A notable phenomenon in topological semimetals is the violation of Kohler’s rule, which dictates that the magnetoresistance MR obeys a scaling behavior of $\mathrm{MR}=f(H/{\rho }_0)$, where $\mathrm{MR}=[\rho (H)-{\rho }_0]/{\rho }_0$ and $H$ is the magnetic field, with $\rho (H)$ and ${\rho }_0$ being the resistivity at $H$ and zero field, respectively. Here, we report a violation originating from thermally induced change in the carrier density. We find that the magnetoresistance of the Weyl semimetal TaP follows an extended Kohler’s rule $\mathrm{MR}=f[H/(n_T{\rho }_0)]$, with $n_T$ describing the temperature dependence of the carrier density. We show that $n_T$ is associated with the Fermi level and the dispersion relation of the semimetal, providing a new way to reveal information on the electronic band structure. We offer a fundamental understanding of the violation and validity of Kohler’s rule in terms of different temperature responses of $n_T$. We apply our extended Kohler’s rule to ${\mathrm{BaFe}}_2{({\mathrm{As}}_{1-x}{\mathrm{P}}_x)}_2$ to settle a long-standing debate on the scaling behavior of the normal-state magnetoresistance of a superconductor, namely, $\mathrm{MR}\sim {\tan }^2{\theta }_H$, where ${\theta }_H$ is the Hall angle. We further validate the extended Kohler’s rule and demonstrate its generality in a semiconductor, InSb, where the temperature-dependent carrier density can be reliably determined both theoretically and experimentally.

Engineering quantum phases using light is a novel route to designing functional materials, where light-induced superconductivity is a successful example. Although this phenomenon has been realized experimentally, especially for the high-$T_c$ cuprates, the underlying mechanism remains mysterious. Using the recently developed variational non-Gaussian exact diagonalization method, we investigate a particular type of photoenhanced superconductivity by suppressing a competing charge order in a strongly correlated electron-electron and electron-phonon system. We find that the $d$-wave superconductivity pairing correlation can be enhanced by a pulsed laser, consistent with recent experiments based on gap characterizations. However, we also find that the pairing correlation length is heavily suppressed by the pump pulse, indicating that light-enhanced superconductivity may be of fluctuating nature. Our findings also imply a general behavior of nonequilibrium states with competing orders, beyond the description of a mean-field framework.

We develop a fundamental theory of the long-range electrostatic interactions in two-dimensional crystals by performing a rigorous study of the nonanalyticities of the Coulomb kernel. We find that the dielectric functions are best represented by $2\times 2$ matrices, with nonuniform macroscopic potentials that are two-component hyperbolic functions of the out-of-plane coordinate $z$. We demonstrate our arguments by deriving the long-range interatomic forces in the adiabatic regime, where we identify a formerly overlooked dipolar coupling involving the out-of-plane components of the dynamical charges. The resulting formula is exact up to an arbitrary multipolar order, which we illustrate in practice via the explicit inclusion of dynamical quadrupoles. By performing numerical tests on monolayer BN, ${\mathrm{SnS}}_2$, and ${\mathrm{BaTiO}}_3$ membranes, we show that our method allows for a drastic improvement in the description of the long-range electrostatic interactions, with comparable benefits to the quality of the interpolated phonon band structure.

Upon femtosecond-laser stimulation, generally materials are expected to recover back to their thermal-equilibrium conditions, with only a few exceptions reported. Here, we demonstrate that deviation from the thermal-equilibrium pathway can be induced in canonical 3D antiferromagnetically (AFM) ordered ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$ by a single 100-fs-laser pulse, appearing as losing long-range magnetic correlation along one direction into a glassy condition. We further discover a “critical-threshold ordering” behavior for fluence above approximately $12\mathrm{mJ}/{\mathrm{cm}}^2$, which we show corresponds to the smallest thermodynamically stable $c$-axis correlation length needed to maintain long-range quasi-two-dimensional AFM order. We suggest that this behavior arises from the crystalline anisotropy of the magnetic-exchange parameters in ${\mathrm{Sr}}_2{\mathrm{IrO}}_4$, whose strengths are associated with distinctly different timescales. As a result, they play out very differently in the ultrafast recovery processes, compared with the thermal-equilibrium evolution. Thus, our observations are expected to be relevant to a wide range of problems in the nonequilibrium behavior of low-dimensional magnets and other related ordering phenomena.

