We investigate a bilayer honeycomb lattice model of spin-1/2 fermions at half-filling with local Heisenberg coupling of fermion spins across the two layers. Using variational Monte Carlo (VMC) simulation, we demonstrate that the system undergoes a direct transition from a Dirac semimetal phase to a symmetric gapped phase, known as symmetric mass generation (SMG), as the Heisenberg coupling strength is increased. The transition does not involve spontaneous symmetry breaking or topological order and has been proposed as an example of the fermionic deconfined quantum critical point (fDQCP). Our simulation shows that a fermionic parton bilinear mass opens at the transition point while all symmetries are still preserved thanks to the quantum fluctuations introduced by the correlation factor in the variational wave function. From the simulation data, we extract the critical exponent $\nu =0.96\pm 0.03$ and the fermion scaling dimension ${\mathrm{\Delta }}_c=1.31\pm 0.04$ at the SMG critical point, which are consistent with the field theoretical prediction of fDQCP in (2+1)D. These findings support the hypothesis that the fermion fractionalizes at the SMG critical point.

Three-dimensional topological Dirac semimetals have recently attracted significant attention since they possess exotic quantum states. When Josephson junctions are constructed utilizing these materials as the weak link, the fractional ac Josephson effect emerges in the presence of a topological supercurrent contribution. We investigate the ac Josephson effect in a Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ nanowire using two complementary methods: by probing the radiation spectrum and by measuring Shapiro patterns. With both techniques, we find that the conventional supercurrent dominates at all investigated doping levels and that any potentially present topological contribution falls below our detection threshold. The inclusion of thermal noise in a resistively and capacitively shunted junction (RCSJ) model allows us to reproduce the microwave characteristics of the junction. With this refinement, we explain how weak superconducting features can be masked and provide a framework to account for elevated electronic temperatures present in realistic experimental scenarios.

In non-Hermitian systems, the eigenvalues near exceptional points of order $N$ ($\mathrm{EP}N\mathrm{s}$) usually exhibit $E\sim {\mathrm{\Lambda }}^{1/N}$ dispersion/splitting under a small perturbation $\mathrm{\Lambda }$. Such high sensitivity to perturbation makes them ideal candidates for sensors. However, $E\sim {\mathrm{\Lambda }}^{1/m}$ dispersions with $m=1,2,\cdots ,N-1$ are also possible for $\mathrm{EP}N\mathrm{s}$. Using a transposed Jordan block (TJB) matrix $H_0$ as a representative Hamiltonian, we present general rules that provide a unified understanding of the splitting behaviors of $\mathrm{EP}N\mathrm{s}$ in diverse systems. Specifically, when the $k$-diagonal entries ${\left(H_0\right)}_{i,i+k}$ of $H_0$ are perturbed by $\mathrm{\Lambda }$, we observe a dispersion of the form $E\sim {\mathrm{\Lambda }}^{1/m}$, where $m=k+1$. The phase rigidity's exponent $\chi$ and discriminant number $\nu$ together can serve as topological invariants to completely characterize an $\mathrm{EP}N$ with $E\sim {\mathrm{\Lambda }}^{1/m}$ splitting, and they are proportional, i.e., $\chi =\nu /N=(N-1)/m$. The results are demonstrated experimentally using electrical circuits. Next, we demonstrate the applicability of the splitting rules to general non-TJB Hamiltonians that exhibit an $\mathrm{EP}N$ through an example. Moreover, we observe that the splitting of $\mathrm{EP}N\mathrm{s}$ can lead to the emergence of lower-order EP structures, such as $\mathrm{EP}2$ ellipses in the parameter space. We find that the $\mathrm{EP}2$ ellipses exhibit two types of coalescence: with and without an increase in the EP order.

We consider a paradigmatic solvable model of topological order in two dimensions, Kitaev's honeycomb Hamiltonian, and turn it into a measurement-only dynamics consisting of stochastic measurements of two-qubit bond operators. We find an entanglement phase diagram that resembles that of the Hamiltonian problem in some ways, while being qualitatively different in others. When one type of bond is dominantly measured, we find area-law entangled phases that protect two topological qubits (on a torus) for a time exponential in system size. This generalizes the recently proposed idea of Floquet codes, where logical qubits are dynamically generated by a time-periodic measurement schedule, to a stochastic setting. When all types of bonds are measured with comparable frequency, we find a critical phase with a logarithmic violation of the area law, which sharply distinguishes it from its Hamiltonian counterpart. The critical phase has the same set of topological qubits, as diagnosed by the tripartite mutual information, but protects them only for a time polynomial in system size. Furthermore, we observe an unusual behavior for the dynamical purification of mixed states, characterized at late times by the dynamical exponent $z=\frac{1}{2}$, a superballistic dynamics made possible by measurements.

