High-performance batteries, heterogeneous catalysts, and next-generation photovoltaics often centrally involve transition metal oxides (TMOs) that undergo charge or spin-state changes. Demand for accurate DFT modeling of TMOs has increased in recent years, driving improved quantification and correction schemes for approximate DFT's characteristic errors, notably those pertaining to self-interaction and static correlation. Of considerable interest, meanwhile, is the use of DFT-accessible quantities to compute parameters of coarse-grained models such as for magnetism. To understand the interference of error corrections and model mappings, we probe the prototypical Mott-Hubbard insulator NiO, calculating its electronic structure in its antiferromagnetic I/II and ferromagnetic states. We examine the pronounced sensitivity of the first-principles calculated Hubbard parameters U and J to choices concerning projector augmented wave (PAW) based population analysis, we reevaluate spin quantification conventions for the Heisenberg model, and we seek to develop best practices for calculating Hubbard parameters specific to energetically metastable magnetic orderings of TMOs. Within this framework, we assess several corrective functionals using in situ calculated U and J parameters, e.g., DFT+U and DFT+U+J. We find that while using a straightforward workflow with minimal empiricism, the NiO Heisenberg parameter RMS error with respect to experiment was reduced to 13%, an advance upon the state-of-the-art. Methodologically, we used a linear-response implementation for calculating the Hubbard U available in the open-source plane-wave DFT code Abinit. We have extended its utility to calculate the intra-atomic exchange coupling J; however, our findings are anticipated to be applicable to any DFT+U implementation.

We explore the transformation of a surface plasmon on dynamic graphene with a periodic modulation of carrier density. We treat the stages of carrier density increases and decreases by using different constitutive relations, which are adequate to the physical mechanisms of carrier injection and removal. The cases of rapid and slow (compared to the plasmon period) changes of carrier density are considered. In both cases our results refute recent predictions that periodic modulation can lead to plasmon amplification.

Position scaling eigenfunctions are generated by transforming compactly supported orthonormal scaling functions and utilized for faster alternatives to maximally localized Wannier functions (MLWFs). The position scaling eigenfunctions are first applied to numerical procedures solving Schrödinger and Maxwell's equations, and the solutions well agree with the preceding results. Subsequently, by projecting the position scaling eigenfunctions onto the space spanned by the Bloch functions, approximated MLWFs are obtained. They show good agreement with the preceding results using MLWFs. In addition, analytical explanations of the agreements and an estimate of the error associated with the approximation are provided.

The anomalous self-energy plays an important role in the analysis of superconducting states. Its spectral weight provides information on the pairing glue of superconductors, but it can change in sign. In many numerical approaches, for example, Monte Carlo methods based on the Nambu formalism, the anomalous self-energy is obtained on the Matsubara axis, and nonpositive spectral weight cannot be directly obtained using the standard maximum entropy analytic continuation method. Here, we introduce an auxiliary self-energy corresponding to a linear combination of the normal and anomalous self-energies. We analytically and numerically prove that this auxiliary function has non-negative spectral weight independent of the pairing symmetry, which allows to compute the sign-changing spectrum of the original self-energy using the maximum entropy approach. As an application, we calculate the momentum-resolved spectral function of ${\mathrm{K}}_3{\mathrm{C}}_{60}$ in the superconducting state.

In two-dimensional electronic systems, direct first-order phase transitions are prohibited as a consequence of the long-range Coulomb interaction, which implies a stiff energetic penalty for macroscopic phase separation. A prominent proposal is that any direct first-order transition is instead replaced by a sequence of “microemulsion” phases, in which the two phases are mixed in patterns of mesoscopic domains. In this Letter, we comment on the range $\mathrm{\Delta }n$ of average electron density that such microemulsion phases may occupy. We point out that, even without knowing the value of a phenomenological parameter associated with surface tension between the two phases, one can place a fairly strong upper bound on the value of $\mathrm{\Delta }n$. We make numerical estimates for $\mathrm{\Delta }n$ in the case of the Fermi liquid to Wigner crystal transition and find $\mathrm{\Delta }n$ to be on the order of ${10}^7$ ${\mathrm{cm}}^{-2}$. This value is much smaller than the width of the phase transition observed in experiments, suggesting that disorder is a more likely explanation for the apparent broadening of the transition.

