Variational wave function Ansätze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte Carlo and modern variational optimization techniques including automatic differentiation. The resulting Ansatz, consisting of several slices of optimized projectors, is highly expressive and systematically improvable. We benchmark this form on the two-dimensional Hubbard model, using both cylindrical and large, fully periodic supercells. The computed ground-state energies are competitive with the best variational results. Moreover, the optimized wave functions predict the correct ground-state order with near full symmetry restoration (i.e., translation invariance) despite initial states with incorrect orders. The Ansatz can become a tool for local order prediction, leading to a new paradigm for variational studies of bulk systems. It can also be viewed as an approach to produce accurate and systematically improvable wave functions in a convenient form of nonorthogonal Slater determinants (e.g., for quantum chemistry) at polynomial computational cost.

It is well known that elementary particles in the real $3+1$-dimensional world are either bosons or fermions, without exception, and not both. Here, we show that a quantized current-biased Josephson junction (CBJJ), as an artificial macroscopic “particle,” can serve as either a boson or a fermion or the combination, depending on the amplitude of the biased dc current. By using high vacuum two-angle electron beam evaporations, we fabricated CBJJ devices and calibrated their physical parameters by applying low-frequency signal drivings. At $50\mathrm{mK}$ temperature environment, the microwave transmission characteristics of the fabricated CBJJ devices were measured at the low power limit. The experimental results verify the relevant theoretical predictions, i.e., when the bias current is significantly lower than the critical ones of the junctions, the device works in a very linear regime and thus behaves as a harmonic oscillator “boson”; while if the biased current is sufficiently large (especially approaching the junctions' critical currents), the device works manifestly in the nonlinear regime and thus behaves as a two-level artificial atom “fermion.” Therefore, by adjusting the biased dc current, the CBJJ device can be effectively switched from a Bose-type macroscopic particle to a Fermi-type one and thus might open an approach for quantum technology applications at a macroscopic scale.

We experimentally demonstrate a virtual two-qubit gate and characterize it using quantum process tomography (QPT). The virtual two-qubit gate decomposes an actual two-qubit gate into single-qubit unitary gates and projection gates in quantum circuits for expectation-value estimation. We implement projection gates via midcircuit measurements. The deterministic sampling scheme reduces the number of experimental circuit evaluations required for decomposing a virtual two-qubit gate. We also apply quantum error mitigation to suppress the effect of measurement errors and improve the average gate fidelity of a virtual controlled-$Z$ (CZ) gate to $f_{\mathrm{av}}=0.9938\pm 0.0002$. Our results highlight a practical approach to implement virtual two-qubit gates with high fidelities, which are useful for simulating quantum circuits using fewer qubits and implementing two-qubit gates on a distant pair of qubits.

The demonstration of spontaneous symmetry breaking in a system consisting of a pair of self-modulated ring resonators is performed. In addition, the critical effect of thermal heating induced by optical absorption is studied, where experimental results with numerical calculations reveal that optical absorption contributing as an optical nonlinearity is greatly dominant over the optical Kerr effect under certain operation speeds, depicting a significant impact on the system performance. Our analysis of the operation characteristics outlines important characteristics of self-modulated nonlinear resonators and their function as an optical binary state system.

Entanglement plays crucial roles in quantum optics, providing a prerequisite for these recent unprecedented leaps. Nevertheless, the study of quantum entanglement under the influence of relativity, an important ingredient of quantum optics, still needs to be explored. In parallel, integrated photonic chips, particularly those with the aid of transformation optics, have simulated various relativity phenomena including gravitational lensing and Unruh radiation. However, thus far, studying relativistic quantum optics on this type of platform has not yet occurred. Here, we propose and experimentally realize quantum walks of entangled photons near an emulated Rindler horizon. Remarkably, we find that quantum interference near the synthetic horizon leads to a counterintuitive phenomenon of optical escape. Our study paves the way to a tabletop platform for studying quantum phenomena in various relativistic space-time metrics, and may bring an implication for the test of quantum theory in relativity.

Precursor elastic effects are investigated in a displacive anharmonic spring model and shown to extend greatly into the paraelastic phase. Weak precursor effects can be detected near $2T_{\mathrm{tr}}$, where $T_{\mathrm{tr}}$ is the ferroelastic transition temperature. The precursor effects become strong at $T<1.7T_{\mathrm{tr}}$. Two effects were identified in our two-dimensional model: the symmetry-breaking strain $e_3 \left({\varepsilon }_{xy}\right)$ leads to softening of the elastic modulus $C_{33}$, while the nonsymmetry-breaking strain $e_1+e_2$ (${\varepsilon }_{\mathrm{xx}}+{\varepsilon }_{\mathrm{yy}}$) leads to hardening of $C_{11}$. The strain $e_3$ is proportional to the order parameter and scales as $|e_1+e_2|$ $\sim e_3^2$. The temperature evolutions of the elastic moduli are surprisingly well described by power laws and Vogel-Fulcher equations. The power-law exponents are ∼−0.5 for $\mathrm{\Delta }{C}_{33}$ and ∼−1 for $\mathrm{\Delta }{C}_{11}$, Δ($C_{11}+C_{12}$) and Δ($C_{11}-C_{12}$). The Vogel-Fulcher temperatures are very similar, while the Vogel-Fulcher energies differ between the excess elastic moduli. The origin of the precursor effect is the evolution of short-range order in the paraelastic phase which gives rise to a characteristic local nanostructure. In the case of the symmetry-breaking strain, this microstructure resembles dynamical twinning patterns corresponding to the ferroelastic nanostructure, which weakens the material. In the case of the nonsymmetry-breaking strain, we find density fluctuations which make the material harder.