Quantum circuit dynamics with local projective measurements can realize a rich spectrum of entangled states of quantum matter. Motivated by the physics of the Kitaev quantum spin liquid [A. Kitaev, Ann. Phys. 321, 2 (2006)], we study quantum circuit dynamics in $2+1$ dimensions involving local projective measurements, in which the monitored trajectories realize (i) a phase with topological quantum order or (ii) a “critical” phase with a logarithmic violation of area-law scaling of the entanglement entropy along with long-range tripartite entanglement. A Majorana parton description of these dynamics, which provides an out-of-equilibrium generalization of the parton description of the Kitaev honeycomb model, permits an analytic understanding of the universal properties of these two phases, including the entanglement properties of the steady state, the dynamics of the system on the approach to equilibrium, and the phase transition between these states. In the topologically ordered phase, two logical qubits can be encoded in an initial state and protected for a time which scales exponentially in the linear dimension of the system, while no robust encoding of quantum information persists in the critical phase. Extensive numerical simulations of these monitored dynamics confirm our analytic predictions.

By solving the classical kinetic equation near the boundary, it is studied how the boundary conditions for two-dimensional (2D) electron gas in the hydrodynamic transport regime are modified in the presence of a magnetic field $B$ perpendicular to the 2D layer. The results are compared to the predictions of an approximate theory that describes the boundary conditions in terms of the components of the viscosity tensor. The first boundary condition relates the tangential current near the boundary with its normal derivative through the slip length. The dependence of the slip length on the magnetic field follows the approximate theory with good accuracy if the probability of specular reflection of the particles from the boundary is high. However, if this probability is low, the calculated slip length decreases with $B$ much stronger than the approximate theory suggests, in the region where the cyclotron radius $R_c$ becomes comparable to the mean free path $l$ determined by electron-electron scattering. If the boundary is current penetrable (as, for example, the interfaces with the contacts in the Corbino disks), there is a need in the second boundary condition relating the jump of electrochemical potential at the boundary with the current through the boundary. It is shown that in the magnetic field there exists a $B$-dependent contribution to the potential jump, proportional to the normal derivative of the tangential current. The approximate theory describing this contribution through the Hall viscosity works reasonably well for weak magnetic fields, $R_c\gg l$, though considerably underestimates the potential jump when $R_c\sim l$. A possibility of experimental observation of the magnetic-field dependence of the slip length and potential jump is discussed.

We demonstrate that the cubic antifluorite-type halides ${\mathrm{K}}_2{\mathrm{OsCl}}_6,{\mathrm{K}}_2{\mathrm{OsBr}}_6$, and ${\mathrm{Rb}}_2{\mathrm{OsBr}}_6$ are excellent realizations of nonmagnetic $J=0$ compounds. The magnetic susceptibility shows the corresponding Van Vleck type of behavior and no sign of defects. We investigate the electronic excitations with two complementary techniques, resonant inelastic x-ray scattering and optical spectroscopy. This powerful combination allows us to thoroughly study, e.g., on-site intra-$t_{2g}$ excitations and $t_{2g}$-to-$e_g$ excitations as well as intersite excitations across the Mott gap and an exciton below the gap. In this way, we determine the electronic parameters with high accuracy, altogether yielding a comprehensive picture. In ${\mathrm{K}}_2{\mathrm{OsCl}}_6$, we find the spin-orbit coupling constant $\zeta =0.34\mathrm{eV}$, Hund's coupling $J_H=0.43\mathrm{eV}$, the onset of excitations across the Mott gap at $\mathrm{\Delta }=2.2$ eV, the cubic crystal-field splitting $10Dq=3.3$ eV, and the charge-transfer energy ${\mathrm{\Delta }}_{\mathrm{CT}}=4.6$ eV. With $J_H/\zeta =1.3,{\mathrm{K}}_2{\mathrm{OsCl}}_6$ is in the intermediate-coupling regime. In a $t_{2g}$-only Kanamori picture, the above values correspond to ${\zeta }^{\mathrm{eff}}=0.41\mathrm{eV}$ and $J_H^{\mathrm{eff}}=0.28\mathrm{eV}$, which is very close to results reported for related $5d^4$ iridates. In the tetragonal phase at 5 K, the noncubic crystal field causes a peak splitting of the $J=1$ state as small as 4 meV. Compared to ${\mathrm{K}}_2{\mathrm{OsCl}}_6$, the bromides ${\mathrm{K}}_2{\mathrm{OsBr}}_6$ and ${\mathrm{Rb}}_2{\mathrm{OsBr}}_6$ show about 12–14% smaller values of $10Dq$ and ${\mathrm{\Delta }}_{\mathrm{CT}}$, while the spin-orbit entangled intra-$t_{2g}$ excitations below 2 eV and hence $\zeta$ and $J_H$ are reduced by less than 4%. Furthermore, the Mott gap in ${\mathrm{K}}_2{\mathrm{OsBr}}_6$ is reduced to about 1.8 eV.

