A formal procedure to construct the contributions to the frequency-dependent density-density (potential-density) response function in a series expansion with respect to the coupling constant of the electrons is presented. The required input quantities are obtained from static perturbation theory along the adiabatic connection. The contributions to the response function up to a given order are shown to determine the corresponding contributions in a coupling constant expansion of the frequency-dependent exchange-correlation kernel, the key quantity in time-dependent density-functional theory (TDDFT) in the linear response regime. Both the frequency-dependent response function as well as the exchange-correlation kernel thus are accessible in an order by order fashion. By exploiting the relations between the expansions of the response function and the exchange-correlation kernel, various methods are proposed to calculate the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem, including a hierarchy of ACFD methods towards the exact Kohn-Sham correlation energy. For a recently introduced ACFD method relying on a truncated power series approximation of the correlation kernel, a formal justification for the underlying ansatz is provided. The presented formal approach to construct the exchange-correlation kernel in an order by order fashion not only represents a basis for new ACFD methods for the Kohn-Sham correlation energy but additionally is of interest to devise new TDDFT methods in the linear response regime.

Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian generalizations, as exemplified by a general breakdown of bulk-boundary correspondence and a localization of all states at the boundary, termed the non-Hermitian skin effect. In this paper, we present a completely analytical unifying framework for studying these systems using generalized transfer matrices, a real-space approach suitable for systems with periodic as well as open boundary conditions. We show that various qualitative properties of these systems can be easily deduced from the transfer matrix. For instance, the connection between the breakdown of the conventional bulk-boundary correspondence and the existence of a non-Hermitian skin effect, previously observed numerically, is traced back to the transfer matrix having a determinant not equal to unity. The vanishing of this determinant signals real-space exceptional points, whose order scales with the system size. We also derive previously proposed topological invariants such as the biorthogonal polarization and the Chern number computed on a complexified Brillouin zone. Finally, we define an invariant for and thereby clarify the meaning of topologically protected boundary modes for non-Hermitian systems.

Magnetic properties of the substitution series ${\mathrm{Ru}}_{1-x}{\mathrm{Cr}}_x{\mathrm{Cl}}_3$ were investigated to determine the evolution from the anisotropic Kitaev magnet $\alpha \text{−}{\mathrm{RuCl}}_3$ with $J_{\mathrm{eff}}=1/2$ magnetic ${\mathrm{Ru}}^{3+}$ ions to the isotropic Heisenberg magnet ${\mathrm{CrCl}}_3$ with $S=3/2$ magnetic ${\mathrm{Cr}}^{3+}$ ions. Magnetization measurements on single crystals revealed a reversal of the magnetic anisotropy under doping, which we argue to arise from the competition between anisotropic Kitaev and off-diagonal interactions on the Ru-Ru links and approximately isotropic Cr-Ru and isotropic Cr-Cr interactions. In addition, combined magnetization, ac susceptibility, and specific-heat measurements clearly show the destabilization of the long-range magnetic order of $\alpha \text{−}{\mathrm{RuCl}}_3$ in favor of a spin-glass state of ${\mathrm{Ru}}_{1-x}{\mathrm{Cr}}_x{\mathrm{Cl}}_3$ for a low doping of $x\backsimeq 0.1$. The corresponding freezing temperature as a function of Cr content shows a broad maximum around $x\backsimeq 0.45$.

Classifications of symmetry-protected topological (SPT) phases provide a framework to systematically understand the physical properties and potential applications of topological systems. While such classifications have been widely explored in the context of Hermitian systems, a complete understanding of the roles of more general non-Hermitian symmetries and their associated classification is still lacking. Here, we derive a periodic table for noninteracting SPTs with general non-Hermitian symmetries. Our analysis reveals additional non-Hermitian topological classes, while also naturally incorporating the entire classification of Hermitian systems as a special case of our scheme. Building on top of these results, we derive two independent generalizations of Kramers theorem to the non-Hermitian setting, which constrain the spectra of the system and lead to different topological invariants. To elucidate the physics behind the periodic table, we provide explicit constructions of non-Hermitian topological invariants, focusing on the symmetry classes in zero, one, and two dimensions with non-Hermitian topological classifications beyond those previously discussed (e.g., $\mathbb{Z}$ in zero dimensions, ${\mathbb{Z}}_2$ in one and two dimensions). These results thus provide a framework for the design and engineering of non-Hermitian symmetry-protected topological systems.

