In any bosonic lattice system, which is not dominated by local interactions and thus “frozen” in a Mott-type state, numerical methods have to cope with the infinite size of the corresponding Hilbert space even for finite lattice sizes. While it is common practice to restrict the local occupation number basis to $N_c$ lowest occupied states, the presence of a finite condensate fraction requires the complete number basis for an exact representation of the many-body ground state. In this work we present a truncation scheme to account for contributions from higher number states. By simply adding a single coherent-tail state to this common truncation, we demonstrate increased numerical accuracy and the possible increase in numerical efficiency of this method for the Gutzwiller variational wave function and within dynamical mean-field theory.

It was recently shown that odd-frequency superconducting pair amplitudes can be induced in conventional superconductors subjected to a spatially nonuniform time-dependent drive. It has also been shown that, in the presence of interband scattering, multiband superconductors will possess bulk odd-frequency superconducting pair amplitudes. In this work we build on these previous results to demonstrate that by subjecting a multiband superconductor with interband scattering to a time-dependent drive, even-frequency pair amplitudes can be converted to odd-frequency pair amplitudes and vice versa. We will discuss the physical conditions under which these pair symmetry conversions can be achieved and possible experimental signatures of their presence.

Heterostructures combining topological and nontopological materials constitute the next frontier in the effort to incorporate topological insulators (TIs) into electronic devices. We show that the properties of the interface states appearing at the boundary between a topologically trivial semiconductor (SE) and a TI are controlled by the lowering of the interface symmetry due to the presence of the SE. For the [111]-grown heterostructure, SE-TI interface states exhibit elliptical contours of constant energy and complex spin textures with broken helicity, in contrast to the well-studied helical Dirac surface states. We derive a general effective Hamiltonian for SE-TI junctions, and propose experimental signatures such as an out of plane spin accumulation under a transport current and the opening of a spectral gap that depends on the direction of an applied in-plane magnetic field.

Gapless topological phases of matter may host emergent quasiparticle excitations which have no analog in quantum field theory. This is the case of so called triple point fermions (TPF), quasiparticle excitations protected by crystal symmetries, which show fermionic statistics but have an integer (pseudo)spin degree of freedom. TPFs have been predicted in certain three-dimensional nonsymmorphic crystals, where they are pinned to high symmetry points of the Brillouin zone. In this Rapid Communication, we introduce a minimal, three-band model which hosts TPFs protected only by the combination of a $C_4$ rotation and an anticommuting mirror symmetry. Unlike current nonsymmorphic realizations, our model allows for TPFs which are anisotropic and can be created or annihilated pairwise. It provides a simple, numerically affordable platform for their study.

Many realizations of solid-state qubits involve couplings to leakage states lying outside the computational subspace, posing a threat to high-fidelity quantum gate operations. Mitigating leakage errors is especially challenging when the coupling strength is unknown, e.g., when it is caused by noise. Here we show that simple pulse sequences can be used to strongly suppress leakage errors for a qubit embedded in a three-level system. As an example, we apply our scheme to the recently proposed charge quadrupole (CQ) qubit for quantum dots. These results provide a solution to a key challenge for fault-tolerant quantum computing with solid-state elements.

The surface states in three-dimensional (3D) topological insulators can be described by a two-dimensional (2D) continuous Dirac Hamiltonian. However, there exists the fermion doubling problem when putting the continuous 2D Dirac equation into a lattice model. In this paper, we introduce a Wilson term with a zero bare mass into the 2D lattice model to overcome the difficulty. By comparing with a 3D Hamiltonian, we show that the modified 2D lattice model can faithfully describe the low-energy electrical and transport properties of surface states of 3D topological insulators. So this 2D lattice model provides a simple and cheap way to numerically simulate the surface states of 3D topological-insulator nanostructures. Based on the 2D lattice model, we also establish the wormhole effect in a topological-insulator nanowire by a magnetic field along the wire and show the surface states being robust against disorder. The proposed 2D lattice model can be extensively applied to study the various properties and effects, such as the transport properties, Hall effect, universal conductance fluctuations, localization effect, etc. So, it paves a way to study the surface states of the 3D topological insulators.

The gyromagnetic factor is an important physical quantity relating the magnetic-dipole moment of a particle to its spin. The electron spin $g$-factor in vacuo is one of the best model-based theoretical predictions ever made, showing agreement with the measured value up to ten parts per trillion [J. Schwinger, Phys. Rev. 73, 416 (1948); R. S. Van Dyck, Jr. et al., Phys. Rev. Lett. 59, 26 (1987); D. Hanneke et al., Phys. Rev. Lett. 100, 120801 (2008); T. Aoyama et al., Phys. Rev. Lett. 109, 111807 (2012)]. However, for electrons in a material the $g$-factor is modified with respect to its value in vacuo because of environment interactions. Here, we show how interaction effects lead to the spin $g$-factor correction in graphene by considering the full electromagnetic interaction in the framework of pseudo-QED [A. Kovner et al., Phys. Rev. B 42, 4748 (1990); N. Dorey et al., Nucl. Phys. B 386, 614 (1992); S. Teber, Phys. Rev. D 86, 025005 (2012); S. Teber, Phys. Rev. D 89, 067702 (2014); E. C. Marino, Nucl. Phys. B 408, 551 (1993)]. We compare our theoretical prediction with experiments performed on graphene deposited on ${\mathrm{SiO}}_2$ and SiC, and we find a very good agreement between them.