The entanglement dynamics in a non-Hermitian quantum system is studied numerically and analyzed from the viewpoint of quasiparticle picture. As a concrete model, we consider a one-dimensional tight-binding model with asymmetric hopping (Hatano-Nelson model) under onsite disorder and nearest-neighbor interaction. As opposed to an assertion of previous studies, the entanglement dynamics in this non-Hermitian quantum system is very different from the one in its Hermitian counterpart, especially in the delocalized regime with weak disorder; there the entanglement entropy $S_{\mathrm{ent}}\left(t\right)$ shows a characteristic nonmonotonic time evolution. We have clarified and quantified the nature of this behavior in the quasiparticle picture. In the asymptotic regime of $t\to \infty$, the entanglement entropy $S_{\mathrm{ent}}\left(t\right)$ in this regime saturates to a much suppressed value, which increases only logarithmically with respect to the size of the subsystem.

Rare-earth ($R$) kagome-lattice magnets offer an excellent platform to discover the novel magnetic phase as well as quantum phase transition tuned by nonthermal control parameters, while the experimental realizations remain largely unexplored. Here, we report the discovery of magnetic field ($B$) -induced anisotropic quantum phase transition in a distorted kagome antiferromagnet ${\mathrm{Nd}}_3{\mathrm{BWO}}_9$ with $T_{\mathrm{N}}\sim 0.32\mathrm{K}$. The isothermal magnetizations at 0.05 K exhibit the spin-flop-like metamagnetic crossover behaviors with different fractional magnetization anomalies for $B$ perpendicular ($B\left|\right|c$ axis) and parallel ($B\left|\right|a^{*}$ axis) to the kagome plane, respectively. In combination with the thermodynamic measurements, the field-temperature ($B\text{−}T$) phase diagrams for both field directions are constructed and reveal the existence of several field-induced magnetic states. Along the $c$ axis, a proximate quantum bicritical point is observed near the metamagnetic crossover, which separates the low-field antiferromagnetic (AFM) phase and the intermediate AFM phase; while, for $B\left|\right|a^{*}$, another intermediate magnetic phase (IAFM2) appears between the low-field AFM phase and the intermediate AFM (IAFM1) phase, giving rise to a tetracritical point. These results support the anisotropic field-induced metamagnetic quantum criticalities in ${\mathrm{Nd}}_3{\mathrm{BWO}}_9$, making it a rare kagome antiferromagnet to investigate the quantum multicriticality driven by spin frustration.

${\mathrm{Fe}}_{1.057\left(7\right)}\mathrm{Te}$ undergoes a first-order structural transition from a high temperature tetragonal phase to a low temperature monoclinic phase at $T_S\sim 70\mathrm{K}$, breaking the fourfold $C_4$ high temperature lattice symmetry. At the same temperature, time reversal symmetry is broken with magnetic iron ions ordering in a commensurate (with the nuclear lattice) bicollinear arrangement. The low-energy magnetic dynamics proximate to this magnetostructural transition are, however, incommensurate and have been reported on previously [Stock et al., Phys. Rev. B 95, 144407 (2017)]. In this current work, we investigate the soft acoustic lattice dynamics near this combined magnetostructural transition. We apply spherically neutron polarimetry to study the static magnetism near this transition, characterized with x-ray powder diffraction, and find no evidence of static incommensurate magnetic correlations near the onset of monoclinic and bicollinear antiferromagnetic order. This fixes the position of our single crystal sample in the ${\mathrm{Fe}}_{1+x}\mathrm{Te}$ phase diagram in the magnetic bicollinear region and illustrates that our sample statically undergoes a transition from a paramagnetic phase to a low-temperature bicollinear phase. We then apply neutron spectroscopy to study the acoustic phonons, related to elastic deformations of the lattice. We find a temperature dependent soft acoustic branch for phonons propagating along [010] and polarized along [100]. The slope of this acoustic phonon branch is sensitive to the elastic constant $C_{66}$ and the shear modulus. The temperature dependence of this branch displays a softening with a minimum near the magnetostructural transition of $T_S\sim 70\mathrm{K}$ and a recovery within the magnetically ordered low temperature phase. Soft acoustic instabilities are present in the collinear phases of the chalcogenides ${\mathrm{Fe}}_{1+x}\mathrm{Te}$, while nematic order found in ${\mathrm{Fe}}_{1+\delta }\mathrm{Se}$ is absent. We speculate, based on localized single-ion magnetism, that the relative energy scale of magnetic spin-orbital coupling on the ${\mathrm{Fe}}^{2+}$ transition metal ion is important for the presence of a nematicity in the chalcogenides.

