.

Electronic states play a crucial role in many quantum systems of moiré superlattices, quasicrystals, and fractals. As recently reported for Sierpiński lattices [Yao et al., Phys. Rev. B 107, 115424 (2023)], the critical states are revealed by the energy-level-correlation spectra, which are caused by the interplay between aperiodicity and determined self-similarity characters. In the case of the Sierpiński carpet, our results further demonstrate that there is some degree of spatial overlap between these electronic states. These states could be strongly affected by the “seed lattice” of the generator and slightly modulated by the dilation pattern and the geometrical self-similarity level. These electronic states are made multifractal by scaling the $q\mathrm{th}$-order inverse participation ratio or fractal dimension, which correlates with the subdiffusion behavior. In the gene pattern, an average state-based multifractal dimension of second order would increase as its Hausdorff dimension increases. Our findings could potentially contribute to understanding quantum transports and single-particle quantum dynamics in fractals.

The quantum geometric tensor (QGT) reveals local geometric properties and associated topological information of quantum states. Here a generalization of the QGT to mixed quantum states at finite temperatures based on the Sjöqvist distance is developed. The resulting Sjöqvist QGT is invariant under gauge transformations of individual spectrum levels of the density matrix. A Pythagorean-like relation connects the distances and gauge transformations, which clarifies the role of the parallel-transport condition. The real part of the QGT naturally decomposes into a sum of the Fisher-Rao metric and Fubini-Study metric, allowing a distinction between different contributions to the quantum distance. The imaginary part of the QGT is proportional to a weighted summation of the Berry curvatures, which leads to a geometric phase for mixed states under certain conditions. We present three examples of different dimensions to illustrate the temperature dependence of the QGT and a discussion on possible implications.

In this paper, we investigate the relationship between entanglement and nonstabilizerness (also known as magic) in matrix product states (MPSs). We study the relation between magic and the bond dimension used to approximate the ground state of a many-body system in two different contexts: full state of magic and mutual magic (the nonstabilizer analog of mutual information, thus free of boundary effects) of spin-1 anisotropic Heisenberg chains. Our results indicate that obtaining converged results for nonstabilizerness is typically considerably easier than entanglement. For full state magic at critical points and at sufficiently large volumes, we observe convergence with $1/{\chi }^2$, with $\chi$ being the MPS bond dimension. At small volumes, magic saturation is so quick that, within error bars, we cannot appreciate any finite-$\chi$ correction. Mutual magic also shows a fast convergence with bond dimension, whose specific functional form is however hindered by sampling errors. As a byproduct of our study, we show how Pauli-Markov chains (originally formulated to evaluate magic) resets the state of the art in terms of computing mutual information for MPS. We illustrate this last fact by verifying the logarithmic increase of mutual information between connected partitions at critical points. By comparing mutual information and mutual magic, we observe that, for connected partitions, the latter is typically scaling much slower—if at all—with the partition size, while for disconnected partitions, both are constant in size.

${\mathrm{EuAl}}_4$ is a rare-earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge-density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal x-ray diffraction, inelastic x-ray scattering, and lattice-dynamics calculations to clarify the origin of the CDW in ${\mathrm{EuAl}}_4$. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at $T_{\text{CDW}}=142$ K, freezes out in an atomic displacement mode described by the superspace group $Immm\left(00\gamma \right)s00$. In the context of previous work, our observation is a clear confirmation that the CDW in ${\mathrm{EuAl}}_4$ is driven by electron-phonon coupling. This result is relevant for a wider family of ${\mathrm{BaAl}}_4$ and ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism.

It has been predicted that new physics and technology are enabled for quantum systems that suffer from partial decoherence, in the intermediate range between coherent quantum evolution and incoherent classical physics. We explore the asymmetric transmission through a classical analogue of the Aharonov-Bohm (AB) mesoscopic ring that supports a 3:1 asymmetry in transmission times, augmented with lossy features that act preferentially on the longer-lingering waves. Such a device is realized as a linear microwave graph utilizing a gyrator to create the 3:1 transmission time delay asymmetry, along with both homogeneous and localized losses, to produce an imbalance in wave transmission through the device. We demonstrate asymmetric transmission through the microwave-ring graph as a function of loss in both simulation and experiment, and in both the frequency- and time-domain. The microwave ring-graph results are compared to a numerical simulation representative of a class of recent models proposing dephasing-induced transport asymmetry in few-channel quantum systems, and parallels are noted.

