Motivated by recent discoveries of superconductivity in lightly doped multilayer graphene systems, we present a low-energy model to study superconductivity in two-dimensional materials whose Fermi surface consists of two valleys at $\pm \mathit{K}$ points. We assume a triplet odd-valley superconducting order with a pair potential that is isotropic in each valley but has a different sign in the two different valleys. Our theory predicts the emergence of an almost flat band of edge states centered at zero energy for certain edge orientations. As a result, a prominent experimental signature of this type of superconductivity is the presence of a large zero-energy peak in the local density of states near specific edges. The results of the effective low-energy theory are confirmed by numerically analyzing a specific microscopic tight-binding realization of odd-valley superconductivity: $f$-wave superconductivity on a honeycomb lattice in a ribbon geometry. Our work provides a test for odd-valley superconductivity through edge spectroscopy.

The hope that copper-doped lead apatite ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ is a room-temperature superconductor has largely been dashed by global research efforts. Nevertheless, the material has interesting magnetic properties, and research groups around the world have prepared high-quality samples. We use a fluctuation exchange (FLEX) approximation approach to study the magnetic tendencies in ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$. We find ferromagnetic (FM) fluctuations very close to the filling of the stoichiometric compound which can be understood from Fermi surface nesting at the $M$ point. This is like the one-band triangular lattice Hamiltonian at $\frac{3}{4}$ filling. Interestingly, the special $k_z$ dependence of the ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ band structure makes it very sensitive to doping. Only slight charge doping switches between antiferromagnetic and ferromagnetic fluctuations. If the material could become superconducting, it might be easily switchable between singlet and triplet superconductivity.

We discuss the link between the quasielectron wave functions proposed by Laughlin and by Jain and show both analytically and numerically that Laughlin's quasielectron is a nonlocal composite-fermion state. Composite-fermion states are typically discussed in terms of the composite-fermion Landau levels (also known as lambda levels). In standard composite-fermion quasielectron wave functions the excited lambda levels have subextensive occupation numbers. However, once the Laughlin's quasielectron is reformulated as a composite fermion, an overall logarithmic occupation of the first lambda level is made apparent, which includes orbitals that are localized at the boundary of the droplet. Even though the wave function proposed by Laughlin features a localized quasielectron with well-defined fractional charge, it exhibits some nontrivial boundary properties which motivate our interpretation of Laughlin's quasielectron as a nonlocal object. This has an important physical consequence: Laughlin's quasielectron fractionalizes an incorrect spin, deeply related to the anyonic braiding statistics. We conclude that Laughlin's quasielectron is not a good candidate for a quasielectron wave function.

We show that in the continuum limit, the average spectrum method (ASM) is equivalent to maximizing Rényi entropies of order $\eta$, of which Shannon entropy is the special case $\eta =1$. The order of Rényi entropy is determined by the way the spectra are sampled. Our derivation also suggests a modification of Rényi entropy, giving it a nontrivial $\eta \to 0$ limit. We show that the sharper peaks generally obtained in ASM are associated with entropies of order $\eta <1$. Our paper provides a generalization of the maximum entropy method that enables extracting more structure than the traditional method.

We present an inelastic neutron scattering study of the crystal electric field (CEF) levels in the intermetallic ferrimagnets ${\mathrm{RECo}}_5$ ($\mathrm{RE}=\mathrm{Nd}$ and Y). In ${\mathrm{NdCo}}_5$, measurements at $5\mathrm{K}$ reveal two levels at approximately 28.9 and 52.9 meV. Crystal-field calculations including the exchange field $B_{\text{exc}}$ from the Co sites account for both of these, as well as the spectrum at temperatures above the spin-reorientation transition at $\sim 280$ K. In particular, it is found that both a large hexagonal crystal field parameter $A_6^6\langle r^6\rangle$ and $B_{\text{exc}}$ are required to reproduce the data, with the latter having a much larger value than that deduced from previous computational and experimental studies. Our study sheds light on the delicate interplay of terms in the rare-earth Hamiltonian of ${\mathrm{RECo}}_5$ systems, and is therefore expected to stimulate further experimental and computational work on the broader family of rare-earth permanent magnets.

The distortion of corner-sharing octahedra in isovalent perovskite transition-metal oxide interfaces have proven to be an excellent way to tailor the electronic and magnetic properties of their heterostructures. Combining depth-dependent magnetic characterization using polarized neutron reflectivity (PNR) and theoretical calculations (density functional theory), we report interface-driven magnetic exchange interactions due to modification in the octahedral rotations at the interfaces of the isovalent ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}{\mathrm{MnO}}_3/{\mathrm{La}}_{0.67}{\mathrm{Sr}}_{0.33}{\mathrm{MnO}}_3$ heterostructures. PNR results determined a length scale of $\sim 8$ unit cells at the interface, which demonstrated a modification in magnetic properties. The results also predicted a low-temperature exchange bias for these ferromagnetic heterostructures with a maximum exchange bias for the heterostructure, which showed an enhanced antiferromagnetic coupling at the interfaces.