Tellurium (Te) is one of the $p$-orbital chalcogens, which shows attractive physical properties at ambient pressure. Here, we systematically investigate both structural and electronic evolution of Te single crystal under high pressure up to 40 GPa. The pressure dependence of the experimental Raman spectrum reveals the occurrence of multiple phase transitions, which is consistent with high-pressure synchrotron x-ray diffraction measurements. The appearance of superconductivity in high-pressure phase of Te is accompanied by structural phase transitions. The high-pressure phases of Te reveal a nonmonotonic evolution of superconducting temperature $T_c$ with notably different upper critical fields. The theoretical calculations demonstrate that the pressure dependence of the density of states agrees well with the variation of $T_c$. Our results provide a systematic phase diagram for the pressure-induced superconductivity of Te.

We identify properties of the energy eigenstates in a family of chaotic spin-chain systems with local interactions, which distinguish them both from integrable systems and from nonlocal chaotic systems. We study the relation between the energy eigenstates of the full system and products of energy eigenstates of two extensive subsystems. The magnitudes of the coefficients relating the two bases have a simple form as a function of $\omega$, the energy difference between the full system eigenstate and the product of eigenstates. This form explains the exponential decay with time of the probability for a product of eigenstates to return to itself during thermalization. We also find certain statistical properties of the coefficients. While it is generally expected that the coefficients are uncorrelated random variables, we point out that correlations implied by unitarity are important for understanding the transition probability between two products of eigenstates, and the evolution of operator expectation values during thermalization. Moreover, we find that there are additional correlations resulting from locality, which lead to a slower growth of the second Rényi entropy than the one predicted by an uncorrelated random variable approximation. We expect that the above properties are universal in chaotic systems with local interactions.

We study operator spreading in many-body quantum systems by its potential to generate an informationally complete measurement record in quantum tomography. We adopt continuous weak measurement tomography for this purpose. We generate the measurement record as a series of expectation values of an observable evolving under the desired dynamics, which can show a transition from integrability to complete chaos. We find that the amount of operator spreading, as quantified by the fidelity in quantum tomography, increases with the degree of chaos in the system. We also observe a remarkable increase in information gain when the dynamics transitions from integrable to nonintegrable. We find our approach in quantifying operator spreading is a more consistent indicator of quantum chaos than Krylov complexity as the latter may correlate/anticorrelate or show no explicit behavior with the level of chaos in the dynamics. We support our argument through various metrics of information gain for two models: the Ising spin chain with a tilted magnetic field and the Heisenberg XXZ spin chain with an integrability-breaking field. Our paper gives an operational interpretation for operator spreading in quantum chaos.

We employ spin-cluster perturbation theory to investigate the evolution of the spin excitation spectra of the mixed-dimensional antiferromagnetic $s=\frac{1}{2}$ Heisenberg models from the one-dimensional chain to the two-dimensional square and honeycomb lattices by varying the spin interactions $J_{\perp }$ across the chains relative to $J_{\parallel }$ along the chains. In addition to the well-defined magnon excitations, the spectra of the Néel phases for both lattices exhibit anomalous high-energy continua that evolve continuously from the continuum of one-dimensional chain through increasing $J_{\perp }$. Notably, the key features of the continua at the two-dimensional limit for $J_{\perp }/J_{\parallel }=1$ are well consistent with experimental observations in real materials. Our results indicate that these high-energy continua in the Néel phases are a result of spinon deconfinement, which is further supported by a random-phase-approximation analysis based on the spinon Hubbard models.

The large magnetostriction at the ferromagnetic morphotropic phase boundary (MPB) relies on easy magnetization switching under external magnetic fields. It has been proposed that both domain wall motion and magnetization rotation occur under external magnetic fields at the ferromagnetic MPB. However, direct experimental evidence of the latter is still lacking. Here we report direct evidence of both magnetization rotation and domain wall motion under an external magnetic field at the MPB of the ${\mathrm{Tb}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Fe}}_2$ system through in situ synchrotron x-ray diffraction experiments, which are further confirmed by phase field simulations. This work unravels the origin of the large magnetostriction at the ferromagnetic MPB and could shed light on the design of magnetostrictive materials.

Quantum computers and simulators promise to enable the study of strongly correlated quantum systems. Yet, surprisingly, it is hard for them to compute ground states. They can, however, efficiently compute the dynamics of closed quantum systems. We propose a method to study the quantum thermodynamics of strongly correlated electrons from quantum dynamics. We define time-averaged classical shadows (TACS) and prove it is a classical shadow(CS) of the von Neumann ensemble, the time-averaged density matrix. We then show that the diffusion maps, an unsupervised machine learning algorithm, can efficiently learn the phase diagram and phase transition of the one-dimensional transverse field Ising model both for ground states using CS and state trajectories using TACS. It does so from state trajectories by learning features that appear to be susceptibility and entropy from a total of 90 000 shots taken along a path in the microcanonical phase diagram. Our results suggest a low number of shots from quantum simulators can produce quantum thermodynamic data with a quantum advantage.

