The exponential growth or decay with time of the out-of-time-order commutator (OTOC) is one widely used diagnostic of many-body chaos in spatially extended systems. In studies of many-body classical chaos, it has been noted that one can define a velocity-dependent Lyapunov exponent, $\lambda \left(\mathbf{v}\right)$, which is the growth or decay rate along rays at that velocity. We examine the behavior of $\lambda \left(\mathbf{v}\right)$ for a variety of many-body systems, both chaotic and integrable. The so-called light cone for the spreading of operators is defined by $\lambda \left(\widehat{\mathbf{n}}{v}_B\left(\widehat{\mathbf{n}}\right)\right)=0$, with a generally direction-dependent butterfly speed $v_B\left(\widehat{\mathbf{n}}\right)$. In spatially local systems, $\lambda \left(v\right)$ is negative outside the light cone where it takes the form $\lambda \left(v\right)\sim -{(v-v_B)}^{\alpha }$ near $v_B$, with the exponent $\alpha$ taking on various values over the range of systems we examine. The regime inside the light cone with positive Lyapunov exponents may only exist for classical, semiclassical, or large-$N$ systems, but not for “fully quantum” chaotic systems with strong short-range interactions and local Hilbert space dimensions of order one.

The Berry curvature of a Bloch band can be interpreted as a local magnetic field in reciprocal space. This analogy can be extended by defining an electric field analog in reciprocal space which arises from the time-dependent Berry connection. We explore the term in the semiclassical equation of motion that gives rise to this phenomenon, and show that it can lead to anomalous drift in wave-packet motion. A similar effect arises from changes in the band population due to periodic driving, where the resulting drift depends on the nature of the drive and can be expressed in terms of a shift vector. Finally, these effects can be combined to build a pump with a net anomalous drift during a cyclic evolution in momentum space.

The link between macroscopic electric polarizations and microscopic charge densities, a fundamental problem of condensed matter physics, has been addressed by quantum theory involving geometric quantum phases for calculating polarization differences. While such work has provided quantitative insight into stationary electric polarizations of crystalline ferroelectrics, polarization dynamics driven by elementary electronic and/or lattice excitations are still far from understood. X-ray diffraction with a femtosecond time resolution allows for mapping of charge and lattice motions on their intrinsic time scales and provides time-dependent maps of electron density. We present a combined theoretical and experimental approach which allows for determining time-dependent macroscopic polarization changes from transient microscopic charge density maps. In an extension of existing theory, the key steps consist of deriving a microscopic current density from the charge density maps and calculating the macroscopic polarization change from this current density. Using femtosecond x-ray diffraction data for crystalline $({\mathrm{NH}}_4{)}_2{\mathrm{SO}}_4$ and ${\mathrm{KH}}_2{\mathrm{PO}}_4$, prototype materials displaying ferro- and paraelectric phases, we determine the ultrafast macroscopic polarization dynamics induced by coherent phonon motions. The results establish femtosecond x-ray diffraction as a key method for grasping transient polarization changes and for validating theoretical predictions for a wide range of polar and ferroelectric materials.

Bloch oscillations originate from the translational symmetry of crystals. These oscillations occur with a fundamental period that a semiclassical wave packet takes to traverse a Brillouin-zone loop. We introduce a new type of Bloch oscillations whose periodicity is an integer $\left(\mu >1\right)$ multiple of the fundamental period. The period multiplier $\mu$ is a topological invariant protected by the space groups of crystals, which include more than just translational symmetries. For example, $\mu$ divides $n$ for crystals with an $n$-fold rotational or screw symmetry; with a reflection, inversion or glide symmetry, $\mu$ equals two. We identify the commonality underlying all period-multiplied oscillations: the multiband Berry-Zak phases, which encode the holonomy of adiabatic transport of Bloch functions in quasimomentum space, differ pairwise by integer multiples of $2\pi /\mu$. For a class of multiband subspaces whose projected-position operators commute, period multiplication has a complementary explanation through the real space distribution of Wannier functions. This complementarity follows from a one-to-one correspondence between Berry-Zak phases and the centers of Wannier functions. A Wannier description of period multiplication does not always exist, as we exemplify with band subspaces with either a nonzero Chern number or ${\mathbb{Z}}_2$ Kane-Mele topological order. In the former case, we present general constraints between Berry-Zak phases and Chern numbers, as well as introduce a recipe to construct nontrivial Chern bands—by splitting elementary band representations. To help identify band subspaces with $\mu >1$, a general theorem is presented that outputs Zak phases that are symmetry-protected to integer multiples of $2\pi /n$, given the point-group symmetry representation of any gapped band subspace. A cold-atomic experiment that has observed period-multiplied Bloch oscillations is discussed, and directions are provided for future experiments.