We investigate the quantum tunneling and Andreev reflection in a top-gated quantum anomalous Hall insulator proximity coupled with a superconductor junction. A quantized perfect crossed Andreev reflection with its coefficient being integer 1 is obtained and all other scattering processes (the normal reflection, normal tunneling, and local Andreev reflection) are completely suppressed when the topological superconductor phase with Chern number $\mathcal{N}=1$ is realized. This perfect crossed Andreev reflection originates from the tunneling of the chiral Majorana edge states, and the phase of tunneling amplitude only being 0 and $\pi$ plays a decisive role. Furthermore, because of the chiral characteristic of the Majorana edge states, the perfect crossed Andreev reflection is robust against the disorder and can work in a wide range of system parameters.

We evaluate the energetic stabilities of white, red, and black allotropes of phosphorus using density functional theory (DFT) and hybrid functional methods, van der Waals (vdW) corrections (DFT+vdW and hybrid+vdW), vdW density functionals, and random phase approximation (RPA). We find that stability of black phosphorus over red-V (i.e., the violet form) is not ubiquitous among these methods, and the calculated enthalpies for the reaction phosphorus (red-V)$\to \mathrm{phosphorus}$ (black) are scattered between $-20$ and 40 meV/atom. With local density and generalized gradient approximations, and hybrid functionals, mean absolute errors (MAEs) in densities of P allotropes relative to experiments are found to be around 10%–25%, whereas with vdW-inclusive methods, MAEs in densities drop below $\sim 5$%. While the inconsistency among the density functional methods could not shed light on the stability puzzle of black versus red phosphorus, comparison of their accuracy in predicting densities and the supplementary RPA results on relative stabilities indicate that opposite to the common belief, black and red phosphorus are almost degenerate, or the red-V (violet) form of phosphorus might even be the ground state.

The equation of state $P(V,T)$ for solid argon is determined by the calculation of accurate static and vibrational terms in the free energy. The static component comes from a quantum theoretical many-body expansion summing over all energetic contributions from two-, three-, and four-body fragments treated with relativistic coupled cluster theory, while the lattice vibrations are described at an anharmonic level including two- and three-body forces as well as temperature effects. The dynamic part is calculated within the Debye and Einstein approximation, as well as by a more accurate phonon treatment where the vibrational motions in the lattice are coupled. Our results are in good agreement with room-temperature high-pressure experimental data up to $\sim 20$ GPa. In the 20–100 GPa pressure range, however, we see considerable deviations between experiment and theory, perhaps indicating missing four-body contributions (beyond the quadruple dipole terms included here), missing five and higher-body effects, and the need to go beyond the coupled cluster singles-doubles with perturbative triples treatment in such higher-body forces. This contrasts with the results for solid neon, where excellent agreement has been achieved taking only two- and three-body forces into account [P. Schwerdtfeger and A. Hermann, Phys. Rev. B 80, 064106 (2009)]. We demonstrate that the phase transition from fcc to hcp cannot account for the large discrepancies observed. Density functional calculations give very mixed results in the high-pressure region, but some functionals such as optB88-vdW (proposed by Lundqvist and co-workers) describe the many-body forces in argon reasonably well over the range of pressures investigated. Theoretical investigations of the heavier rare gas solids reaching experimental accuracy in the high-pressure regime therefore remain a significant challenge.

With a decomposition scheme for the bath correlation function, the hierarchy equation of motion (HEOM) is extended to the zero-temperature sub-Ohmic spin-boson model, providing a numerically accurate prediction of quantum dynamics. As a dynamic approach, the extended HEOM determines the delocalized-localized (DL) phase transition from the extracted rate kernel and the coherent-incoherent dynamic transition from the short-time oscillation. As the bosonic bath approaches from the strong to weak sub-Ohmic regimes, a crossover behavior is identified for the critical Kondo parameter of the DL transition, accompanied by the transition from the coherent to incoherent dynamics in the localization.

