The representation of ground states of fermionic quantum impurity problems as superpositions of Gaussian states has recently been given a rigorous mathematical foundation [S. Bravyi and D. Gosset, Commun. Math. Phys. 356, 451 (2017)]. It is natural to ask how many parameters are required for an efficient variational scheme based on this representation. An upper bound is $O\left(N^2\right)$, where $N$ is the system size, which corresponds to the number parameters needed to specify an arbitrary Gaussian state. We provide an alternative representation, with more favorable scaling, only requiring $O\left(N\right)$ parameters, that we illustrate for the interacting resonant-level model. We achieve the reduction by associating mean-field-like parent Hamiltonians with the individual terms in the superposition, using physical insight to retain only the most relevant channels in each parent Hamiltonian. We benchmark our variational ansatz against the numerical renormalization group, and compare our results to other variational schemes of a similar nature to ours. Apart from the ground-state energy, we also study the spectrum of the covariance matrix—a very stringent measure of accuracy. Our approach outperforms some existing variational schemes and remains quantitatively accurate in the numerically challenging near-critical regime.

We investigate the low-energy physics of non-Hermitian quantum spin models with $PT$ symmetry. To this end, we consider the one-dimensional Ising chain and the two-dimensional toric code in a non-Hermitian staggered field. For both systems, dual descriptions in terms of non-Hermitian staggered Ising interactions in a conventional transverse field exist. We perform high-order series expansions about the high- and low-field limit for both systems to determine the ground-state energy per site and the one-particle gap. The one-dimensional non-Hermitian Ising chain is known to be exactly solvable. Its ground-state phase diagram consists of second-order quantum phase transitions, which can be characterized by logarithmic singularities of the second derivative of the ground-state energy and, in the symmetry-broken phase, the gap closing of the low-field gap. In contrast, the gap closing from the high-field phase is not accessible perturbatively due to the complex energy and the occurrence of exceptional lines in the high-field gap expression. For the two-dimensional toric code in a non-Hermitian staggered field, we study the quantum robustness of the topologically ordered phase by the gap closing of the low-field gap. We find that the well-known second-order quantum phase transition of the toric code in a uniform field extends into a large portion of the non-Hermitian parameter space. However, the series expansions become unreliable for a dominant anti-Hermitian field. Interestingly, the analysis of the high-field gap reveals the potential presence of an intermediate region.

Recent theoretical calculations predict the presence of Dirac nodal lines with $\pi$ Berry phase and related topological surface states in elemental alkaline-earth metals. Here we provide experimental and theoretical evidence for the existence of similar nodal lines also in hexagonal close-packed Yb, an element of the lanthanide series, in the limit of zero spin-orbit coupling. These topological properties emerge after taking into account self-energy corrections, which permit one to correctly describe the experimental low-energy electronic structure of Yb. By angle-resolved photoemission spectroscopy we demonstrate the occurrence of topological surface states in Yb which are robust in the presence of the large spin-orbit coupling.

The precise control of spins in semiconductor spintronic devices requires electrical means to generate spin packets with a well-defined initial phase. We demonstrate a pulsed electrical scheme that triggers the spin ensemble phase in a similar way as circularly polarized optical pulses generate phase coherent spin packets. Here, we use fast current pulses to initialize phase coherent spin packets, which are injected across an Fe/GaAs Schottky barrier into $n$-GaAs. By means of time-resolved Faraday rotation, we demonstrate phase coherence by the observation of multiple Larmor precession cycles for current pulse widths down to 500 ps at 17 K. We show that the current pulses are broadened by the charging and discharging time of the Schottky barrier. At high frequencies, the observable spin coherence is limited only by the finite bandwidth of the current pulses, which is of the order of 2 GHz. These results therefore demonstrate that all-electrical injection and phase control of electron spin packets at microwave frequencies is possible in metallic-ferromagnet–semiconductor heterostructures.

Inverted-gap InAs/GaSb quantum wells have long been predicted to show quantum spin Hall insulator (QSHI) behavior. The experimental characterization of the QSHI phase in these systems has relied on the presence of quantized edge transport near charge neutrality. However, experimental data showing the presence of edge conductance in the trivial regime suggest that additional experimental signatures are needed to characterize the QSHI phase. Here we show that electric field-induced gap oscillations can be used as an indicator of the presence of helical edge states in the system. By studying a realistic low-energy model InAs/GaSb quantum wells derived from $\mathbf{k}·\mathbf{p}$ band theory, we show that such oscillations are bound to appear in narrow samples as the system is driven to the topological phase by the electric field. Our results can serve as a guide for the search of additional experimental signatures of the presence of topologically protected helical edge states in InAs/GaSb systems.

