The current work presents a natural orbital functional (NOF) for electronic systems with any spin value independent of the external potential being considered, that is, a global NOF (GNOF). It is based on a new two-index reconstruction of the two-particle reduced density matrix for spin multiplets. The emergent functional describes the complete intrapair electron correlation, and the correlation between orbitals that make up both the pairs and the individual electrons. The interorbital correlation is composed of static and dynamic terms. The concept of dynamic part of the occupation numbers is introduced. To evaluate the accuracy achieved with the GNOF, calculation of a variety of properties is presented. They include the total energies and energy differences between the ground state and the lowest-lying excited state with different spin of atoms from H to Ne, ionization potentials of the first-row transition-metal atoms (Sc-Zn), and the total energies of a selected set of 55 molecular systems in different spin states. The GNOF is also applied to the homolytic dissociation of selected diatomic molecules in different spin states and to the rotation barrier of ethylene, both paradigmatic cases of systems with significant multiconfigurational character. The values obtained agree with those reported at high level of theory and experimental data.

In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Nevertheless, whether the nonzero Chern number ($C\ne 0$) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed $C=2$ phase [Deng et al., Science 367, 895 (2020)]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with $C=1$. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a $C=2$ phase. Eventually, we present a phase diagram of a disordered ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ which indicates more coexistence states of QAH and QH to be verified by future experiments.

We prove the Lieb-Schultz-Mattis theorem on the energy spectrum of a general two- or three-dimensional quantum many-body system with the U(1) particle number conservation and translation symmetry. Especially, it is demonstrated that the theorem holds in a system with long-range interactions. To this end, we introduce approximate magnetic translation symmetry under the total magnetic flux $\mathrm{\Phi }=2\pi$ instead of the exact translation symmetry, and explicitly construct low energy variational states. The energy spectrum at $\mathrm{\Phi }=2\pi$ is shown to agree with that at $\mathrm{\Phi }=0$ in the thermodynamic limit, which concludes the Lieb-Schultz-Mattis theorem.

Symmetry and topology govern many electronic, magnetic, and photonic phenomena in condensed matter physics and optics, resulting in counterintuitive skyrmion, meron, and other phenomena important for modern technologies. Here we demonstrate photonic spin lattices as a new topological construct governed by the spin-orbit coupling in an optical field. The symmetry of the electromagnetic field in the presence of the spin-orbit interaction may result in only two types of photonic spin lattices: either hexagonal spin-skyrmion or square spin-meron lattices. We show that these spin structures correspond to the lowest energy of the electromagnetic field configuration, therefore, energetically stable. We further show that in the absence of spin-orbit coupling these spin topologies are degenerated in dynamic field skyrmions, unifying the description of electromagnetic field topologies. The results provide a new understanding of electromagnetic field topology and its transformations as well as new opportunities for applications in quantum technologies, spin optics, and topological photonics.

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.

We discuss spontaneously broken quantum field theories with a continuous global symmetry group via the constraint effective potential. Employing lattice simulations with constrained values of the order parameter, we demonstrate explicitly that the path integral is dominated by inhomogeneous field configurations and that these are unambiguously related to the flatness of the effective potential in the broken phase. We determine characteristic features of these inhomogeneities, including their topology and the scaling of the associated excess energy with their size. Concerning the latter we introduce the differential surface tension—the generalization of the concept of a surface tension pertaining to discrete symmetries. Within our approach, spontaneous symmetry breaking is captured merely via the existence of inhomogeneities, i.e., without the inclusion of an explicit breaking parameter and a careful double limiting procedure to define the order parameter. While here we consider the three-dimensional O(2) model, we also elaborate on possible implications of our findings for the chiral limit of QCD.

The Rashba-Dresselhaus effect is the splitting of doubly degenerate band extrema in semiconductors, accompanied by the emergence of counterrotating spin textures and spin-momentum locking. Here we investigate how this effect is modified by lattice vibrations. We show that, in centrosymmetric nonmagnetic crystals, for which a bulk Rashba-Dresselhaus effect is symmetry-forbidden, electron-phonon interactions can induce a phonon-assisted, dynamic Rashba-Dresselhaus spin splitting in the presence of an out-of-equilibrium phonon population. In particular, we show how Rashba, Dresselhaus, or Weyl spin textures can selectively be established by driving coherent infrared-active phonons, and we perform ab initio calculations to quantify this effect for halide perovskites.

We develop a variational approach to simulating the dynamics of open quantum many-body systems using deep autoregressive neural networks. The parameters of a compressed representation of a mixed quantum state are adapted dynamically according to the Lindblad master equation by employing a time-dependent variational principle. We illustrate our approach by solving the dissipative quantum Heisenberg model in one dimension for up to 40 spins and in two dimensions for a $4\times 4$ system and by applying it to the simulation of confinement dynamics in the presence of dissipation.

We employ ($1+1$)-dimensional quantum cellular automata to study the evolution of entanglement and coherence near criticality in quantum systems that display nonequilibrium steady-state phase transitions. This construction permits direct access to the entire space-time structure of the underlying nonequilibrium dynamics, and allows for the analysis of unconventional correlations, such as entanglement in the time direction between the “present” and the “past.” We show how the uniquely quantum part of these correlations—the coherence—can be isolated and that, close to criticality, its dynamics displays a universal power-law behavior on approach to stationarity. Focusing on quantum generalizations of classical nonequilibrium systems: the Domany-Kinzel cellular automaton and the Bagnoli-Boccara-Rechtman model, we estimate the universal critical exponents for both the entanglement and coherence. As these models belong to the one-dimensional directed percolation universality class, the latter provides a key new critical exponent, one that is unique to quantum systems.