Transition metal dichalcogenides (TMDs) exhibit a remarkable exciton physics including bright and optically forbidden dark excitonic states. Here, we show how dark excitons can be experimentally revealed by probing the intraexcitonic $1s-2p$ transition. Distinguishing the optical response shortly after the excitation and after the exciton thermalization allows us to reveal the relative position of bright and dark excitons. We find both in theory and experiment a clear blueshift in the optical response demonstrating the transition of bright exciton populations into lower-lying dark excitonic states.

The spreading of correlations after a quantum quench is studied in a wide class of lattice systems, with short- and long-range interactions. Using a unifying quasiparticle framework, we unveil a rich structure of the correlation cone, which encodes the footprints of several microscopic properties of the system. When the quasiparticle excitations propagate with a bounded group velocity, we show that the correlation edge and correlation maxima move with different velocities that we derive. For systems with a divergent group velocity, especially relevant for long-range interacting systems, the correlation edge propagates slower than ballistic. In contrast, the correlation maxima propagate faster than ballistic in gapless systems but ballistic in gapped systems. Our results shed light on existing experimental and numerical observations and pave the way to the next generation of experiments. For instance, we argue that the dynamics of correlation maxima can be used as a witness of the elementary excitations of the system.

In this work, motivated by the sine-square deformation (SSD) for (1+1)-dimensional quantum critical systems, we study the nonequilibrium quantum dynamics of a conformal field theory (CFT) with SSD, which was recently proposed to have a continuous energy spectrum and continuous Virasoro algebra. In particular, we study the time evolution of entanglement entropy after a quantum quench from a uniform CFT, which is defined on a finite space of length $L$, to a sine-square deformed CFT. We find that there is a crossover time $t^{*}$ that divides the entanglement evolution into two interesting regions. For $t\ll t^{*}$, the entanglement entropy does not evolve in time; for $t\gg t^{*}$, the entanglement entropy grows as $S_A\left(t\right)\simeq \frac{c}{3}logt$, which is independent of the lengths of the subsystem and the total system. This $logt$ growth with no revival indicates that a sine-square deformed CFT effectively has an infinite length, in agreement with previous studies based on energy spectrum analysis. Furthermore, we study the quench dynamics for a CFT with Möbius deformation, which interpolates between a uniform CFT and a sine-square deformed CFT. The entanglement entropy oscillates in time with period $L_{\text{eff}}=Lcosh\left(2\theta \right)$, with $\theta =0$ corresponding to the uniform case and $\theta \to \infty$ corresponding to the SSD limit. Our field theory calculation is confirmed by a numerical study on a (1+1)-dimensional critical fermion chain.

We provide a definition and explicit expressions for $n$-body Gaussian process (GP) kernels, which can learn any interatomic interaction occurring in a physical system, up to $n$-body contributions, for any value of $n$. The series is complete, as it can be shown that the “universal approximator” squared exponential kernel can be written as a sum of $n$-body kernels. These recipes enable the choice of optimally efficient force models for each target system, as confirmed by extensive testing on various materials. We furthermore describe how the $n$-body kernels can be “mapped” on equivalent representations that provide database-size-independent predictions and are thus crucially more efficient. We explicitly carry out this mapping procedure for the first nontrivial (three-body) kernel of the series, and we show that this reproduces the GP-predicted forces with $\mathrm{meV}/\AA$ accuracy while being orders of magnitude faster. These results pave the way to using novel force models (here named “M-FFs”) that are computationally as fast as their corresponding standard parametrized $n$-body force fields, while retaining the nonparametric character, the ease of training and validation, and the accuracy of the best recently proposed machine-learning potentials.