The ${\mathrm{Ce}}^{3+}$ pseudospin-$1/2$ degrees of freedom in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ possess both dipolar and octupolar character which enables the possibility of novel quantum spin liquid ground states in this material. Here we report muon spin relaxation and rotation ($\mu \mathrm{SR}$) measurements on single-crystal samples of ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ in zero magnetic field and in magnetic fields directed along the $[1,\overline{1},0]$ and $[1,1,1]$ crystallographic directions, and for magnetic fields directed both longitudinal and transverse to the direction of muon polarization. Our zero-field results show no signs of magnetic ordering or spin freezing, consistent with earlier zero-field $\mu \mathrm{SR}$ measurements on a powder sample of ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$, and also with the expectations for a quantum spin ice. However, we measure a more gentle relaxation rate for ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ in zero field at low temperatures than was previously reported. This difference in relaxation rate is likely due to the low oxidation and, correspondingly, the high stoichiometry of our single-crystal samples. Longitudinal field measurements confirm that the magnetic dipole moments in ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$ remain dynamic at $T=0.1$ K on the microsecond timescale. For both $[1,\overline{1},0]$ and $[1,1,1]$ magnetic fields, our $\mu \mathrm{SR}$ Knight shift measurements show a field-induced leveling off of the magnetic susceptibility at low temperature which is qualitatively consistent with corresponding calculations using the numerical-linked-cluster method in combination with recent estimates for the nearest-neighbor exchange parameters of ${\mathrm{Ce}}_2{\mathrm{Zr}}_2{\mathrm{O}}_7$.

Thermal equilibrium properties of nanoscale systems deviate from standard macroscopic predictions due to non-negligible coupling to the environment. For anisotropic three-dimensional materials, we derive the mean force corrections to the equilibrium state of a classical spin vector. Specifically, we consider cubic, orthorhombic, and monoclinic symmetries, and compare their spin expectation values as a function of temperature. The results are valid at arbitrary coupling strength. We underpin the correctness of the mean force state by evidencing its match with the steady state of the simulated non-Markovian spin dynamics. The results show an explicit dependence on the symmetry of the confining material. In addition, some coupling symmetries show a spin-alignment transition at zero temperature. Finally, we quantify the work extraction potential of the mean force-generated inhomogeneities in the energy shells. Such inhomogeneities constitute a classical equivalent to quantum coherences.

High-quality rare-earth iron garnet (ReIG) ${\mathrm{Tb}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ (TbIG) thin films are epitaxially grown on a series of (111)-oriented garnet substrates with various lattice constants. The coherent growth induces a substrate-dependent in-plane tensile or compressive strain in the TbIG film. Measurements of the anomalous Hall-like effect in TbIG/Pt heterostructures show that the compensation temperature of TbIG films monotonically changes with the film strain. The strain results in a variation of the distances between magnetic atoms in the TbIG crystal and therefore the corresponding exchange interactions. The latter is explicitly calculated as a function of the lattice strain based on density-functional theory, reproducing the observed experimental results. This work provides a versatile way to optimize ReIG-based spin-orbit torque devices.

${\mathrm{YbRh}}_3{\mathrm{Si}}_7$ is a heavy fermion compound that stands out among Yb-based heavy fermions, with its relatively high magnetic ordering temperature and large Yb-Yb distance. To investigate the origin of the magnetic properties in this compound, we synthesized Co doped ${\mathrm{YbRh}}_3{\mathrm{Si}}_7$, achieving a record-high ferromagnetic ordering temperature $T_{\mathrm{C}}=15.6\mathrm{K}$, only limited by the Co solubility of 20%. Furthermore, we find a crossover from antiferromagnetic to ferromagnetic order with Co doping. The specific heat and magnetotransport measurements show heavy fermion behavior and the persistence of Kondo latticelike behavior in the $\mathrm{Yb}{\left({\mathrm{Rh}}_{1-x}{\mathrm{Co}}_x\right)}_3{\mathrm{Si}}_7$ series.