In this work, we foresee the structure of a new class of borophenes with smaller two-dimensional (2D) densities of atoms than those explored so far for 2D boron crystals. Boron atoms in the porous borophenes tend to be five-coordinated in contrast with commonly investigated structures with hexagonal holes for which the number of nearest neighbors of each atom varies from three to six. High metallic character is the usual feature of borophenes, however, we have also identified a semimetallic borophene that turns into a semiconductor upon unit-cell expansion. A $10\%$ increase in lattice constant of this structure gives rise to an energy gap of $0.3\text{eV}$. This extends to semiconductor industry the possible application of 2D boron crystals.

We construct a valley dynamics model, involving both bright and dark excitonic states, to determine magneto-optical properties of excitons and singlet and triplet trions (charged excitons), in monolayer ${\mathrm{WSe}}_2$ subjected to magnetic fields. Our computed excitonic peak energy and valley Zeeman splitting, which are essential for the magnetic-field-associated valley dynamics, in great agreement with experimental data by Lyons et al. [Nat. Commun. 10, 2330 (2019)]. In addition, we find that the valley polarizations of excitons and trions respectively exhibit the “X”- and “V”-shape dependence on magnetic field, consistent with experimental measurements by Aivazian et al. [Nat. Phys. 11, 148 (2015)]. Remarkably, beyond available experimental measurements, our theory predicts an X-V shape conversion and even a new paradigm more than the X and V shapes, which depend on the trion fine structure arising from exchange interactions and involving a magnetic swap of ground states between singlet and triplet trions. Our results are helpful for elucidating recent experimental data about the valley-degeneracy-lifting-mediated valley dynamics of different trion species and should stimulate experiments probing relevant new magneto-optical features.

Recent numerical and experimental works have revealed a disorder-free many-body localization (MBL) in an interacting system subjected to a linear potential, known as the Stark MBL. The conventional MBL, induced by disorder, has been widely studied by using quantum simulations based on superconducting circuits. Here, we consider the Stark MBL in two types of superconducting circuits, i.e., the one-dimensional array of superconducting qubits, and the circuit where nonlocal interactions between qubits are mediated by a resonator bus. We calculate the entanglement entropy and participate entropy of the highly excited eigenstates, and study the nonequilibrium properties of the Stark MBL. In particular, we observe an anomalous relaxation of the imbalance, dominated by the power-law decay $t^{-\xi }$. The exponent $\xi$ satisfies $\xi \propto |\gamma -{\gamma }_c{|}^{\nu }$ when $\gamma <{\gamma }_c$, and vanishes for $\gamma \ge {\gamma }_c$, which can be employed to estimate the ${\gamma }_c$. Our work indicates that superconducting circuits are a promising platform for investigating the critical properties of the Stark MBL transition.

The real part of optical conductivity $\text{Re}\sigma \left(\omega \right)$ of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization group, we study $\text{Re}\sigma \left(\omega \right)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $\text{Re}\sigma \left(\omega \right)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well defined. The emergence of an excitonic peak in $\text{Re}\sigma \left(\omega \right)$ implies the formation of a spin polaron. Examining the dependence of $\text{Re}\sigma \left(\omega \right)$ on the on-site Coulomb interaction and next-nearest-neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $\text{Re}\sigma \left(\omega \right)$ by modeling the electron-phonon coupling present in ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and ${\mathrm{Nd}}_2{\mathrm{CuO}}_4$, we obtain $\text{Re}\sigma \left(\omega \right)$ comparable with experiments.

Microcavity exciton-polaritons are two-dimensional bosonic quasiparticles composed by excitons and photons. Using a model Hamiltonian with parameters generated from ab initio density-functional theory and Bethe-Salpeter equation calculations, we investigate the exciton and the exciton-polariton properties of hexagnonal boron nitride (hBN) based microcavity. We show that hBN-based microcavities, including monolayer and all-dielectric ones, are promising in optoelectronic applications. Room temperature exciton-polariton Bose-Einstein condensation can be achieved because of the large oscillator strength and binding energy of the exciton, and the strong interaction between the exciton-polaritons and the longitudinal optical phonons. Based on this BEC state, an exciton-polariton mediated superconducting device can also be fabricated at a few tens of kelvin using the microcavity structure proposed by Laussy et al. Phys. Rev. Lett. 104, 106402 (2010).

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-$\frac{1}{2}$ chain. Here, we quantitatively analyze this behavior by establishing the relation between system size and correlation length required for the fermionic gaussianity to emerge. Importantly, we demonstrate that this behavior can be observed through the applicability of Wick's theorem, and thus, it is experimentally accessible. To establish the relevance of our results to possible experimental realizations of XYZ-related models, we demonstrate that the emergent gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities, and local random potentials.