Silicon nitride $\left({\mathrm{Si}}_3{\mathrm{N}}_4\right)$ is commonly used as the charge storage layer of nonvolatile charge trap flash (CTF) memory devices. Previous theoretical investigations have shown a large variety of possible trapping centers in ${\mathrm{Si}}_3{\mathrm{N}}_4$ which might contribute to the memory effect, including vacancies, dangling bonds, and overcoordinated atoms. So far, the high H concentration detected in silicon nitride thin films, resulting in a large number of passivated Si–H and N–H bonds, has not been considered in depth in theoretical studies regarding the charge trapping properties. In this work, we show that this passivation of dangling bonds with H gives rise to the formation of hole and electron (bi)polarons at fully coordinated sites and hole traps at Si–H bonds. We employ density functional theory combined with a hybrid functional to demonstrate that both holes and electrons can localize at intrinsic, fully coordinated sites in the amorphous ${\mathrm{Si}}_3{\mathrm{N}}_4$:H network. We classify precursor configurations of the polaron states by analyzing bond lengths, partial charges, maximally localized Wannier functions, bond orders, and electronic states introduced in the band gap upon charge trapping. All trapping sites are characterized according to their thermodynamic properties, such as charge transition level (CTL) and relaxation energy on a statistical level. The CTLs of the (bi)polarons are in the energetic vicinity of the band edges of a Si substrate, showing that these intrinsic sites can trap charges from Si under applied voltages and contribute to the memory effect.

We propose a quantum sensing protocol that leverages the dynamical response of physical observables to quenches in quantum systems. Specifically, we use the nitrogen-vacancy (NV) color center in diamond to realize both scalar and vector magnetometry via quantum response. Furthermore, we suggest a method for detecting the instantaneous motion of magnetic nanoparticles. To achieve this, we derive the closed exact form of the Berry curvature corresponding to NV centers and design quenching protocols to extract the Berry curvature via dynamical response. By constructing and solving nonlinear equations, the magnetic field and instantaneous motion velocity of the magnetic nanoparticle can be deduced. We investigate the feasibility of our sensing scheme in the presence of decoherence and show through numerical simulations that it is robust to decoherence. Intriguingly, we have observed that a vanishing nuclear spin polarization in diamond benefits our dynamic sensing scheme, which stands in contrast with conventional Ramsey-based schemes. In comparison with Ramsey-based sensing schemes, our proposed scheme can sense an arbitrary time-dependent magnetic field if its time dependence is nearly adiabatic.

Topological flat bands are increasingly recognized as an important paradigm to study the effects of quantum geometry and topology in strongly correlated systems. The recently discovered theory of fragile topology offers an alternative approach toward the understanding and realization of topological phases of matter. In Bosonic systems, though fragile topological phases have been experimentally realized, specific proposals of the experimental platform of topological flat bands have not been reported much. In this work, we introduce a photonic lattice obtained from coupled Kagome and triangular lattices designed based on the topological quantum chemistry theory, which supports topologically nontrivial flat bands. We further discuss the potential experimental realization in a microcavity array, as a platform that can be extended into the interacting regime through the formation of exciton-polaritons via coupling the optical modes to excitons. Notably, we show that the inevitable in-plane polarization splitting in optical microcavities will not hinder the construction of topological quasiflat bands. This work paves the way toward the experimental exploration of nontrivial topology in Bosonic flat bands, offering potential channels for its direct observation.

The atomic structure and electronic properties of the (100) surface of the Au-Si-Ho Tsai-type quasicrystalline approximant has been investigated under ultrahigh vacuum conditions. After annealing the sample between 853 K and 878 K, Au-Si-Ho(100) exhibits a ($2\times 1$) surface reconstruction with a topography described by large terraces separated by a single step height equal to half the unit-cell parameter. The surface appears to terminate at specific bulk planes intercepting the Tsai-type clusters at their center. The electronic density of states is dominated by the $5d$ states of Au below the Fermi level and by the $5d$ states of Ho above the Fermi level with a metalliclike Fermi edge.

We study a classical Ising model on the honeycomb lattice with local two-body interactions and present strong evidence that at low temperature it realizes a higher-rank Coulomb liquid with fracton excitations. We show that the excitations are (type-I) fractons, appearing at the corners of membranes of spin flips. Because of the threefold rotational symmetry of the honeycomb lattice, these membranes can be locally combined such that no excitations are created, giving rise to a set of ground states described as a liquid of membranes. We devise a cluster Monte Carlo algorithm purposefully designed for this problem that moves pairs of defects, and use it to study the finite-temperature behavior of the model. We show evidence for a first order transition from a high-temperature paramagnet to a low-temperature phase whose correlations precisely match those predicted for a higher-rank Coulomb phase.