The spin-$1/2$ Heisenberg model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram. Besides hosting several ordered phases, the model is debated to possess a spin-liquid ground state when only nearest-neighbor antiferromagnetic interactions are present. Here, we contest this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employ a resonating-valence-bond-like, many-variable, Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to $4\times 4^3$ and $4\times 3^3$ spins, respectively. We demonstrate that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. We consider the $(\lambda ,j_2/j_1)$ parameter space, with $j_2$, $j_1$ being nearest and next-to-nearest neighbor interactions and $\lambda$ the $XXZ$ interaction anisotropy. Our main results are (1) the determination of the phase transition between the putative spin-liquid phase and the neighboring magnetically ordered phase and (2) a careful characterization of the ground state in terms of symmetry-breaking tendencies. We find clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless quantum spin liquid into question. Our work showcases how many-variable variational techniques can be used to make progress in answering challenging questions about three-dimensional frustrated quantum magnets.

Dynamical phase transitions extend the notion of criticality to nonstationary settings and are characterized by sudden changes in the macroscopic properties of time-evolving quantum systems. Investigations of dynamical phase transitions combine aspects of symmetry, topology, and nonequilibrium physics; however, progress has been hindered by the notorious difficulties of predicting the time evolution of large, interacting quantum systems. Here, we tackle this outstanding problem by determining the critical times of interacting many-body systems after a quench using Loschmidt cumulants. Specifically, we investigate dynamical topological phase transitions in the interacting Kitaev chain and in the spin-1 Heisenberg chain. To this end, we map out the thermodynamic lines of complex times, where the Loschmidt amplitude vanishes, and identify the intersections with the imaginary axis, which yield the real critical times after a quench. For the Kitaev chain, we can accurately predict how the critical behavior is affected by strong interactions, which gradually shift the time at which a dynamical phase transition occurs. We also discuss the experimental perspectives of predicting the first critical time of a quantum many-body system by measuring the energy fluctuations in the initial state, and we describe the prospects of implementing our method on a near-term quantum computer with a limited number of qubits. Our work demonstrates that Loschmidt cumulants are a powerful tool to unravel the far-from-equilibrium dynamics of strongly correlated many-body systems, and our approach can immediately be applied in higher dimensions.

The Fermi-polaron problem of a mobile impurity interacting with fermionic medium emerges in various contexts, ranging from the foundations of Landau’s Fermi-liquid theory to electron-exciton interaction in semiconductors, to unusual properties of high-temperature superconductors. While classically the medium provides only a dissipative environment to the impurity, the quantum picture of polaronic dressing is more intricate and arises from the interplay of few- and many-body aspects of the problem. The conventional expectation for the dynamics of Fermi polarons is that it is dissipative in character, and any excess energy is rapidly emitted away from the impurity as particle-hole excitations. Here we report a strikingly different type of polaron dynamics in a one-dimensional system of the impurity interacting repulsively with the fermions. When the total momentum of the system equals the Fermi momentum, there emerges a sharp collective mode corresponding to long-lived oscillations of the polaronic cloud surrounding the impurity. This mode can be observed experimentally with ultracold atoms using Ramsey interferometry and radio-frequency spectroscopy.

The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming a magnetic insulator at strong coupling. In this multimethod study, we combine a finite-temperature tensor network method, minimally entangled thermal typical states (METTS), with two Green-function-based methods, connected-determinant diagrammatic Monte Carlo and cellular dynamical mean-field theory, to establish several aspects of this model. We elucidate the evolution from the metallic to the insulating regime from the complementary perspectives brought by these different methods. We compute the full thermodynamics of the model on a width-four cylinder using METTS in the intermediate to strong coupling regime. We find that the insulating state hosts a large entropy at intermediate temperatures, which increases with the strength of the coupling. Correspondingly, and consistently with a thermodynamic Maxwell relation, the double occupancy has a minimum as a function of temperature which is the manifestation of the Pomeranchuk effect of increased localization upon heating. The intermediate coupling regime is found to exhibit both pronounced chiral as well as stripy antiferromagnetic spin correlations. We propose a scenario in which time-reversal symmetry-broken states compete with stripy-spin states at lowest temperatures.