We present a molecular orbital candidate ${\mathrm{Ba}}_4{\mathrm{TaMn}}_3{\mathrm{O}}_{12}$ with a face-sharing octahedra trimer, by comparing it with a related compound ${\mathrm{Ba}}_4{\mathrm{NbMn}}_3{\mathrm{O}}_{12}$. The synthesis of the polycrystalline powder is optimized by suppressing the secondary impurity phase via x-ray diffraction. Magnetic susceptibility measurements on the optimized samples reveal a weak magnetic hysteresis with magnetic transitions consistent with heat capacity results. The effective magnetic moments from susceptibility indicate a strongly coupled $S=2$ antiferromagnetic trimer at around room temperature, whereas the estimated magnetic entropy from heat capacity suggests the localized $S=3/2$ timer. These results can be explainable by a partial molecular orbital state, in which three $t_{2g}$ electrons are localized in each Mn ion and one $e_g$ electron is delocalized over two-end Mn ions of the trimer based on density functional theory calculations. This unconventional 3d orbital state is comprehended as a consequence of competition between the hybrid interatomic orbitals within the Mn trimer and the local moment formation by on-site Coulomb correlations.

We calculate the screened electron-electron interaction for the charge-disproportionated insulator ${\mathrm{CaFeO}}_3$ using the constrained random-phase approximation (cRPA). While in many correlated materials the formation of a Mott-insulating state is driven by a large local Coulomb repulsion, represented by the Hubbard $U$, several cases have been identified more recently in which $U$ is strongly screened and instead the Hund's interaction $J$ dominates the physics. Our results confirm a strong screening of the local Coulomb repulsion $U$ in ${\mathrm{CaFeO}}_3$, whereas $J$ is much less screened and can thus stabilize a charge-disproportionated insulating state. This is consistent with the case of the rare-earth nickelates, where similar behavior has been demonstrated. In addition, we validate some common assumptions used for parametrizing the local electron-electron interaction in first-principles calculations based on density-functional theory (DFT), we assess the dependence of the interaction on the choice of correlated orbitals, and we discuss the use of the calculated interaction parameters in $\mathrm{DFT}+U$ calculations of ${\mathrm{CaFeO}}_3$. Our work also highlights certain limitations for the direct use of cRPA results in DFT-based first-principles calculations, in particular for systems with strong entanglement between the correlated and uncorrelated bands.

Skyrmioniums are doughnutlike topological spin textures in chiral magnets, which are able to move with zero skyrmion Hall effect. The annihilation of a skyrmionium involves the topological transition through singularity formation at the continuum level. Here we analytically and numerically study a type of thermal annihilation of a skyrmionium under the framework of micromagnetism. The skyrmionium initially exists in an ultrathin ferromagnetic film in the exchange-dominated regime and is stabilized under a uniform perpendicular magnetic field. The thermal annihilation of the “skyrmion” inside the skyrmionium results in the transformation of the skyrmionium to a skyrmion. We derive an analytical formula in the Arrhenius form describing the annihilation rate of this process. We find that the analytical solutions agree well with the micromagnetic simulation results. Besides, from the large deviation point of view, we derive the dynamical path for the collapse of a skyrmionium. Our results are useful for understanding the thermal stability of skyrmioniums and may lead to spintronic applications based on the thermal manipulation of skyrmioniums.

Magnetic anisotropies often originate from the spin-orbit coupling and determine magnetic ordering patterns. We develop a microscopic theory for dc electric-field controls of magnetic anisotropies in magnetic Mott insulators and discuss its applications to Kitaev materials and topological spin textures. Throughout this paper, we take a microscopic approach based on Hubbard-type lattice models, tight-binding models with onsite interactions. We derive a low-energy spin Hamiltonian from a fourth-order perturbation expansion of the Hubbard-type model. We show in the presence of a strong intra-atomic spin-orbit coupling that dc electric fields add non-Kitaev interactions such as a Dzyaloshinskii-Moriya interaction and an off-diagonal ${\mathrm{\Gamma }}^{\prime }$ interaction to the Kitaev-Heisenberg model and can induce a topological quantum phase transition between Majorana Chern insulating phases. We also investigate the interatomic Rashba spin-orbit coupling and its effects on topological spin textures. dc electric fields turn out to create and annihilate magnetic skyrmions, hedgehogs, and chiral solitons. We propose several methods of creating topological spin textures with external electromagnetic fields. Our theory clarifies that the strong but feasible electric field can control Kitaev spin liquids and topological spin textures.