The optical response of a matter excitation embedded in nanophotonic devices is commonly described by the Drude-Lorentz model. Here, we demonstrate that this widely used approach fails in the case where quantum-confined plasmons of a two-dimensional electron gas interact strongly with optical phonons. We propose a quantum model which contains the semiclassical Drude-Lorentz one for simple electronic potentials, but predicts very different results in symmetry-broken potentials. We unveil a mechanism for the oscillator strength transfer between bright phonon-polariton and dark plasmon modes, enabling thus new quantum degrees of freedom for designing the optical response of nanostructures.

We study the interplay of lattice, spin, and orbital degrees of freedom in a two-dimensional model system: a flat square lattice of $\mathrm{Te}$ atoms on a $\mathrm{Au}\left(100\right)$ surface. The atomic structure of the Te monolayer is determined by scanning tunneling microscopy and quantitative low-energy electron diffraction. Using spin- and angle-resolved photoelectron spectroscopy and density functional theory, we observe a Te-Au interface state with highly anisotropic Rashba-type spin-orbit splitting at the $\overline{\mathrm{X}}$ point of the Brillouin zone. Based on a profound symmetry and tight-binding analysis, we show how in-plane square lattice symmetry and broken inversion symmetry at the Te-Au interface together enforce a remarkably anisotropic orbital Rashba effect which strongly modulates the spin splitting.

We introduce a maximally localized Wannier function representation of Bloch excitons, two-particle correlated electron-hole excitations, in crystalline solids, where the excitons are maximally localized with respect to an average electron-hole coordinate in real space. As a proof-of-concept, we illustrate this representation in the case of low-energy spin-singlet and -triplet excitons in cubic lithium fluoride, computed using the ab initio Bethe-Salpeter equation approach. We visualize the resulting maximally localized exciton Wannier functions (MLXWFs) in real space, detail the convergence of the exciton Wannier spreads, and demonstrate how Wannier-Fourier interpolation can be leveraged to obtain exciton energies and states at arbitrary exciton crystal momenta in the Brillouin zone. We further introduce an approach to treat the long-range dipolar coupling between singlet MLXWFs and discuss it in depth. The MLXWF representation sheds light on the fundamental nature of excitons and paves the way toward Wannier-based post-processing of excitonic properties, enabling the construction of ab initio exciton tight-binding models, efficient interpolation of the exciton-phonon vertex, the computation of Berry curvature associated with exciton bands, and beyond.

We analyze the renormalization group (RG) flows of two effective Lagrangians, one for measurement-induced transitions of monitored quantum systems and one for entanglement transitions in random tensor networks. These Lagrangians, previously proposed on grounds of replica symmetry, are derived in a controlled regime for an illustrative family of tensor networks. They have different forms in the two cases, and involve distinct replica limits. The perturbative RG is controlled by working close to a critical dimensionality, $d_c=6$ for measurements and $d_c=10$ for random tensors, where interactions become marginal. The resulting RG flows are surprising in several ways. They indicate that in high dimensions $d>d_c$ there are at least two (stable) universality classes for each kind of transition, separated by a nontrivial tricritical point. In each case one of the two stable fixed points is Gaussian, while the other is nonperturbative. In lower dimensions, $d<d_c$, the flow always runs to the nonperturbative regime. This picture clarifies the “mean-field theory” of these problems, including the phase diagram of all-to-all quantum circuits. It suggests a way of reconciling exact results on tree tensor networks with field theory. Most surprisingly, the perturbation theory for the random tensor network (which also applies to a version of the measurement transition with “forced” measurements) formally possesses a dimensional reduction property analogous to that of the random-field Ising model. When only the leading interactions are retained, perturbative calculations in $d$ dimensions reduce to those in a simple scalar field theory in $d-4$ dimensions. We show that this holds to all orders by writing the action in a superspace formulation.