Recently discovered $Z_2$ topological kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) exhibit charge-density-wave (CDW) phases and novel superconducting paring states providing a versatile platform for studying the interplay between electron correlation and quantum orders. Here we directly visualize CDW-induced bands renormalization and energy gaps in ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$ using angle-resolved photoemission spectroscopy pointing to the key role of tuning van Hove singularities to the Fermi energy in mechanisms of ordering phases. Near the CDW transition temperature, the bands around the Brillouin zone (BZ) boundary are shifted to high-binding energy, forming an $\mathsf{M}$-shaped band with singularities near the Fermi energy. The Fermi surfaces are partially gapped, and the electronic states on the residual ones should be possibly dedicated to the superconductivity. Our findings are significant in understanding CDW formation and its associated superconductivity.

Motivated by recent core-level x-ray photoemission spectroscopy, x-ray absorption spectroscopy (XAS), and resonant inelastic x-ray scattering (RIXS) experiments for the newly discovered superconducting infinite-layer nickelate, we investigate the core-level spectra of the parent compounds ${\mathrm{NdNiO}}_2$ and ${\mathrm{LaNiO}}_2$ using the combination of local density approximation and dynamical mean-field theory ($\mathrm{LDA}+\mathrm{DMFT}$). Adjusting a charge-transfer energy to match the experimental spectra, we determine the optimal model parameters and discuss the nature of the ${\mathrm{NdNiO}}_2$ ground state. We find that self-doping from the Nd $5d$ states in the vicinity of the Fermi energy prohibits opening of a Mott-Hubbard gap in ${\mathrm{NdNiO}}_2$. The present Ni $L_3$ XAS and RIXS calculation for ${\mathrm{LaNiO}}_2$ cannot explain the difference from ${\mathrm{NdNiO}}_2$ spectra.

Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the nonperturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In the accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group approach, capable of efficiently evaluating these spectral representations, to compute local three- and four-point correlators of quantum impurity models. The key objects in our scheme are partial spectral functions, encoding the system’s dynamical information. Their computation via numerical renormalization group allows us to simultaneously resolve various multiparticle excitations down to the lowest energies. By subsequently convolving the partial spectral functions with appropriate kernels, we obtain multipoint correlators in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms. We present exemplary results for the connected four-point correlators of the Anderson impurity model, and for resonant inelastic x-ray scattering spectra of related impurity models. Our method can treat temperatures and frequencies—imaginary or real—of all magnitudes, from large to arbitrarily small ones.

The many-body problem is usually approached from one of two perspectives: the first originates from an action and is based on Feynman diagrams, the second is centered around a Hamiltonian and deals with quantum states and operators. The connection between results obtained in either way is made through spectral (or Lehmann) representations, well known for two-point correlation functions. Here, we complete this picture by deriving generalized spectral representations for multipoint correlation functions that apply in all of the commonly used many-body frameworks: the imaginary-frequency Matsubara and the real-frequency zero-temperature and Keldysh formalisms. Our approach separates spectral from time-ordering properties and thereby elucidates the relation between the three formalisms. The spectral representations of multipoint correlation functions consist of partial spectral functions and convolution kernels. The former are formalism independent but system specific; the latter are system independent but formalism specific. Using a numerical renormalization group method described in the accompanying paper, we present numerical results for selected quantum impurity models. We focus on the four-point vertex (effective interaction) obtained for the single-impurity Anderson model and for the dynamical mean-field theory solution of the one-band Hubbard model. In the Matsubara formalism, we analyze the evolution of the vertex down to very low temperatures and describe the crossover from strongly interacting particles to weakly interacting quasiparticles. In the Keldysh formalism, we first benchmark our results at weak and infinitely strong interaction and then reveal the rich real-frequency structure of the dynamical mean-field theory vertex in the coexistence regime of a metallic and insulating solution.

