Phases of matter are sharply defined in the thermodynamic limit. One major challenge of accurately simulating quantum phase diagrams of interacting quantum systems is due to the fact that numerical simulations usually deal with the energy density, a local property of quantum wave functions, while identifying different quantum phases generally relies on long-range physics. In this paper, we construct generic fully symmetric quantum wave functions under certain assumptions using a type of tensor networks (projected entangled pair states), and provide practical simulation algorithms based on them. We find that quantum phases can be organized into crude classes distinguished by short-range physics, which is related to the fractionalization of both onsite symmetries and space-group symmetries. Consequently, our simulation algorithms, which are useful to study long-range physics as well, are expected to be able to sharply determine crude classes in interacting quantum systems efficiently. Examples of these crude classes are demonstrated in half-integer quantum spin systems on the kagome lattice. Limitations and generalizations of our results are discussed.

We present an experimental and theoretical analysis of the self- and cross-Kerr effect of extended plasma resonances in Josephson junction chains. We calculate the Kerr coefficients by deriving and diagonalizing the Hamiltonian of a linear circuit model for the chain and then adding the Josephson nonlinearity as a perturbation. The calculated Kerr coefficients are compared with the measurement data of a chain of 200 junctions. The Kerr effect manifests itself as a frequency shift that depends linearly on the number of photons in a resonant mode. By changing the input power on a low signal level, we are able to measure this shift. The photon number is calibrated using the self-Kerr shift calculated from the sample parameters. We then compare the measured cross-Kerr shift with the theoretical prediction, using the calibrated photon number.

Below $\sim 630$ mK, the ${}^4\mathrm{He}$ atom mass flux $F$, which passes through a cell filled with solid hcp ${}^4\mathrm{He}$ in the pressure range 25.6–26.4 bar, rises with falling temperature and, at a temperature $T_d$, the flux drops sharply. The flux above $T_d$ has characteristics that are consistent with the presence of a bosonic Luttinger liquid. We study $F$ as a function of ${}^3\mathrm{He}$ concentration, $\chi =0.17–220\mathrm{ppm}$, to explore the effect of ${}^3\mathrm{He}$ impurities on the mass flux. We find that the strong reduction of the flux is a sharp transition, typically complete within a few mK and a few hundred seconds. Modest concentration-dependent hysteresis is present. We find that $T_d$ is an increasing function of $\chi$ and the $T_d\left(\chi \right)$ dependence differs somewhat from the predictions for bulk phase separation for $T_{ps}$ vs $\chi$. We conclude that ${}^3\mathrm{He}$ plays an important role in the flux extinction. The dependence of $F$ on the solid helium density is also studied. We find that $F$ is sample dependent, but that the temperature dependence of $F$ above $T_d$ is universal; data for all samples scale and collapse to a universal temperature dependence, independent of ${}^3\mathrm{He}$ concentration or sample history. The universal behavior extrapolates to zero flux in the general vicinity of $T_h\approx 630\mathrm{mK}$. With increases in temperature, it is possible that a thermally activated process contributes to the degradation of the flux. The possibility of the role of disorder and the resulting phase slips as quantum defects on one-dimensional conducting pathways is discussed.

Multilayer fractional quantum Hall wave functions can be used to construct the non-Abelian states of the ${\mathbb{Z}}_k$ Read-Rezayi series upon symmetrization over the layer index. Unfortunately, this construction does not yield the complete set of ${\mathbb{Z}}_k$ ground states on the torus. We develop an alternative projective construction of ${\mathbb{Z}}_k$ Read-Rezayi states that complements the existing one. On the multilayer torus geometry, our construction consists of introducing twisted boundary conditions connecting the layers before performing the symmetrization. We give a comprehensive account of this construction for bosonic states, and numerically show that the full ground state and quasihole manifolds are recovered for all computationally accessible system sizes. Furthermore, we analyze the neutral excitation modes above the Moore-Read on the torus through an extensive exact diagonalization study. We show numerically that our construction can be used to obtain excellent approximations to these modes. Finally, we extend our symmetrization scheme to the plane and sphere geometries.

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the nonprojective method and more efficient information storage, data compression, and less computational effort.

We study the renormalized perturbation theory of the single-impurity Anderson model, particularly the high-order terms in the expansion of the self-energy in powers of the renormalized coupling $\tilde{U}$. Though the presence of counterterms in the renormalized theory may appear to complicate the diagrammatics, we show how these can be seamlessly accommodated by carrying out the calculation order-by-order in terms of skeleton diagrams. We describe how the diagrams pertinent to the renormalized self-energy and four vertex can be automatically generated, translated into integrals, and numerically integrated. To maximize the efficiency of our approach we introduce a generalized $k$-particle/hole propagator, which is used to analytically simplify the resultant integrals and reduce the dimensionality of the integration. We present results for the self-energy and spectral density to fifth order in $\tilde{U}$, for various values of the model asymmetry, and compare them to a numerical renormalization group calculation.