The lowest-order Josephson coupling, $J_1\left(\theta \right)cos\left(\varphi \right)$, between two $d$-wave superconductors with a phase difference $\varphi$ across the junction vanishes when their relative orientation is rotated by $\theta =\pi /4$. However, in the presence of inhomogeneity, $J_1\left(\mathbf{r}\right)$ is nonzero locally, with a sign that fluctuates in space. We show that such a random $J_1$ generates a global second-harmonic Josephson coupling, $J_{2}cos\left(2\varphi \right)$, with a sign that favors $\varphi =\pm \pi /2$, i.e., spontaneous breaking of time-reversal symmetry. The magnitude of $J_2$ is substantially enhanced if the spatial correlations of $J_1\left(\mathbf{r}\right)$ extend over large distances, such as would be expected in the presence of large-amplitude twist-angle disorder or significant local electronic nematicity. We argue that this effect likely accounts for the recent observations in twisted Josephson junctions between high-temperature superconductors.

The development of two-dimensional materials has resulted in a diverse range of novel, high-quality compounds with increasing complexity. A key requirement for a comprehensive quantitative theory is the accurate determination of these materials' band structure parameters. However, this task is challenging due to the intricate band structures and the indirect nature of experimental probes. In this work, we introduce a general framework to derive band structure parameters from experimental data using deep neural networks. We applied our method to the penetration field capacitance measurement of trilayer graphene, an effective probe of its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance.

We extend optical spin-noise spectroscopy on single (InGa)As quantum dots to high magnetic fields at which the splitting between the two optically active Zeeman branches of the positively charged quantum dot trion transition is significantly larger than the homogeneous linewidth. Under such conditions, the standard theoretical approximations concerning the decoupling of spin and charge dynamics are generally not valid anymore, and the Kerr rotation fluctuations show significantly richer detuning-dependent features in the spectral region between the two Zeeman-split resonances. A comparison of the experimental data with an extended theory suggests that the typical Auger recombination can be neglected at high magnetic fields in favor of a probe-laser-induced photoeffect that not only shuffles the resident hole out of the quantum dot but also activates acceptor-bound holes, which recharge the empty quantum dot.

Starting from the recently proposed dynamical exchange-correlation field framework, the equation of motion of the diagonal part of the many-electron Green function is derived, from which the spectral function can be obtained. The resulting equation of motion takes the form of the continuity equation of charge and current densities in electrodynamics with a source. An unknown quantity in this equation is the divergence of the temporal current density, corresponding to the kinetic energy. A procedure à la Kohn-Sham scheme is then proposed, in which the difference between the kinetic potential of the interacting system and the noninteracting Kohn-Sham system is shifted into the exchange-correlation field. The task of finding a good approximation for the exchange-correlation field should be greatly simplified since only the diagonal part is needed. A formal solution to the continuity equation provides an explicit expression for calculating the spectral function, given an approximate exchange-correlation field.

We study systematically the role of temperature in the optical response of doped two-dimensional semiconductors. By making use of a finite-temperature Fermi-polaron theory, we reveal a crossover from a quantum-degenerate regime with well-defined polaron quasiparticles to an incoherent regime at high temperature or low doping where the lowest-energy “attractive” polaron quasiparticle is destroyed, becoming subsumed into a broad trion-hole continuum. We demonstrate that the crossover is accompanied by significant qualitative changes in both absorption and photoluminescence. In particular, with increasing temperature (or decreasing doping), the emission profile of the attractive branch evolves from a symmetric Lorentzian to an asymmetric peak with an exponential tail involving trions and recoil electrons at finite momentum. We discuss the effect of temperature on the coupling to light for structures embedded into a microcavity, and we show that there can exist well-defined polariton quasiparticles even when the exciton-polaron quasiparticle has been destroyed, where the transition from weak to strong light-matter coupling can be explained in terms of the polaron linewidths and spectral weights.