Protected by the interplay of on-site Coulomb interactions and spin-orbit coupling, ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ at high pressure is a rare example of a Mott insulator with a paramagnetic ground state. Here, using optical Raman scattering, we measure both the phonon and magnon evolution in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ under pressure and identify three different magnetically-ordered phases, culminating in a spin-disordered state beyond 18 GPa. A strong first-order structural phase transition drives the magnetic evolution at $\sim 10$ GPa with reduced structural anisotropy in the ${\mathrm{IrO}}_6$ cages, leading to increasingly isotropic exchange interactions between the Heisenberg spins and a spin-flip transition to $c$-axis-aligned antiferromagnetic order. In the disordered phase of Heisenberg $J_{\mathrm{eff}}=1/2$ pseudospins, the spin excitations are quasielastic and continuous to 10 meV, potentially hosting a gapless quantum spin liquid in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$.

We use magnetotransport measurements to probe quantum Hall ground states in graphene/${\mathrm{WSe}}_2$ heterobilayers. Compared to pristine graphene, inter-Landau level (LL) gaps at half-filled quartets away from filling factor $\nu =0$ show significantly weaker dependence on the magnetic field $B$, while odd $\nu$ fillings show a stronger dependence. We interpret this behavior using a model incorporating Ising and Rashba spin-orbit coupling (SOC) along with Coulomb interactions within the self-consistent Hartree-Fock framework. A model fit yields Ising SOC in range $\sim 1–2 \mathrm{meV}$, Rashba $\sim 10 \mathrm{meV}$, and the in-plane dielectric constant $\sim 12$, in agreement to previously found values. In the zeroth LL quartet, the $\nu =0$ gap as a function of magnetic field exhibits a plateau near 5 T, compared to $\sim 20–25 \mathrm{T}$ for pristine graphene. This behavior is in agreement with a model in which the SOC causes a phase transition from a canted antiferromagnetic state to a ferromagnetic state to occur at a much lower field. Our studies demonstrate how the interplay of SOC and electronic interactions affect graphene's electronic structure.

Based on the Boltzmann transport equation, we demonstrate that the thermal conductance per unit width of a sufficiently thin polar nanofilm supporting the propagation of surface-phonon polaritons along its surfaces is independent of the material properties and is given by $12z\left(3\right)k_B^3{T}^2/c{h}^2$, where $k_B$ and $h$ are the respective Boltzmann and Planck constants, while $c$ is the light speed in vacuum, $T$ is the temperature, and $z\left(3\right)$ is the Riemann zeta function. The huge propagation length of these energy carriers establishes that this quantization holds not only for temperatures much smaller than 1 K, as is the case of electrons and phonons, but also for those comparable to room temperature, which can significantly facilitate its observation and implementation in the thermal management of nanoscale electronics and photonics.

Moiré superlattices in the twisted bilayer graphene provide an unprecedented platform to investigate a wide range of exotic quantum phenomena. Recently, the twist degree of freedom has been introduced into various classical wave systems, giving rise to new ideas for the wave control. The question is whether twistronics and moiré physics can be extended to electronics with potential applications in the twist-enabled signal processing. Here, we demonstrate both in theory and experiment that lots of fascinating moiré physics can be engineered using electric circuits with extremely high degrees of freedom. By suitably designing the interlayer coupling and biasing of one sublattice for the twisted bilayer circuit, the low-energy flat bands with large band gaps away from other states can be realized at various twist angles. Based on the moiré circuit with a fixed twist angle, we experimentally demonstrate the effect of band narrowing as well as the localization of electric energy when a magic value of the interlayer coupling is applied. Furthermore, the topological edge states, which originate from the moiré potential induced pseudomagnetic field, are also observed. Our findings suggest a flexible platform to study twistronics beyond natural materials and other classical wave systems, and may have potential applications in the field of intergraded circuit design.