Dispersion relations for acoustic and electromagnetic waves guided by resonant inclusions located at the surface of an elastic solid or an interface between two media are analyzed theoretically within the effective medium approximation. Oscillators on the surface of an elastic half-space are shown to give rise to a Love-type surface acoustic wave only existing below the oscillator frequency. A simple dispersion relation governing this system is shown to also hold for electromagnetic waves guided by Lorentz oscillators at an interface between two media with equal dielectric constants. Different kinds of behavior of the dispersion of the resonantly guided mode are identified, depending on whether the bulk wave in the absence of oscillators can propagate along the surface or interface.

The magnetism in the ferromagnetic superconductor UCoGe has been studied using a combination of magnetic Compton scattering, bulk magnetization, x-ray magnetic circular dichroism, and electronic structure calculations, in order to determine the spin and orbital moments. The experimentally observed total spin moment $M_s$ was found to be $-0.24\pm 0.05{\mu }_B$ at 5 T. By comparison with the total moment of $0.16\pm 0.01{\mu }_B$, the orbital moment $M_l$ was determined to be $0.40\pm 0.05{\mu }_B$. The U and Co spin moments were determined to be antiparallel. We find that the U $5f$ electrons carry a spin moment of ${\mathrm{U}}_s\approx -0.30{\mu }_B$ and that there is a Co spin moment of ${\mathrm{Co}}_s\approx 0.06{\mu }_B$ induced via hybridization. The ratio ${\mathrm{U}}_l/{\mathrm{U}}_s$, of $-1.3\pm 0.3$, shows the U moment to be itinerant. In order to ensure an accurate description of the properties of $5f$ systems, and to provide a critical test of the theoretical approaches, it is clearly necessary to obtain experimental data for both the spin and orbital moments, rather than just the total magnetic moment. This can be achieved simply by measuring the spin moment with magnetic Compton scattering and comparing this to the total moment from bulk magnetization.

Majorana fermions are rising as a promising key component in quantum computation. Although the prevalent approach is to use a quadratic (i.e., noninteracting) Majorana Hamiltonian, when expressed in terms of Dirac fermions, generically the Hamiltonian involves interaction terms. Here we focus on the possible pair correlations in a simple model system. We study a model of Majorana fermions coupled to a boson mode and show that the anomalous correlator between different Majorana fermions, located at opposite ends of a topological wire, exhibits odd-frequency behavior. It is stabilized when the coupling strength $g$ is above a critical value $g_c$. We use both, conventional diagrammatic theory and a functional integral approach, to derive the gap equation, the critical temperature, the gap function, the critical coupling, and a Ginzburg-Landau theory that allows discussing a possible subleading admixture of even-frequency pairing.

The electron-hole symmetry in graphene monolayer, which is analogous to the inherent symmetric structure between electrons and positrons of the Universe, plays a crucial role in the chirality and chiral tunneling of massless Dirac fermions. Here we demonstrate that both strain and charged-defect scattering could break this symmetry dramatically in a graphene monolayer. In our experiment, the Fermi velocities of electrons $v_F^e$ and holes $v_F^h$ are measured directly through Landau level spectroscopy. In strained graphene with lattice deformation and curvature, the $v_F^e$ and $v_F^h$ are measured as $(1.21\pm 0.03)\times {10}^6\mathrm{m}/\mathrm{s}$ and $(1.02\pm 0.03)\times {10}^6\mathrm{m}/\mathrm{s}$, respectively. This giant asymmetry originates from enhanced next-nearest-neighbor hopping in the strained region. Around positively charged defect, we observe opposite electron-hole asymmetry, and the $v_F^e$ and $v_F^h$ are measured to be $(0.86\pm 0.02)\times {10}^6\mathrm{m}/\mathrm{s}$ and $(1.14\pm 0.03)\times {10}^6\mathrm{m}/\mathrm{s}$, respectively. Such a large asymmetry is attributed to the fact that the massless Dirac fermions in a graphene monolayer are scattered more strongly when they are attracted to the charged defect than when they are repelled from it.

We investigate the stability and the nature of the chiral spin liquids which were recently uncovered in extended Heisenberg models on the kagome lattice. Using a Gutzwiller projected wave function approach, i.e., a parton construction, we obtain large overlaps with ground states of these extended Heisenberg models. We further suggest that the appearance of the chiral spin liquid in the time-reversal invariant case is linked to a classical transition line between two magnetically ordered phases.

Many ultrathin films of transition metal oxides exhibit nonmetallic behavior, in contrast to their metallic bulk counterpart, thus displaying a metal-insulator transition (MIT) as the film thickness is reduced. The nature of this MIT has been a long-standing issue in the epitaxial oxide research community. Here, we report the processing dependence of the critical thickness ($t_{\mathrm{c}}$) of MIT and the origin of the insulating phase in $\mathrm{L}{\mathrm{a}}_{2/3}\mathrm{S}{\mathrm{r}}_{1/3}\mathrm{Mn}{\mathrm{O}}_3$ (LSMO) films. A $t_{\mathrm{c}}$ of 3 unit cells (u.c.) is achieved by minimizing oxygen vacancies under optimal growth conditions, diminishing the epitaxial strain with a tunable buffer layer and suppressing surface strain by film capping. The electrical transport measurements demonstrate that the nonmetallic behavior in LSMO thin films is an unavoidable result of localization initiated by inherent disorder but amplified by the reduction in dimensionality.