In the past decade, tremendous efforts have been made towards understanding fermionic symmetry-protected topological (FSPT) phases in interacting systems. Nevertheless, for systems with continuum symmetry, e.g., electronic insulators, it is still unclear how to construct an exactly solvable model with a finite-dimensional Hilbert space in general. In this Letter, we give a lattice model construction and classification for two-dimensional (2D) interacting electronic insulators. Based on the physical picture of $\mathrm{U}{\left(1\right)}_f$ charge decorations, we illustrate the key idea by considering the well-known 2D interacting topological insulator. Then we generalize our construction to an arbitrary 2D interacting electronic insulator with symmetry $G_f=\mathrm{U}{\left(1\right)}_f{⋊}_{{\rho }_1,{\omega }_2}G$, where $\mathrm{U}{\left(1\right)}_f$ is the charge conservation symmetry and ${\rho }_1,{\omega }_2$ are additional data which fully characterize the group structure of $G_f$. Finally, we study more examples, including the full interacting classification of 2D crystalline topological insulators.

The Ferrell-Glover-Tinkham (FGT) sum rule in superconductors defines the superfluid density, ${\rho }_s$, as the optical conductivity spectral weight (SW) that transfers into a $\delta$ function at $\omega =0$ due to the opening of the energy gap below $T_c$. In high-$T_c$ superconductors, strong electron-boson coupling, self-energy effects, and intertwining of energy scales can link ${\rho }_s$ to various high-energy processes, making the question of whether or not the FGT sum rule is valid in cuprates, and at what energy scale, central to a full understanding of the pairing mechanism. Here, we report high-precision measurements of the FGT sum rule in near-optimally doped ${\mathrm{DyBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ thin films. We resolve the low-energy balance of SW by combining submillimeter-microwave interferometry, terahertz time-domain spectroscopy, and infrared ellipsometry to independently obtain the real and imaginary parts of the complex dielectric function between 0.8 meV and 1.1 eV (6–9000 ${\mathrm{cm}}^{-1}$). By applying a Kramers-Kronig consistency analysis to the measured spectra we find that the FGT sum rule is obeyed, and the total intraband SW is conserved to within $\pm 0.2\%$ below an energy scale $\sim 0.6$ eV. We attribute specific anomalies observed in the conductivity spectra below $\sim 0.6$ eV to coupling of charge carriers to the spectrum of collective antiferromagnetic spin fluctuations. The procedure presented here, applied to near-optimally doped ${\mathrm{DyBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$, lays out a protocol for how the FGT sum rule should be studied in other doping levels and compounds.

Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight opens new possibilities for applying FRG methods to models for strongly correlated electrons with projected Hilbert spaces, such as quantum spin models, the $t\text{−}J$ model, or the Hubbard model at infinite on-site repulsion. By representing these models in terms of Hubbard X-operators, we derive exact flow equations for the time-ordered correlation functions of the X-operators (X-FRG), which allow us to calculate the electronic correlation functions in the projected Hilbert space of these models. The Hubbard-I approximation for the single-particle Green function of the Hubbard model is recovered from a trivial truncation of the flow equations where the two-point vertex is approximated by its atomic limit. We use our approach to calculate the quasiparticle residue and damping in the “hidden Fermi liquid” state of the Hubbard model at infinite on-site repulsion where the Hamiltonian consists only of the projected kinetic energy.

Advances in manipulating the structure of optical beams enable the study of interaction between structured light and low-dimensional semiconductor systems. We explore the photocurrents in two-dimensional systems excited by such inhomogeneous radiation with structured electromagnetic field. Besides the contribution associated with the intensity gradient, the photocurrent contains contributions driven by the gradients of the Stokes polarization parameters and the phase of the electromagnetic field. We develop a microscopic theory of the nonlinear, nonlocal intraband transport of electrons induced by electromagnetic field of structured radiation and derive analytical expressions for the photocurrent contributions. The theory is applied to analyze the radial and azimuthal photocurrents excited by twisted radiation beams carrying orbital angular momentum, and possible experiments to detect the photocurrents are discussed.