We performed in situ magnetoresistance measurements in the ultrahigh-vacuum environment to reveal the quantum phase transitions of single unit-layer $\mathrm{NbS}{\mathrm{e}}_2$ epitaxially grown on bilayer graphene. It was found that the superconductor-normal state transition caused by the surface-normal magnetic field was intermediated by a quasimetallic state. This behavior is consistent with the “Bose metal” picture where a finite dissipation is caused by the breaking of phase coherence due to strong gauge-field fluctuation. On one hand, around the mean-field critical temperature, the onset of transition from the normal state to the low-temperature states was governed by the amplitude-fluctuation effect, prominently under the magnetic field. We applied scaling theories to determine the phase boundaries. The result of scaling analyses revealed a complex but essential phase diagram of the single unit-layer $\mathrm{NbS}{\mathrm{e}}_2$ as a two-dimensional superconductor.

Entanglement Hamiltonian holds crucial clues in understanding quantum entanglement and its underlying phenomenon in strongly correlated systems. To date, however, a generic recipe to map out the operator form of entanglement Hamiltonian remains outstanding. Here, we present a systematic framework which explicitly reconstructs entanglement Hamiltonian based on the information of one entangled mode of the reduced density matrix. We demonstrate its successful application to quantum spin lattice models. The obtained entanglement Hamiltonians accurately recover the expectations from analytical theories and faithfully capture all features of the reduced density matrices, which are evidenced by the agreement between the original and reconstructed full entanglement spectra and the high density matrix fidelity.

We demonstrate that achiral electric-dipole scatterers can mimic an interaction of light with chiral matter by generating far-field circular polarization upon scattering, even though the optical chirality of the incident field as well as that of the scattered light is zero. On the one hand, the presented effect originates from the fact that electric-dipole scatterers respond selectively only to the incident electric field, which eventually results in depolarization of the transmitted beam and in generation of far-field circular polarization. On the other hand, although the incident beam does not possess any optical chirality, it lacks reflection symmetry and therefore it is geometrically chiral. To experimentally demonstrate this effect, we utilize a cylindrical vector beam with spiral polarization and a spherical gold nanoparticle positioned on the optical axis—the axis of rotational symmetry of the system. Our experiment and a simple theoretical model address the fundamentals of duality symmetry in optics and chiral light-matter interactions, accentuating their richness and ubiquity yet in highly symmetric configurations.

The domain wall response under constant external magnetic fields reveals a complex behavior where sample disorder plays a key role. Furthermore, the response to alternating magnetic fields has only been explored in limited cases and analyzed in terms of the constant field solution. Here we unveil phenomena in the evolution of magnetic domain walls under the application of alternating magnetic fields within the creep regime, well beyond a small fluctuation limit of the domain wall position. Magnetic field pulses were applied in ultrathin ferromagnetic films with perpendicular anisotropy, and the resulting domain wall evolution was characterized by polar magneto-optical Kerr effect microscopy. Whereas the dc characterization is well predicted by the elastic interface model, striking unexpected features are observed under the application of alternating square pulses: Magneto-optical images show that after a characteristic number of cycles, domain walls evolve toward strongly distorted shapes concomitantly with a modification of domain area. The morphology of domain walls is characterized with a roughness exponent when possible and contrasted with alternative observables which are more suitable for the characterization of this transient evolution. The final stationary convergence as well as the underlying physics is discussed.

We propose a universal driving protocol for the realization of symmetry-protected topological phases in $2+1$-dimensional Floquet systems. Our proposal is based on the theoretical analysis of the possible symmetries of a square lattice model with pairwise nearest-neighbor coupling terms. Among the eight possible symmetry operators we identify the two relevant choices for topological phases with either time-reversal, chiral, or particle-hole symmetry. From the corresponding symmetry conditions on the protocol parameters, we obtain the universal driving protocol where each of the symmetries can be realized or broken individually. We provide specific parameter values for the different cases, and demonstrate the existence of symmetry-protected copropagating and counterpropagating topological boundary states. The driving protocol especially allows us to switch between bosonic and fermionic time-reversal symmetry, and thus between a trivial and nontrivial symmetry-protected topological phase, through continuous variation of a parameter.