The excitation of the linear spin wave modes of a soft ferromagnetic free layer of a nanopillar structure through dc-ac currents that traverse the structure is studied, as well as with ac magnetic fields. There is interest in understanding the magnetization dynamics in these structures since they may be used as microwave sources when these nano-oscillators enter into auto-oscillatory regimes. The free layer is a soft ferromagnet, like Permalloy, in the shape of a circular disk, with a very small thickness in the range of the exchange length. Using a description of the magnetization dynamics in terms of a Hamiltonian for weakly interacting waves, we determine the spin wave modes of the structure under two approximations: a very thin film limit, and under a model that includes the effect of the full magnetostatic interaction. We consider direct and parametric excitations of different spin wave modes with ac currents, i.e., with exciting frequency approximately equal to the frequency of the mode or to twice its value, respectively. The Oersted field mainly plays a role in the direct resonant excitation of the modes. Our main conclusion is that for a dc current below the critical value necessary for the development of auto-oscillations, using parametric excitation, a very high value of the ac current is necessary to reach the auto-oscillatory behavior in this geometry. However, if the out-of-plane component of the spin transfer torque is high enough, the ac critical current for auto-oscillations is significantly reduced, leading to a signature for its detection. We comment on parallel pumping and transverse excitation using ac magnetic fields.

The features of the magnetic $(H,T)$ phase diagram of ${\mathrm{CeCu}}_2{\mathrm{Ge}}_2$ are similar to those of superconducting ${\mathrm{CeCu}}_2{\mathrm{Si}}_2$, but the nature of these phases and transitions is still controversial. For ${\mathrm{CeCu}}_2{\mathrm{Ge}}_2$ we present results on electrical transport, thermodynamic measurements (magnetization, magnetostriction), and elastic neutron diffraction for fields up to 15 T parallel to the [110] direction. Two magnetic phases AF1, AF2 and a third, yet unidentified ferrimagnetic phase AF3 exist below $T_{\text{N}}=4.2$ K and in fields up to approximately 26 T. At temperatures below 2.5 K a first-order transition from AF1 to AF2 at around 7.8 T was found experimentally, characterized by a shift of the observed propagation vector from ${\mathbf{q}}_{\mathbf{1}}=(0.285-0.2850.543)$ to ${\mathbf{q}}_{\mathbf{2}}=(0.34-0.270.55)$. Above 12.5 T reflections belonging neither to the AF1 nor to the AF2 type were found. To interpret the macroscopic measurements and neutron data a mean-field simulation with the McPhase program was carried out, yielding a low-field double-$\mathbf{q}$ magnetic structure AF1 with ${\mathbf{q}}_{\mathbf{1}}\pm =(0.278\pm 0.2780.556)$ that jumps to AF2 with ${\mathbf{q}}_{\mathbf{2}}\pm =(0.286\pm 0.2860.545)$ at about 5 T (to be compared to the experimental value of 7.8 T). This transition is followed by a single-$\mathbf{q}$ structure AF3 with ${\mathbf{q}}_{\mathbf{3}}=\left(0.280.280.56\right)$ at 10 T (as compared to 12.5 T from experiment) that is stable up to saturation at 26 T. These calculations also reveal the principal dependence of the experimental magnetization and susceptibility published earlier. The predicted single-$\mathbf{q}$ structure was not detectable by neutrons because of limitations in the employed scattering geometry.

Superconducting coplanar waveguide (CPW) resonators are powerful and versatile tools used in areas ranging from radiation detection to circuit quantum electrodynamics. Their potential for low intrinsic losses makes them attractive as sensitive probes of electronic properties of bulk materials and thin films. Here we use superconducting MoRe CPW resonators to investigate the high-frequency (up to 0.3 GHz) and low-temperature (down to 3.5 K) permittivity of ${\mathrm{SrTiO}}_3$, a nonlinear dielectric on the verge of a ferroelectric transition (quantum paraelectricity). We perform a quantitative analysis of its dielectric properties as a function of external dc bias (up to $\pm 15\mathrm{V}$), rf power, and mode number and discuss our results within the framework of the most recent theoretical models. We also discuss the origin of a fatigue effect that reduces the tunability of the dielectric constant of ${\mathrm{SrTiO}}_3$, which we relate to the presence of oxygen vacancies.

Cluster expansions with concentration-independent interactions have been widely used to model the formation energies of alloys. In the Sanchez paper [Phys. Rev. B 81, 224202 (2010)], this practice is called into question based on the argument that a truncated cluster expansion with concentration-independent interactions cannot be used to represent the formation energy of a random alloy if the formation energy is a nonlinear function of concentration. To clarify the validity of using cluster expansions with concentration-independent interactions, I demonstrate that this argument is not necessarily correct.

In the Comment, an argument is presented that attempts to point out a conflict between the apparent success of numerous applications of Ising-like models, or cluster expansions with constant effective interactions, with statements made in Sanchez [Phys. Rev. B 81, 224202 (2010)] that bring into question the use of such constant effective interactions to model the energy of formation of alloys. In this response we show that the argument developed by the author of the Comment is fundamentally flawed, circular, and based on misrepresentations and misunderstandings of the results presented in Sanchez.