We realize a suppression of an electromagnetically-induced-transparency-like (EIT-like) transmission in a metasurface induced by a local electric field that is strongly enhanced based on two approaches: squeezing of electromagnetic energy in resonant metasurfaces and enhancement of electromagnetic energy density associated with a low group velocity. The EIT-like metasurface consists of a pair of radiatively coupled cut-wire resonators, and it can effect both field-enhancement approaches simultaneously. The strongly enhanced local electric field generates an air discharge plasma at either of the gaps of the cut-wire resonators, which causes the EIT-like metasurface to change into two kinds of Lorentz-type metasurfaces.

Charge compensation in strontium M-type hexaferrites $A_x^{3+}{\mathrm{Sr}}_{1-x}{\mathrm{Fe}}_{12}{\mathrm{O}}_{19}(A=\text{La},\mathrm{Nd},\text{or}\mathrm{Pr})$ is studied by means of calculations of electronic structure and ${}^{57}\mathrm{Fe}$ nuclear magnetic resonance (NMR) experiments. Two different states are realized in the calculations: a localized scenario as a ground state with the extra valence charge preferentially in the octahedral 2a sites and a delocalized scenario with the charge delocalized over multiple sites. From the calculations and NMR experiments, it is deduced that the localized state ${\mathrm{Fe}}^{2+}$(2a) occurs at low temperatures regardless of the type of used substitution and that the distribution of ferric and ferrous ions within the 2a sublattice is static at low temperatures. The magnetocrystalline anisotropy energy of Sr and La hexaferrites is calculated and the contributions of individual Fe sublattices are evaluated. The temperature dependence of the anisotropy for La hexaferrite is explained as a transition between localized and delocalized states causing changes in the single ion contributions of Fe in 2a and also 12k sites.

The Monte Carlo calculation of Rényi entanglement entropies $S_n^{}$ of interacting fermions suffers from a well-known signal-to-noise problem, even for a large number of situations in which the infamous sign problem is absent. A few methods have been proposed to overcome this issue, such as ensemble switching and the use of auxiliary partition-function ratios. Here, we present an approach that builds on the recently proposed free-fermion decomposition method; it incorporates entanglement in the probability measure in a natural way; it takes advantage of the hybrid Monte Carlo algorithm (an essential tool in lattice quantum chromodynamics and other gauge theories with dynamical fermions); and it does not suffer from noise problems. This method displays no sign problem for the same cases as other approaches and is therefore useful for a wide variety of systems. As a proof of principle, we calculate $S_2^{}$ for the one-dimensional, half-filled Hubbard model and compare with results from exact diagonalization and the free-fermion decomposition method.

We examine finite-temperature phase transitions in the two-orbital Hubbard model with different bandwidths by means of the dynamical mean-field theory combined with the continuous-time quantum Monte Carlo method. It is found that there emerges a peculiar slope-reversed first-order Mott transition between the orbital-selective Mott phase and the Mott insulator phase in the presence of Ising-type Hund's coupling. The origin of the slope-reversed phase transition is clarified by the analysis of the temperature dependence of the energy density. It turns out that the increase of Hund's coupling lowers the critical temperature of the slope-reversed Mott transition. Beyond a certain critical value of Hund's coupling the first-order transition turns into a finite-temperature crossover. We also reveal that the orbital-selective Mott phase exhibits frozen local moments in the wide orbital, which is demonstrated by the spin-spin correlation functions.

We report a thorough study of the reducibility of edge correlation effects in graphene to much simplified effective models for the edge states. The latter have been used before in specially tailored geometries. By a systematic investigation of corrections due to the bulk states in second-order perturbation theory, we show that the reduction to pure edge state models is well justified in general geometries. The framework of reduced models discussed here enables the study of non-mean-field correlation physics for system sizes far beyond the reach of conventional methods, such as, e.g., quantum Monte Carlo.

Interactions between two excitons can result in the formation of bound quasiparticles, known as biexcitons. Their properties are determined by the constituent excitons, with orbital and spin states resembling those of atoms. Monolayer transition metal dichalcogenides (TMDs) present a unique system where excitons acquire a new degree of freedom, the valley pseudospin, from which a novel intervalley biexciton can be created. These biexcitons comprise two excitons from different valleys, which are distinct from biexcitons in conventional semiconductors and have no direct analog in atomic and molecular systems. However, their valley properties are not accessible to traditional transport and optical measurements. Here, we report the observation of intervalley biexcitons in the monolayer TMD ${\mathrm{MoS}}_2$ using ultrafast pump-probe spectroscopy. By applying broadband probe pulses with different helicities, we identify two species of intervalley biexcitons with large binding energies of 60 and 40 meV. In addition, we also reveal effects beyond biexcitonic pairwise interactions in which the exciton energy redshifts at increasing exciton densities, indicating the presence of many-body interactions among them.