We have developed a multiscale computational scheme to describe coupled nonlinear dynamics of light electromagnetic field, electrons, and lattice motions in crystalline solids, where first-principles molecular dynamics based on time-dependent density-functional theory is used to describe the microscopic dynamics. The method is applicable to wide phenomena in nonlinear and ultrafast optics. To show usefulness of the method, we apply it to a pump-probe measurement of coherent phonon in diamond where a stimulated Raman wave is generated and amplified during the propagation of the probe pulse.

We define and study the Pfaffian state on Riemann surfaces with arbitrary metrics and an inhomogeneous magnetic field and derive its universal transport coefficients. Following a path integral approach, we compute the generating functional which encodes the linear response of the system to a variation of the background metric and the magnetic field and use it to compute the leading and subleading corrections to the charge density in a large-$N$ expansion. We also present a derivation of gravitational anomaly contribution at $O\left(k^6\right)$ to the static structure factor for the Pfaffian state in the long wavelength limit.

Correlated insulators and superconductivity have been observed in “magic-angle” twisted bilayer graphene, when the nearly flat bands close to neutrality are partially filled. While a momentum-space continuum model accurately describes these flat bands, interaction effects are more conveniently incorporated in tight-binding models. We have previously shown that no fully symmetric tight-binding model can be minimal, in the sense of capturing just the flat bands, so extended models are unavoidable. Here, we introduce a family of tight-binding models that capture the flat bands while simultaneously retaining all symmetries. In particular, we construct three concrete models with five, six, or ten bands per valley and per spin. These models are also faithful, in that the additional degrees of freedom represent energy bands further away from neutrality, and they serve as optimal starting points for a controlled study of interaction effects. Furthermore, our construction demonstrates the “fragile topology” of the nearly flat bands; i.e., the obstruction to constructing exponentially localized Wannier functions can be resolved when a particular set of trivial bands is added to the model.

Formation of electronic nematicity is a common thread of unconventional superconductors. We use ultrafast electron diffraction to probe the lattice interactions with electronic degrees of freedom in superconducting FeSe and find a significant lattice response to local nematicity. We observe that a perturbation by a laser pulse leads to a surprising enhancement of the high-symmetry crystalline order as a result of suppression of low-symmetry local lattice distortions, which are signatures of nematic fluctuations. The distortions are present at temperatures both below and above the nematic phase transition, as corroborated by our x-ray pair distribution function analysis and transmission electron microscopy measurements. Nonequilibrium lattice behavior of FeSe reveals two distinct time scales of nematic response to photoexcitation, 130(20) and 40(10) ps, corresponding to diffusive and percolative dynamics of nematic fluctuations respectively.

Bulk studies have revealed a first-order valence phase transition in ${\mathrm{Ba}}_2{\mathrm{PrRu}}_{1-x}{\mathrm{Ir}}_x{\mathrm{O}}_6$ ($0.10\le x\le 0.25$), which is absent in the parent compounds with $x=0$ (${\mathrm{Pr}}^{3+}$) and $x=1$ (${\mathrm{Pr}}^{4+}$), which exhibit antiferromagnetic order with transition temperatures $T_{\mathrm{N}}=120$ and 72 K, respectively. In the present study, we have used magnetization, heat capacity, neutron diffraction, inelastic neutron scattering, and x-ray absorption measurements to investigate the nature of the Pr ion in $x=0.1$. The magnetic susceptibility and heat capacity of $x=0.1$ show a clear sign of the first-order valence phase transition below 175 K, where the Pr valence changes from 3+ to 4+. Neutron diffraction analysis reveals that $x=0.1$ crystallizes in a monoclinic structure with space group $P{2}_1/n$ at 300 K, but below 175 K two phases coexist, the monoclinic having the Pr ion in a 3+ valence state and a cubic one ($Fm\overline{3}m$) having the Pr ion in a 4+ valence state. Clear evidence of an antiferromagnetic ordering of the Pr and Ru moments is found in the monoclinic phase of the $x=0.1$ compound below 110 K in the neutron diffraction measurements. Meanwhile, the cubic phase remains paramagnetic down to 2 K, a temperature below which heat capacity and susceptibility measurements reveal a ferromagnetic ordering. High energy inelastic neutron scattering data reveal well-defined high-energy magnetic excitations near 264 meV at temperatures below the valence transition. Low energy INS data show a broad magnetic excitation centered at 50 meV above the valence transition, but four well-defined magnetic excitations at 7 K. The high energy excitations are assigned to the ${\mathrm{Pr}}^{4+}$ ions in the cubic phase and the low energy excitations to the ${\mathrm{Pr}}^{3+}$ ions in the monoclinic phase. Further direct evidence of the Pr valence transition has been obtained from the x-ray absorption spectroscopy. The results on the $x=0.1$ compound are compared with those for $x=0$ and 1.