This work addresses the study of the high-temperature phase sequence of ${\mathrm{Bi}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{FeO}}_3$ by undertaking temperature-dependent high-resolution neutron powder diffraction (NPD) and Raman spectroscopy measurements. A determination of lattice parameters, phase fractions, and modulation wave vector was performed by Pawley refinement of the NPD data. The analysis revealed that ${\mathrm{Bi}}_{0.7}{\mathrm{La}}_{0.3}{\mathrm{FeO}}_3$ exhibits an incommensurate modulated orthorhombic $Pn{2}_{1}a\left(00\gamma \right)000$ structure at room temperature, with a weak ferromagnetic behavior, likely arising from a canted antiferromagnetic ordering. Above $T_1=543\mathrm{K}$, the low-temperature modulated $Pn{2}_{1}a\left(00\gamma \right)000$ evolves monotonically into a fractionally growing Pnma structure up to $T_{\mathrm{N}}=663\mathrm{K}$. At 663 K, the low-temperature canted antiferromagnetic phase is suppressed concurrently with the switching of the former into a nonmodulated $Pn{2}_{1}a$ structure that continues to coexist with the Pnma one, until the latter is expected to reach the 100% fraction of the sample volume at high temperatures above 733 K. The $Pn{2}_{1}a$ space group is obtained from the Pnma one through the ${\mathrm{\Gamma }}_4^{-}$ polar distortion. Neutron diffraction and Raman spectroscopy results provide evidence for the emergence of noteworthy linear spin-phonon coupling. In this regard, magnetostructural coupling is observed below $T_{\mathrm{N}}$, revealed by the relation between the weak ferromagnetism of the canted iron spins and the ${\mathrm{FeO}}_6$ octahedra symmetric stretching mode. The correlation between magnetization and structural results from NPD provides definite evidence for the magnetic origin of the structural modulation. The analysis of the temperature-dependent magnetization and the magnetic peak intensity as well yields a critical exponent (β) value of 0.38. The lower limit of the phase coexistence temperature $T_1=543\mathrm{K}$, marking the emergence of the Pnma phase, is also associated with the temperature whereupon the modulation magnitude starts to decrease.

Density-functional theory within a Berry-phase formulation of the dynamical polarization is used to determine the second-order susceptibility ${\chi }^{\left(2\right)}$ of lithium niobate $\left({\mathrm{LiNbO}}_3\right)$. Defect-trapped polarons and bipolarons are found to strongly enhance the nonlinear susceptibility of the material, in particular when localized at ${\mathrm{Nb}}_{\mathrm{V}}\text{−}{\mathrm{V}}_{\mathrm{Li}}$ defect pairs. This is essentially a consequence of the formation of polaronic states inside the band gap. The population of these levels, for example, by illumination leads to strongly enhanced ${\chi }^{\left(2\right)}$ coefficients and thus allows for the spatial and transient modification of the second-harmonic generation in macroscopic samples.

Two-dimensional (2D) disordered superconductor (SC) in class D exhibits a disorder-induced quantum multicritical phenomenon among diffusive thermal metal (DTM), topological superconductor (TS), and conventional localized (AI) phases. To characterize the quantum tricritical point where these three phases meet, we carry out a two-loop renormalization group (RG) analysis for 2D Dirac fermion with random mass in terms of the $\epsilon$-expansion in the spatial dimension $d=2-\epsilon$. In two dimensions $(\epsilon =0)$, the random mass is marginally irrelevant around a clean-limit fixed point of the gapless Dirac fermion, while there exists an IR unstable fixed point at finite disorder strength that corresponds to the tricritical point. The critical exponent, dynamical exponent, and scaling dimension of the (uniform) mass term are evaluated around the tricritical point by the two-loop RG analysis. Using a mapping between an effective theory for the 2D random-mass Dirac fermion and the $(1+1)$-dimensional Gross-Neveu model, we further deduce the four-loop evaluation of the critical exponent, and the scaling dimension of the uniform mass around the tricritical point. Both the two-loop and four-loop results suggest that criticalities of a AI-DTM transition line as well as TS-DTM transition line are controlled by other saddle-point fixed point(s) at finite uniform mass.

Magnetic properties of an antiferromagnetic double perovskite oxide ${\mathrm{Ba}}_2{\mathrm{CaReO}}_6$, where ${\mathrm{Re}}^{6+}$ $\left(5d^1\right)$ ions with large spin-orbit coupling are arranged on the face-centered-cubic lattice, are investigated using pulsed high magnetic field up to 66 T. Magnetization and magnetostriction measurements have revealed a magnetic field-induced phase transition at around 50 T. The phase transition accompanies a jump of magnetization and longitudinal magnetostriction of approximately $2\times {10}^{–4}$ with the change of power-law behavior, indicating sizable coupling between the electronic degrees of freedom and the lattice. The high-field phase exhibits a magnetic moment approximately 0.2 ${\mu }_{\mathrm{B}}$, which is close to the values observed in $5d^1$ double perovskite oxides with noncollinear magnetic structure. We argue that ${\mathrm{Ba}}_2{\mathrm{CaReO}}_6$ is an antiferromagnet that sits close to the phase boundary between the collinear and noncollinear phases, providing the target material for investigating the interplay between spin-orbital entangled electrons and magnetic field.