Corundum oxide ${\mathrm{Ti}}_2{\mathrm{O}}_3$ shows the metal-insulator transition around 400–600 K accompanying the nearest ${\mathrm{Ti}}^{3+}\text{−}{\mathrm{Ti}}^{3+}$ bond ($a_{1g}{a}_{1g}$ singlet state) formation along the $c$ axis. In order to clarify the hole-doping effect for the $a_{1g}{a}_{1g}$ singlet bond in ${\mathrm{Ti}}_2{\mathrm{O}}_3$, we investigated Ti $3d$ orbital anisotropy between corundum-type ${\mathrm{Ti}}_2{\mathrm{O}}_3$ and ilmenite-type ${\mathrm{MgTiO}}_3$ using linear dichroism of soft x-ray absorption spectroscopy of the Ti $L_{2,3}$ edge. From the linear dichroic spectral weight in ${\mathrm{Mg}}_y{\mathrm{Ti}}_{2-y}{\mathrm{O}}_3$, we confirmed that the $a_{1g}{a}_{1g}$ state is dominant not only in $y=0.01$ (almost ${\mathrm{Ti}}_2{\mathrm{O}}_3$), but also in $y=0.29$, indicating that the Ti-Ti bond survives against a certain level of hole doping. In $y=0.63$ corresponding to 46% hole doping per Ti, the $3d$ orbital symmetry changes from $a_{1g}$ to $e_g^{\pi }$.

Hilbert space fragmentation is an intriguing paradigm of ergodicity breaking in interacting quantum many-body systems with applications to quantum information technology, but it is usually adversely compromised in the presence of perturbations. In this work, we demonstrate the protection of constrained dynamics arising due to a combination of mirror symmetry and Hilbert space fragmentation by employing the concept of quantum Zeno dynamics. We focus on an Ising spin ladder with carefully chosen quantum fluctuations, which in the ideal case guarantee a perfect disentanglement under Hamiltonian dynamics for a large class of initial conditions. This is known to be a consequence of the interplay of Hilbert space fragmentation with a mirror symmetry, and we show numerically the effect of breaking the latter. To evince the power of this perfect disentanglement, we study the effect of generic perturbations around the fine-tuned model and show that we can protect against the undesirable growth of entanglement entropy by using a local Ising interaction on the rungs of the ladder. This allows us to suppress the entanglement entropy to an arbitrarily small value for an arbitrarily long time by controlling the strength of the rung interaction. Our work demonstrates the experimentally feasible viability of quantum Zeno dynamics in the protection of quantum information against thermalization.

We present a resonant inelastic x-ray scattering (RIXS) study across the $\mathrm{temperature}(T$) driven $\gamma \text{−}\alpha$ transition in ${\mathrm{Ce}}_{0.93}{\mathrm{Sc}}_{0.07}$. RIXS measurements across the Ce ${\mathrm{M}}_5$ edge unambiguously identify the $f^1\to f^0$ and $f^1\to f^2$ charge excitations, which provide a quantification of the Ce on-site Coulomb repulsion energy, $U_{ff}$. Calculation with a simplified single-impurity Anderson model combined with full multiplet theory reproduces the charge excitations and establishes that the very different Kondo temperatures of the $\gamma$ to $\alpha$ phase are reflected in RIXS spectra. A systematic $T$-dependent hysteresis is observed for the $f^0$ final state spectral intensity upon cycling across the $\gamma \text{−}\alpha$ transition. In addition, a fluorescencelike structure also follows the same hysteretic behavior and shows it is directly connected to the weight of the $f^0$ configuration in the ground state. The results indicate that the Ce M-edge RIXS is a reliable quantitative probe of the electronic structure of strongly correlated Ce-based Kondo systems and is sensitive to the emergent Kondo energy scale.

Numerical treatment of two-dimensional strongly-correlated systems is both extremely challenging and of fundamental importance. Infinite projected entangled-pair states (PEPS), a class of tensor networks, have demonstrated cutting-edge performance for ground-state calculations, working directly in the thermodynamic limit. Furthermore, in recent years the application of PEPS has been extended to also low-lying excited states, using an ansatz that targets quasiparticle states above the ground state with high accuracy. A major technical challenge for those simulations is the accurate evaluation of summations of two- and three-point correlation functions with reasonable computational cost. In this paper, we show how a reformulation of $n$-point functions in the context of PEPS leads to extra contributions to the results that prove to play an important role. Benchmarks for the frustrated $J_1-J_2$ Heisenberg model illustrate the improved precision, efficiency, and stability of the simulations compared to previous approaches. Leveraging automatic differentiation to generate the most tedious and error-prone parts of the computation, the straightforward implementation presented here is a step towards broader adoption of the PEPS excitation ansatz in future applications.

Lately there are many SLAC fermion investigations on the $(2+1)\mathrm{D}$ Gross-Neveu criticality of a single Dirac cone. While the SLAC fermion construction indeed gives rise to the linear energy-momentum relation for all lattice momenta at the noninteracting limit, the long-range hopping and its consequent violation of locality on the Gross-Neveu quantum critical point (GN-QCP)—which a priori requires short-range interaction—has not been verified. Here we show, by means of large-scale quantum Monte Carlo simulations, that the interaction-driven antiferromagnetic insulator in this case is fundamentally different from that on a purely local $\pi$-flux Hubbard model on the square lattice. In particular, the antiferromagnetic long-range order has a finite temperature continuous phase transition, which appears to violate the Mermin-Wagner theorem, and smoothly connects to the previously determined GN-QCP. The magnetic excitations inside the antiferromagnetic insulator are gapped without Goldstone mode, even though the state spontaneously breaks continuous $SU\left(2\right)$ symmetry. These unusual results point out the fundamental difference between the QCP in SLAC fermion and that of GN-QCP with short-range interaction.