In (2+1)-dimensional materials, nonlocal topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries (e.g., time reversal ${\mathcal{T}}^2=+1$). Additionally, they support topologically protected spin-1 edge states, which are fundamentally different than spin-$\frac{1}{2}$ and pseudo-spin-$\frac{1}{2}$ edge states arising in fermionic and pseudofermionic systems. The striking feature of the edge state is that all electric and magnetic field components vanish at the boundary, in stark contrast to analogs of Jackiw-Rebbi domain wall states. This surprising open boundary solution of Maxwell's equations, dubbed the quantum gyroelectric effect [Phys. Rev. A 98, 023842 (2018)], is the supersymmetric partner of the topological Dirac edge state where the spinor wave function completely vanishes at the boundary. The defining feature of such phases is the presence of temporal and spatial dispersion in conductivity (the linear response function). In this paper, we generalize these topological electromagnetic phases beyond the continuum approximation to the exact lattice field theory of a periodic atomic crystal. To accomplish this, we put forth the concept of microscopic photonic band structure of solids, analogous to the traditional theory of electronic band structure. Our definition of topological invariants utilizes optical Bloch modes and can be applied to naturally occurring crystalline materials. For the photon propagating within a periodic atomic crystal, our theory shows that besides the Chern invariant $\mathfrak{C}\in \mathbb{Z}$, there are also symmetry-protected topological (SPT) invariants $\nu \in {\mathbb{Z}}_N$ which are related to the cyclic point group $C_N$ of the crystal $\nu =\mathfrak{C}modN$. Due to the rotational symmetries of light $\mathcal{R}\left(2\pi \right)=+1$, these SPT phases are manifestly bosonic and behave very differently from their fermionic counterparts $\mathcal{R}\left(2\pi \right)=-1$ encountered in conventional condensed-matter systems. Remarkably, the nontrivial bosonic phases $\nu \ne 0$ are determined entirely from rotational (spin-1) eigenvalues of the photon at high-symmetry points in the Brillouin zone. Our work accelerates progress toward the discovery of bosonic phases of matter where the electromagnetic field within an atomic crystal exhibits topological properties.

The moiré superlattice formed by ABC stacked trilayer graphene aligned with a hexagonal boron nitride substrate (TG/h-BN) provides an interesting system where both the bandwidth and the topology can be tuned by an applied perpendicular electric field $D$. Thus the TG/h-BN system can simulate both Hubbard model physics and nearly flat Chern band physics within one sample. We derive lattice models for both signs of $D$ (which controls the band topology) separately through explicit Wannier orbital construction and mapping of Coulomb interaction. When the bands are topologically trivial, we discuss possible candidates for Mott insulators at integer number of holes per site (labeled as ${\nu }_T$). These include both broken symmetry states and quantum spin liquid insulators which may be particularly favorable in the vicinity of the Mott transition. We propose feasible experiments to study carefully the bandwidth tuned and the doping tuned Mott metal-insulator transition at both ${\nu }_T=1$ and ${\nu }_T=2$. We discuss the interesting possibility of probing experimentally a bandwidth (or doping) controlled continuous Mott transition between a Fermi liquid metal and a quantum spin liquid insulator. Finally we also show that the system has a large valley Zeeman coupling to a small out-of-plane magnetic field, which can be used to control the valley degree of freedom.