We calculate the zero-temperature dc electrical conductivity in the collisionless $\hslash \omega /k_{B}T\to \infty$ limit at superconductor-insulator transitions in the $(2+1)\mathrm{d}$ XY model universality class. We use a dual model consisting of a single Dirac fermion at zero density, coupled to a Chern-Simons gauge field and in the presence of a quenched random mass, with or without an unscreened Coulomb interaction. Our calculation is performed in a $1/N_f$ expansion, where $N_f$ is the number of Dirac fermions. At the fixed point without Coulomb interaction, we obtain the universal conductivities $({\sigma }_{xx},{\sigma }_{xy})=(0.97-0.52/N_f,-0.24+1.64/N_f)·{\left(2e\right)}^2/h$. At the fixed point with Coulomb interaction, we find $({\sigma }_{xx},{\sigma }_{xy})=(0.97+1.09/N_f,-0.24+0.93N_f)·{\left(2e\right)}^2/h$. At zeroth order, the model exhibits particle-vortex self-dual electrical transport with ${\sigma }_{xx}\lesssim {\left(2e\right)}^2/h$ and small, but finite ${\sigma }_{xy}$. Corrections of $\mathcal{O}(1/N_f)$ due to fluctuations in the Chern-Simons gauge field and disorder produce violations of self-duality. These fluctuations reduce/enhance the longitudinal conductivity at the fixed point without/with the Coulomb interaction.

In this paper, we propose an analytic continuation method to extract real-frequency spectral functions from imaginary-frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara Green's function and a stochastic sampling procedure is utilized to optimize the amplitudes and locations of poles. In order to capture narrow peaks and sharp band edges in the spectral functions, a constrained sampling algorithm and a self-adaptive sampling algorithm are developed. To demonstrate the usefulness and performance of this method, we at first apply it to study the spectral functions of representative fermionic and bosonic correlators. Then we employ this method to tackle the analytic continuation problems of matrix-valued Green's functions. The synthetic Green's functions, as well as realistic correlation functions from finite-temperature quantum many-body calculations, are used as input. The benchmark results demonstrate that this method is capable of reproducing most of the key characteristics in the spectral functions. The sharp, smooth, and multipeak features in both low- and high-frequency regions of spectral functions could be accurately resolved, which overcomes one of the main limitations of the traditional maximum entropy method. More importantly, it exhibits excellent robustness with respect to noisy and incomplete input data. The causality of spectral function is always satisfied even in the presence of sizable noises. As a by-product, this method could derive a fitting formula for the Matsubara data, which provides a compact approximation to the many-body Green's functions. Hence, we expect that this method could become a pivotal workhorse for numerically analytic continuation and be broadly useful in many applications.

A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing a hedgehog structure as a result of a radial magnetic field. We elaborate on a relation between the formation of an entangled wavefunction at one pole, in a two-spins model, and an interesting pair of one-half topological numbers. Similar to Cooper pairs in superconductors, an Einstein-Podolsky-Rosen pair or Bell state at one pole produces a half-flux quantum, which here refers to the halved flux of the Berry curvature on the surface. These 1/2 numbers also refer to the presence of a free Majorana fermion at a pole on each sphere. The topological responses can be measured when driving from north to south and from a circularly polarized field at the poles revealing the quantized or half-quantized nature of the protected transverse currents. We show applications of entangled wavefunctions in band structures, introducing a local marker in momentum space, to characterize the topological response of two-dimensional semimetals in bilayer geometries.

We synthesized cm-sized single crystals of the nanolamellar compound ${\mathrm{Zr}}_3{\mathrm{SnC}}_2$ and performed angle-resolved photoemission spectroscopy (ARPES). A challenging problem to be solved, when studying electronic structure with ARPES, is to differentiate the surface and bulk electronic bands. We found that just after cleavage, the ARPES signal of ${\mathrm{Zr}}_3{\mathrm{SnC}}_2$ is dominated by surface states with well-defined energy dispersions. The (1 × 1) periodicity and the very good match of the electronic structure measured by ARPES with the DFT predictions indicate the absence of surface reconstruction. Mechanical cleavage happens at the Sn-Zr plane boundary, and the ARPES results are consistent with a top surface divided into locally unaltered regions covered with Sn atoms and regions terminated with Zr atoms. We provide a thorough analysis of these surface state bands. Longer-lived surface states are attributed to the Sn-terminated areas. DFT indicates that the surface bands of the Sn-terminated surface do not only involve Sn $p$ orbitals, but also $d$ orbitals of the Zr atoms lying closest to the surface. The orbital nature of the surface bands is further ascertained by ARPES.