In the $0+1$ -dimensional imaginary-time path integral formulation of quantum impurity problems, the retarded action encodes the hybridization of the impurity with the bath. In this article, we explore the computational power of representing the retarded action as matrix product state (RAMPS). We focus on the challenging Kondo regime of the single-impurity Anderson model, where nonperturbative strong-correlation effects arise at very low energy scales. We demonstrate that the RAMPS approach reliably reaches the Kondo regime for a range of interaction strengths $U$, with a numerical error scaling as a weak power law with inverse temperature. We investigate the convergence behavior of the method with respect to bond dimension and time discretization by analyzing the error of local observables in the full interacting problem and find polynomial scaling in both parameters. Our results suggest that the RAMPS approach offers an alternative avenue for exploring quantum impurity problems, thereby setting the stage for future advancements in the method's capability to address more complex quantum impurity scenarios. Overall, our study contributes to the development of efficient and accurate non-wave-function-based tensor-network methods for quantum impurity problems.

We study the frustrated and dimerized ferromagnetic-antiferromagnetic $J_1\text{−}{J}_1^{\prime }\text{−}{J}_2$ chain using the density-matrix renormalization group method. Based on numerical calculations of the second derivative of energy, spin gap, spin-spin correlations, string order parameter (SOP), and entanglement spectrum (ES), we obtain the ground-state phase diagram for a wide range of $J_1^{\prime }/J_1$ and $J_2/\left|J_1\right|$ values. This phase diagram reveals a ferromagnetic phase and two distinct valence bond solid (VBS) phases. The first VBS phase, referred to as ${\mathcal{D}}_3$-VBS, is typified by the formation of valence bonds between third-neighbor spin-1/2's, persisting as a continuation from the $J_1^{\prime }/J_1=1$ limit. Alternatively, the second VBS phase, referred to as mixed-VBS, exhibits a coexistence of both second- and third-neighbor valence bonds, interpreted as a continuation from the $J_1^{\prime }/J_1=0$ case. Remarkably, both VBS states are identified as being of Haldane type, marked by a finite SOP and twofold ES degeneracy. Unexpectedly, our analysis uncovers a significant enhancement of the valence bond stability at the boundary of the two VBS phases. This study provides an empirical demonstration of a nontrivial quantum phase transition between different topological VBS states in spin-1/2 chains. Moreover, we find that the ground state of the relevant quasi-one-dimensional material ${\mathrm{LiCuSbO}}_4$ is classified as the ${\mathcal{D}}_3$-VBS state. Collectively, these results mark a substantial stride forward in our comprehension of quantum phase transitions and topological states.

We propose that a multigraphene of ABC-type stacking yields virtual bound states lying within the Coulomb insulating gap of an Anderson-like adatom. Wondrously, a virtual state constitutes the counterpart of the atomic collapse phenomenon proposed in relativistic atomic physics, while the second emerges as its particle-hole symmetric, analogous to a positron state. Thus, we introduce the effect as the adatomic collapse, which occurs due to a flat band with a dispersionless state and a divergent density of states $\sim |\varepsilon -{\varepsilon }_F{|}^{2/J-1}$ near the Fermi energy ${\varepsilon }_F$ for $J\ge 3,$ where $J\pi$ is the Berry phase. We conclude this scenario based on the Kramers-Kronig transformation of the quasiparticle broadening, from where we observe that the aforementioned van Hove singularity induces virtual bound states. Counterintuitively, near the singularity, we find these states above and below the Fermi energy correlated to the existence of the bottom and top edges of the Coulomb insulating region, respectively. As such a behavior rises without a twist, the system is known as moiréless and the phenomenon emerges also assisted by the adatom Coulomb correlations. Similarly to Science 340, 734 (2013) we find the effective critical atomic number ${\mathcal{Z}}_c\sim 0.96$ in contrast to an ultraheavy nucleus. Thus, we point out that multigraphene is a proper playground for testing a predicted phenomenon of the relativistic atomic physics in the domain of the condensed matter physics.

We study the linear optical response and second-harmonic generation from a nanoparticle-on-mirror (NPoM) plasmonic metasurface composed of a nanoparticle array on top of a metal surface. By using transformation optics, the NPoM system is transformed into a simple geometry for the sake of an analytical solution, relaxing the analytical dilemma faced by the NPoM structure. In linear and nonlinear nanophotonics, our analytical method provides a unique understanding of the underlying physical process and endows an efficient scenario in the optical design for the widely used NPoM system.