As a toy model of chiral interactions in crowded spaces, we consider sphinx tilings in finite regions of the triangular lattice. The sphinx tiles, hexiamonds composed of six equilateral triangles in the shape of a stylized sphinx, come in left and right enantiomorphs. Regions scaled up from the unit sphinx by an integer factor (Sphinx frames) require tiles of both chiral forms to produce tilings, including crystalline, quasicrystalline, and fully disordered tilings. For frames up to order 13, we describe methods that permit exact enumeration and computation of partition functions using accelerated backtracking, seam, and dangler algorithms. For larger frames, we introduce a Monte Carlo method to sample typical tilings. The key to the latter is the identification of fundamental shapes (polyads) that admit multiple tilings and which allow a rejection-free MC simulation.

We study the spreading of elasto-viscoplastic (EVP) droplets under surface tension effects. The non-Newtonian material flows like a viscoelastic liquid above the yield stress and behaves like a viscoelastic solid below it. Hence, the droplet initially flows under surface tension forces but eventually reaches a final equilibrium shape when the stress everywhere inside the droplet falls below the resisting rheological stresses. We use numerical simulations and combine volume-of-fluid (VOF) method and an EVP constitutive model to systematically study the dynamics of spreading and the final shape of the droplets. The spreading process explored in this study finds applications in coating, droplet-based inkjet printing, and 3D printing, where complex fluids such as paints, thermoplastic filaments, or bio-inks are deposited onto surfaces. Additionally, the computational framework enables the study of a wide range of multiphase interfacial phenomena, from elastocapillarity to plastocapillarity.

The neutron capture measurement of natural rhenium was performed with the time-of-flight technique at the Back-n facility of the China Spallation Neutron Source in the energy range from 1 to 500 eV of the resolved resonance region (RRR) and from 5 to 400 keV in the unresolved resonance region (URR). Prompt $\gamma$-rays originating from neutron-induced capture events were detected by four ${\mathrm{C}}_6{\mathrm{D}}_6$ detectors. The pulse height weighting technique and the double-bunch unfolding method based on the Bayesian theory were used in the data analysis. To obtain reliable measurement results, background subtraction, normalization, and corrections were carefully considered. The multilevel R-matrix Bayesian code SAMMY was used to extract the resonance parameters in the RRR. An absence of resonance near 392 eV is observed in our measurement, which has been observed in previous works. The average cross sections in the URR of natural rhenium relative to ${}^{197}\mathrm{Au}$ were obtained in logarithmical equidistant energy bins with 20 bins per energy decade. The talys code was used to describe the average cross sections in the URR; the Maxwellian-averaged cross sections (MACSs) of ${}^{185}\mathrm{Re}$ and ${}^{187}\mathrm{Re}$ are given from $kT=5$ to 100 keV. At a thermal energy of $kT=30$ keV, the MACS value for ${}^{185}\mathrm{Re}$ ($1469\pm 127$ mb) is in good agreement with the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADoNIS) recommended value ($1535\pm 62$ mb) within the error bars. By contrast, the value of $1361\pm 118$ mb for ${}^{187}\mathrm{Re}$ shows a discrepancy with the KADoNiS recommended value ($1160\pm 57$ mb).

Recent study has shown that it can be advantageous to implement a composite channel that partitions the Hamiltonian $H$ for a given simulation problem into subsets $A$ and $B$ such that $H=A+B$, where the terms in $A$ are simulated with a Trotter-Suzuki channel and the $B$ terms are randomly sampled via the Qdrift algorithm. Here we extend Qdrift and composite product formulas to imaginary time, formulating candidate classical algorithms for quantum Monte Carlo calculations. We upper bound the induced Schatten-$1\to 1$ norm on both imaginary-time Qdrift and composite channels. Another recent result demonstrated that simulations of lattice Hamiltonians containing geometrically local interactions can be improved using a Lieb-Robinson argument to decompose $H$ into subsets that contain only terms supported on that subset of the lattice. Here, we provide a quantum algorithm by unifying this result with the composite approach into “local composite channels” and we upper bound the diamond distance. We provide exact numerical simulations of algorithmic cost by counting the number of gates of the form $e^{-i{H}_{j}t}$ and $e^{-H_j\beta }$ to meet a certain error tolerance $\epsilon$. In doing so, we optimize the partitioning into sets $A$ and $B$ using gradient boosted tree models from machine learning. These numerical studies are important given that product formulas have been historically known to outperform analytic upper bounds. We show constant factor advantages for a variety of interesting Hamiltonians, the maximum of which is a $\approx 20$-fold speedup that occurs in the simulation of Jellium.