A wave function subject to unitary time evolution and exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement-induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions. To access this competition despite the randomness of single quantum trajectories, we construct an $n$-replica Keldysh field theory for the ensemble average of the $n$th moment of the trajectory projector. A key finding is that this field theory decouples into one set of degrees of freedom that heats up indefinitely, while $n-1$ others can be cast into the form of pure state evolutions generated by an effective non-Hermitian Hamiltonian. This decoupling is exact for free theories, and useful for interacting ones. In particular, we study locally measured Dirac fermions in ($1+1$) dimensions, which can be bosonized to a monitored interacting Luttinger liquid at long wavelengths. For this model, the non-Hermitian Hamiltonian corresponds to a quantum sine-Gordon model with complex coefficients. A renormalization group analysis reveals a gapless critical phase with logarithmic entanglement entropy growth, and a gapped area law phase, separated by a Berezinskii-Kosterlitz-Thouless transition. The physical picture emerging here is a measurement-induced pinning of the trajectory wave function into eigenstates of the measurement operators, which succeeds upon increasing the monitoring rate across a critical threshold.

Under physiological conditions, ballistic long-range transfer of electronic excitations in molecular aggregates is generally expected to be suppressed by noise and dissipative processes. Hence, quantum phenomena are not considered to be relevant for the design of efficient and controllable energy transfer over significant length scales and timescales. Contrary to this conventional wisdom, here we show that the robust quantum properties of small configurations of repeating clusters of molecules can be used to tune energy-transfer mechanisms that take place on much larger scales. With the support of an exactly solvable model, we demonstrate that coherent exciton delocalization and dark states within unit cells can be used to harness dissipative phenomena of varying nature (thermalization, fluorescence, nonradiative decay, and weak intersite correlations) to support classical propagation over macroscopic distances. In particular, we argue that coherent delocalization of electronic excitations over just a few pigments can drastically alter the relevant dissipation pathways that influence the energy-transfer mechanism and thus serve as a molecular control tool for large-scale properties of molecular materials. Building on these principles, we use extensive numerical simulations to demonstrate that they can explain currently not-understood measurements of micron-scale exciton diffusion in nanofabricated arrays of bacterial photosynthetic complexes. Based on these results, we provide quantum design guidelines at the molecular scale to optimize both energy-transfer speed and range over macroscopic distances in artificial light-harvesting architectures.

When interacting motile units self-organize into flocks, they realize one of the most robust ordered states found in nature. However, after 25 years of intense research, the very mechanism controlling the ordering dynamics of both living and artificial flocks has remained unsettled. Here, combining active-colloid experiments, numerical simulations, and analytical work, we explain how flocking liquids heal their spontaneous flows initially plagued by collections of topological defects to achieve long-ranged polar order even in two dimensions. We demonstrate that the self-similar ordering of flocking matter is ruled by a living network of domain walls linking all $\pm 1$ vortices and guiding their annihilation dynamics. Crucially, this singular orientational structure echoes the formation of extended density patterns in the shape of interconnected bow ties. We establish that this double structure emerges from the interplay between self-advection and density gradients dressing each $-1$ topological charge with four orientation walls. We then explain how active Magnus forces link all topological charges with extended domain walls, while elastic interactions drive their attraction along the resulting filamentous network of polarization singularities. Taken together, our experimental, numerical, and analytical results illuminate the suppression of all flow singularities and the emergence of pristine unidirectional order in flocking matter.

Fluctuating superconductivity—vestigial Cooper pairing in the resistive state of a material—is usually associated with low dimensionality, strong disorder, or low carrier density. Here, we report single-particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in the heavily hole-doped cuprate superconductor ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ ($T_c=66\mathrm{K}$) despite the high carrier density. With a sign-problem-free quantum Monte Carlo calculation, we show how a partially flat band at $(\pi ,0)$ can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.

Quantum phase transitions are central to our understanding of why matter at very low temperatures can exhibit starkly different properties upon small changes of microscopic parameters. Accurately locating those transitions is challenging experimentally and theoretically. Here, we show that the antithetic strategy of forcing systems out of equilibrium via sudden quenches provides a route to locate quantum phase transitions. Specifically, we show that such transitions imprint distinctive features in the intermediate-time dynamics, and results after equilibration, of local observables in quantum chaotic spin chains. Furthermore, we show that the effective temperature in the expected thermal-like states after equilibration can exhibit minima in the vicinity of the quantum critical points. We discuss how to test our results in experiments with Rydberg atoms and explore nonequilibrium signatures of quantum critical points in models with topological transitions.