Recent experiments have revealed the substantial impact of broken rotational symmetry on the superconductivity. In the pursuit of understanding the role played by this symmetry breaking particularly in cuprate and nickelate superconductors on their superconductivity, we investigated two characteristic symmetry breaking mechanisms arising from (1) structurally orthogonal distortions from $C_4$ to $C_2$ symmetry and (2) anisotropic hybridization between $d_{x^2-y^2}$ orbital and an additional metallic band within the framework of the Hubbard model by employing dynamic cluster quantum Monte Carlo calculations. We discovered that the anisotropy is generically detrimental to the $d$-wave pairing so that the experimental findings of much lower superconducting $T_c$ of infinite-layer nickelates compared with the cuprates may be connected to the intrinsic anisotropy. Our exploration sheds light on the fundamental anisotropy factors governing superconductivity in nickelates and cuprates and offer insights contributing to the broader understanding of unconventional superconductors in anisotropic environment.

Ferroelectricity is commonly understood in terms of dynamical charges, which represent the dipole moments generated by atomic displacements or the forces induced by electric fields. In ferroelectrics with a high degree of symmetry, the dynamical charges are typically symmetric tensors, and can be visualized as ellipsoids. In van der Waals (vdW) materials which break centrosymmetry, a new type of ferroelectricity arises which differs greatly from conventional ferroelectrics. The polarization is purely electronic, arising from an interlayer charge transfer, and most of the polarization generated is perpendicular to atomic motion. We show that the unconventional properties of vdW ferroelectrics are manifested in their dynamical charges, which exhibit spatial modulation and intrinsic asymmetry. Dynamical charges in vdW ferroelectrics, and more generally, any strongly anisotropic ferroelectric, can be visualized as deformable, nonideal ellipsoids dependent on the atomic configuration. Furthermore, we show that, due to the mixed electrostatic boundary conditions employed for two-dimensional (2D) materials, nondiagonal dynamical charges in 2D materials are always asymmetric.

We unveil a relevant non-Hermitian symmetry and hence a dual bulk-boundary correspondence (BBC) from a one-dimensional non-Hermitian Rice-Mele model including on-site dissipation, nonreciprocity, and spin-orbit coupling. To expose this dual BBC, we present the closed-form solutions for spin-up and spin-down edge modes and two explicit topological winding numbers, which are linked to each other to a perfect degree. We also demonstrate the topological zero modes and their strong insensitivity to disorder in the presence of spin-orbit coupling. We anticipate that this dual BBC may offer another route for manipulating spin currents and trigger the research for dual topological insulators in a single zigzag lattice.

The bulk photovoltaic (BPV) effect that converts light into electric current is highly sensitive to the system symmetry and its electronic Bloch wave function. To create a sizable net electric current, it is necessary to break the centrosymmetry $\mathcal{P}$ in its host material. While prior studies mainly focus on $\mathcal{P}$-broken nonmagnetic (time reversal $\mathcal{T}$ reserved) and collinear antiferromagnetic $\mathcal{PT}$ systems, here we adopt magnetic group theory to scrutinize how helical spin polarization breaks $\mathcal{P}$ that is otherwise kept in its crystalline geometry. Such a spin helix widely exists in intrinsic multiferroics and magnon excitation in collinear magnets. We demonstrate that magnetic symmetries are determined by spin spiral configurations, helical propagation wave vectors, magnetic chirality, and spin winding angles at the home site, offering effective and versatile manipulation of BPV generation in helimagnets. This is illustrated by tight-binding model calculations. Furthermore, we apply our theory to monolayer $\mathrm{Ni}{\mathrm{I}}_2$, a realistic showcase for helimagnetic material. Our first-principles calculations show that it could host observable direction-dependent BPV current, which could serve as a photoelectric probe to track the subtle magnetic configurations and potential multiferroic nature. This work reveals the fundamental mechanism of the interplay between spin spiral order and the nonlinear optics process.

We report on the magnetoelectric dynamics in the linear magnetoelectric antiferromagnet ${\mathrm{TbPO}}_4$ studied by broadband dielectric spectroscopy. For the phase transition into the magnetoelectric antiferromagnetic phase at $T_N\approx 2.3\mathrm{K}$, a finite magnetic field $H$ induces critical behavior in the quasistatic permittivity ${\varepsilon }^{\prime }\left(T\right)$. Plotting the corresponding anomaly as a function of $T/T_N\left(H\right)$, we observe the scaling behavior $\mathrm{\Delta }{\varepsilon }^{\prime }\propto H^2$, a clear fingerprint of linear magnetoelectric antiferromagnets. Above the phase transition, we find a critical slowing down of the ferroic fluctuations in finite magnetic field. This behavior can be understood via a magnetic field induced relaxational response that resembles the soft-mode behavior in canonical ferroelectrics and multiferroics.