Resistivity measurements of ${\mathrm{TiSe}}_2$ typically show only a weak change in gradient at the charge density wave transition at $T_{\mathrm{CDW}}\approx 200\mathrm{K}$, but more prominently feature a broad peak at a lower $T_{\mathrm{peak}}\sim 165\mathrm{K}$, which has remained poorly understood despite decades of research on the material. Here we present quantitative simulations of the resistivity using a simplified parametrization of the normal state band structure, based on recent photoemission data. Our simulations reproduce the overall profile of the resistivity of ${\mathrm{TiSe}}_2$, including its prominent peak, without implementing the CDW at all. We find that the peak in resistivity corresponds to a crossover between a low-temperature regime with electronlike carriers only, to a regime around room temperature where thermally activated and highly mobile holelike carriers dominate the conductivity. Even when implementing substantial modifications to model the CDW below the transition temperature, we find that these thermal population effects still dominate the transport properties of ${\mathrm{TiSe}}_2$.

A prominent feature of some one-dimensional non-Hermitian systems is that all right eigenstates of the non-Hermitian Hamiltonian are localized in one end of the chain. The topological and trivial phases are distinguished by the emergence of zero-energy modes within the skin states in the presence of chiral symmetry. Skin states are formed when the system is nonreciprocal, where it is said to be nonreciprocal if the absolute values of the right- and left-going hopping amplitudes are different. Indeed, zero-energy edge modes emerge at both edges in the topological phase of a reciprocal non-Hermitian system. Then, analyzing higher-order topological insulators in nonreciprocal systems, we find the emergence of topological zero-energy modes within the skin states formed in the vicinity of one corner. Explicitly, we explore the anisotropic honeycomb model in two dimensions and the diamond lattice model in three dimensions. We also study an electric-circuit realization of these systems. Electrical circuits with (without) diodes realize nonreciprocal (reciprocal) non-Hermitian topological systems. Topological phase transitions are observable by measuring the impedance resonance due to zero-admittance topological corner modes.

We map the dynamics of entanglement in random unitary circuits, with finite onsite Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary circuits. We demonstrate explicitly the emergence of a “minimal membrane” governing entanglement growth, which in 1+1 dimensions is a directed random walk in spacetime (or a variant thereof). Using the replica trick to handle the logarithm in the definition of the $n\mathrm{th}$ Rényi entropy, $S_n$, we map the calculation of the entanglement after a quench to a problem of interacting random walks. A key role is played by effective classical spins (taking values in a permutation group) which distinguish between different ways of pairing spacetime histories in the replicated system. For the second Rényi entropy, $S_2$, we are able to take the replica limit explicitly. This gives a mapping between entanglement growth and a directed polymer in a random medium at finite temperature (confirming Kardar-Parisi-Zhang scaling for entanglement growth in generic noisy systems). We find that the entanglement growth rate (“speed”) $v_n$ depends on the Rényi index $n$, and we calculate $v_2$ and $v_3$ in an expansion in the inverse local Hilbert space dimension, $1/q$. These rates are determined by the free energy of a random walk and of a bound state of two random walks, respectively, and include contributions of “energetic” and “entropic” origin. We give a combinatorial interpretation of the Page-like subleading corrections to the entanglement at late times and discuss the dynamics of the entanglement close to and after saturation. We briefly discuss the application of these insights to time-independent Hamiltonian dynamics.

Optical dual-pulse pumping actively creates quantum-mechanical superposition of the electronic and phononic states in a bulk solid. We here made transient reflectivity measurements in an $n$-GaAs using a pair of relative-phase-locked femtosecond pulses and found characteristic interference fringes. This is a result of quantum-path interference peculiar to the dual-pulse excitation as indicated by theoretical calculation. Our observation reveals that the pathway of coherent phonon generation in the $n$-GaAs is impulsive stimulated Raman scattering at the displaced potential due to the surface-charge field, even though the photon energy lies in the opaque region.