In a recent report, sum-frequency excitation of a Raman-active phonon was experimentally demonstrated. This mechanism is the sibling of impulsive stimulated Raman scattering, in which the difference-frequency components of a light field excite a Raman-active mode. Here, we propose that also ionic Raman scattering analogously has a sum-frequency counterpart. We compare the four Raman mechanisms, photonic and ionic difference- and sum-frequency excitation, for three different example materials using a generalized oscillator model for which we calculate the parameters with density functional theory. Sum-frequency ionic Raman scattering completes the toolkit for controlling material properties by means of selective excitation of lattice vibrations.

The rich dynamics and phase structure of driven systems include the recently described phenomenon of the “discrete time crystal” (DTC), a robust phase which spontaneously breaks the discrete time translation symmetry of its driving Hamiltonian. Experiments in trapped ions and diamond nitrogen vacancy centers have recently shown evidence for this DTC order. Here, we show nuclear magnetic resonance (NMR) data of DTC behavior in a third, strikingly different, system: a highly ordered spatial crystal in three dimensions. We devise a DTC echo experiment to probe the coherence of the driven system. We examine potential decay mechanisms for the DTC oscillations, and demonstrate the important effect of the internal Hamiltonian during nonzero duration pulses.

Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of freestanding graphene, which show upon cooling a striking classical-quantum evolution of height and angular fluctuations. The crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained. Zero-temperature quantum graphene is flatter and smoother than classical graphene at large scales yet rougher at short scales. The angular fluctuation distribution of the normals can be quantitatively described by coexistence of two Gaussians, one classical strongly $T$-dependent and one quantum about $2^{\circ }$ wide, of zero-point character. The quantum evolution of ripple-induced height and angular spread should be observable in electron diffraction in graphene and other two-dimensional materials, such as ${\mathrm{MoS}}_2$, bilayer graphene, boron nitride, etc.

Using a self-consistent scattered field approach based on fluctuational electrodynamics, we develop compact formulas for radiative heat transfer in many-body systems without the constraint of reciprocity. The formulas allow for efficient numerical calculation for a system consisting of a large number of bodies, and are in principle exact. As a demonstration, for a nonreciprocal many-body system, we investigate persistent heat current at thermal equilibrium and directional heat transfer when the system is away from thermal equilibrium.

We present a numerical and theoretical study that supports and explains recent experimental results on anomalous magnetization fluctuations of a uniaxial ferromagnetic film in its low-temperature phase, which is forced by an oscillating field above the critical period of the associated dynamic phase transition (DPT) [P. Riego, P. Vavassori, and A. Berger, Phys. Rev. Lett. 118, 117202 (2017)]. For this purpose, we perform kinetic Monte Carlo simulations of a two-dimensional Ising model with nearest-neighbor ferromagnetic interactions in the presence of a sinusoidally oscillating field, to which is added a constant bias field. We study a large range of system sizes and supercritical periods and analyze the data using a droplet-theoretical description of magnetization switching. We find that the period-averaged magnetization, which plays the role of the order parameter for the DPT, presents large fluctuations that give rise to well-defined peaks in its scaled variance and its susceptibility with respect to the bias field. The peaks are symmetric with respect to zero bias and located at values of the bias field that increase toward the field amplitude as an inverse logarithm of the field oscillation period. Our results indicate that this effect is independent of the system size for large systems, ruling out critical behavior associated with a phase transition. Rather, it is a stochastic-resonance phenomenon that has no counterpart in the corresponding thermodynamic phase transition, providing a reminder that the equivalence of the DPT to an equilibrium phase transition is limited to the critical region near the critical period and zero bias.