Generalizing the prior work of P. W. Anderson and E. R. Huggins, we show that a “detailed Josephson-Anderson relation” holds for drag on a finite body held at rest in a classical incompressible fluid flowing with velocity $\mathbf{V}$. The relation asserts an exact equality between the instantaneous power consumption by the drag $-\mathbf{F}·\mathbf{V}$ and the vorticity flux across the potential mass current $-(1/2)\int dJ\int {\epsilon }_{ijk}{\mathrm{\Sigma }}_{ij}d{\ell }_k$. Here, ${\mathrm{\Sigma }}_{ij}$ is the flux in the $i$th coordinate direction of the conserved $j$th component of vorticity, and the line integrals over $\mathbf{\ell }$ are taken along streamlines of the potential-flow solution ${\mathbf{u}}_{\varphi }=\mathbf{\nabla }\varphi$ of the ideal Euler equation, carrying mass flux $dJ=\rho {\mathbf{u}}_{\varphi }·d\mathbf{A}$. Drag and dissipation are thus associated with the motion of vorticity relative to this background ideal potential flow solving Euler’s equation. The results generalize the theories of M. J. Lighthill for flow past a body and, in particular, the steady-state relation $(1/2){\epsilon }_{ijk}⟨{\mathrm{\Sigma }}_{jk}⟩={\partial }_i⟨h⟩$, where $h=p+(1/2)|\mathbf{u}{|}^2$ is the generalized enthalpy or total pressure, extends Lighthill’s theory of vorticity generation at solid walls into the interior of the flow. We use these results to explain drag on the body in terms of vortex dynamics, unifying the theories for classical fluids and for quantum superfluids. The results offer a new solution to the “d’Alembert paradox” at infinite Reynolds numbers, provide an explanation for a long-standing puzzle about the experimental conditions required for anomalous turbulent energy dissipation, and imply the necessary and sufficient conditions for turbulent drag reduction.

The combination of nontrivial band topology and symmetry-breaking phases gives rise to novel quantum states and phenomena such as topological superconductivity, quantum anomalous Hall effect, and axion electrodynamics. Evidence of intertwined charge density wave (CDW) and superconducting order parameters has recently been observed in a novel kagome material ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) that features a ${\mathbb{Z}}_2$ topological invariant in the electronic structure. However, the origin of the CDW and its intricate interplay with the topological state has yet to be determined. Here, using hard-x-ray scattering, we demonstrate a three-dimensional CDW with $2\times 2\times 2$ superstructure in $(\mathrm{Rb},\mathrm{Cs}){\mathrm{V}}_3{\mathrm{Sb}}_5$. Unexpectedly, we find that the CDW fails to induce acoustic phonon anomalies at the CDW wave vector but yields a novel Raman mode that quickly damps into a broad continuum below the CDW transition temperature. Our observations exclude strong electron-phonon-coupling-driven CDW in ${A\mathrm{V}}_3{\mathrm{Sb}}_5$ and support an unconventional CDW that was proposed in the kagome lattice at van Hove filling.

The search for topological spin excitations in recently discovered two-dimensional (2D) van der Waals (vdW) magnetic materials is important because of their potential applications in dissipationless spintronics. In the 2D vdW ferromagnetic (FM) honeycomb lattice ${\mathrm{CrI}}_3$ ($T_C=61\mathrm{K}$), acoustic and optical spin waves are found to be separated by a gap at the Dirac points. The presence of such a gap is a signature of topological spin excitations if it arises from the next-nearest-neighbor (NNN) Dzyaloshinskii-Moriya (DM) or bond-angle-dependent Kitaev interactions within the Cr honeycomb lattice. Alternatively, the gap is suggested to arise from an electron correlation effect not associated with topological spin excitations. Here, we use inelastic neutron scattering to conclusively demonstrate that the Kitaev interactions and electron correlation effects cannot describe spin waves, Dirac gaps, and their in-plane magnetic field dependence. Our results support the idea that the DM interactions are the microscopic origin of the observed Dirac gap. Moreover, we find that the nearest-neighbor (NN) magnetic exchange interactions along the $c$ axis are antiferromagnetic (AF), and the NNN interactions are FM. Therefore, our results unveil the origin of the observed $c$-axis AF order in thin layers of ${\mathrm{CrI}}_3$, firmly determine the microscopic spin interactions in bulk ${\mathrm{CrI}}_3$, and provide a new understanding of topology-driven spin excitations in 2D vdW magnets.