We report on a rigorous operator-algebraic renormalization group scheme and construct the free field with a continuous action of translations as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets. Causality follows from Lieb-Robinson bounds for harmonic lattice systems. The scheme is related with the multiscale entanglement renormalization ansatz and augments the semicontinuum limit of quantum systems.

We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response correlation functions, and find that their characteristic timescales are given by the inverse gap of an effective Hamiltonian—or equivalently, a transfer matrix describing a classical Markov process. Our approach allows us to connect directly the Thouless time, $t_{\text{Th}}$, determined by the spectral form factor, to transport properties and linear-response correlators. Using tensor network methods, we determine the dynamical exponent $z$ for a number of constrained, conserving models. We find universality classes with diffusive, subdiffusive, quasilocalized, and localized dynamics, depending on the severity of the constraints. In particular, we show that quantum systems with “Fredkin” constraints exhibit anomalous transport with dynamical exponent $z\simeq 8/3$.

Cosmology relies on a coarse-grained description of the universe, assumed to be valid on large length scales. However, the nonlinearity of general relativity makes coarse graining extremely difficult. We here address this problem by extending the Mori-Zwanzig projection operator formalism, a highly successful coarse-graining method from statistical mechanics, towards general relativity. Using the Buchert equations, we derive a new dynamic equation for the Hubble parameter which captures the effects of averaging through a memory function. This gives an empirical prediction for the cosmic jerk.

We analyze the “vacuum” polarization induced by a quantum charged scalar field near the inner horizon of a charged black hole in quantum states evolving from arbitrary regular in states. Contrary to naive expectations, we find that near an inner horizon, the transversal component of the expected current density can have either sign depending on the black hole and field parameters. Thus, the inner horizon can be charged or discharged. But we find that it is always discharged close to extremality. We also find that quantum effects dominate in that the strength of the blow up of the quantum current at the inner horizon is state independent and stronger than that of the current of a classical solution.

Determining the ultimate precision limit for measurements on a subwavelength particle with coherent laser light is a goal with applications in areas as diverse as biophysics and nanotechnology. Here, we demonstrate that surrounding such a particle with a complex scattering environment does, on average, not have any influence on the mean quantum Fisher information associated with measurements on the particle. As a remarkable consequence, the average precision that can be achieved when estimating the particle’s properties is the same in the ballistic and in the diffusive scattering regime, independently of the particle’s position within its nonabsorbing environment. This invariance law breaks down only in the regime of Anderson localization, due to increased $C_0$-speckle correlations. Finally, we show how these results connect to the mean quantum Fisher information achievable with spatially optimized input fields.

Enantiomer separation opens great opportunities to develop the technologies of pharmaceutics, chemicals, and biomedicine, but faces daunting challenges. Here, we discover a considerable chiral-dependent trapping force to separate nanometer-scale enantiomers in a new silicon-based waveguide platform. The electromagnetic chirality gradient of strongly confined evanescent fields can be largely enhanced by the counterpropagating slot waveguides so that the resulting chiral gradient forces can shift the trapping equilibrium positions of dielectric gradient forces. Especially, there exists a transitional width for the slot waveguides to exchange the trapping equilibrium positions between two opposite enantiomers. Our thoroughly numerical investigations demonstrate that the chiral-separable slot waveguides here can offer high efficiency and feasibility of separating chiral nanoparticles, and may pave a route toward new on-chip chiral optical tweezers or optofluidic transport systems for large-scale chiral separation.

Understanding how atoms interact with hot dense matter is essential for astrophysical and laboratory plasmas. Interactions in high-density plasmas broaden spectral lines, providing a rare window into interactions that govern, for example, radiation transport in stars. However, up to now, spectral line-shape theories employed at least one of three common approximations: second-order Taylor treatment of broadening operator, dipole-only interactions between atom and plasma, and classical treatment of perturbing electrons. In this Letter, we remove all three approximations simultaneously for the first time and test the importance for two applications: neutral hydrogen and highly ionized magnesium and oxygen. We found 15%–50% change in the spectral line widths, which are sufficient to impact applications including white-dwarf mass determination, stellar-opacity research, and laboratory plasma diagnostics.

Fast ion phase-space flow, driven by Alfvén eigenmodes (AEs), is measured by an imaging neutral particle analyzer in the DIII-D tokamak. The flow firstly appears near the minimum safety factor at the injection energy of neutral beams, and then moves radially inward and outward by gaining and losing energy, respectively. The flow trajectories in phase space align well with the intersection lines of the constant magnetic moment surfaces and constant $E-(\omega /n)P_{\zeta }$ surfaces, where $E$, $P_{\zeta }$ are the energy and canonical toroidal momentum of ions; $\omega$ and $n$ are angular frequencies and toroidal mode numbers of AEs. It is found that the flow is so destructive that the thermalization of fast ions is no longer observed in regions of strong interaction. The measured phase-space flow is consistent with nonlinear hybrid kinetic-magnetohydrodynamics simulation. Calculations of the relatively narrow phase-space islands reveal that fast ions must transition between different flow trajectories to experience large-scale phase-space transport.