Willis fluids, or more generally Willis materials, are homogenized composites that exhibit coupling between momentum and strain. This coupling is intrinsic to inhomogeneous media and can play a significant role in the overall response in acoustic metamaterials. In this paper, we draw connections between bianisotropy in electromagnetism and Willis coupling in elastodynamics to provide a qualitative understanding. Building upon these analogies, we introduce a homogenization technique for acoustic metamaterials based on a source-driven, multiple scattering approach that highlights the physical origins of Willis coupling. Moreover, through numerical examples, we compare several macroscopic material descriptions of acoustic metamaterials with non-negligible Willis coupling. The descriptions neglecting Willis coupling may not satisfy restrictions stemming from reciprocity, passivity, and causality, which suggests that including Willis coupling in macroscopic descriptions is necessary to realize physically meaningful macroscopic parameters.

Do quantum correlations play a role in high-temperature dynamics of many-body systems? A common expectation is that thermal fluctuations lead to fast decoherence and make dynamics classical. In this paper we provide a striking example that a single particle created in a featureless, infinite temperature spin bath not only exhibits nonclassical dynamics but it also induces strong long-lived correlations between the surrounding spins. We study the nonequilibrium dynamics of a hole created in a Mott insulator in the atomic limit, which corresponds to a degenerate spin system. In the absence of interactions, the spin correlations arise purely from quantum interference. Furthermore, these correlations are both antiferromagnetic and ferromagnetic, in striking contrast to the equilibrium Nagaoka effect. These results are relevant for a number of condensed matter spin systems and should be observable using state of the art bosonic or fermionic quantum gas microscopes.

A free-standing GaAs membrane is investigated by pump-probe reflectivity measurements with femtosecond laser pulses of 400-nm wavelength. It is found that the detected wide spectrum of laser-generated coherent strain waves in the membrane does not contain a specific hypersonic frequency. Theoretical analysis reveals that this effect is related to zero sensitivity of the acousto-optic detection at a particular frequency defined by the wavelength of the probe laser pulse on the mechanical free surface of the GaAs membrane. We predict that a similar behavior is expected in Si and Au membranes and films, indicating that the presence of zeros in the spectral transformation function of acousto-optic conversion is a rather general phenomenon in picosecond ultrasonics that has so far been neglected.

The strong spin-spin exchange interaction in some low-dimensional magnetic materials can give rise to a high group velocity and thermal conductivity contribution from magnons. Examples are the incommensurate layered compounds ${(\mathrm{Sr},\mathrm{Ca},\mathrm{La})}_{14}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$. The effects of grain boundaries and defects on quasi-one-dimensional magnon transport in these compounds are not well understood. Here we report the microstructural and anisotropic thermal transport properties of textured $\mathrm{S}{\mathrm{r}}_{14}\mathrm{C}{\mathrm{u}}_{24}{\mathrm{O}}_{41}$, which is prepared by solid-state reaction followed by spark plasma sintering. Transmission electron microscopy clearly reveals nanolayered grains and the presence of dislocations and planar defects. The thermal conductivity contribution and mean free paths of magnons in the textured samples are evaluated with the use of a kinetic model for one-dimensional magnon transport and found to be suppressed significantly compared to single crystals at low temperatures. The experimental results can be explained by a one-dimensional magnon-defect scattering model, provided that the magnon-grain boundary scattering mean free path in the anisotropic magnetic structure is smaller than the average length of these nanolayers along the $c$ axis. The finding suggests low transmission coefficients for energy-carrying magnons across grain boundaries.

Solitons are self-preserving traveling waves of great interest in nonlinear physics but hard to observe experimentally. In this report an experimental setup is designed to observe and characterize acoustic solitons in a GaAs(001) substrate. It is based on careful temperature control of the sample and an interferometric detection scheme. Ultrashort acoustic solitons, such as the one predicted by the Korteweg–de Vries equation, are observed and fully characterized. Their particlelike nature is clearly evidenced and their unique properties are thoroughly checked. The spatial averaging of the soliton wave front is shown to account for the differences between the theoretical and experimental soliton profile. It appears that ultrafast acoustic experiments provide a precise measurement of the soliton velocity. It allows for absolute calibration of the setup as well as the response function analysis of the detection layer. Moreover, the temporal distribution of the solitons is also analyzed with the help of the inverse scattering method. It shows how the initial acoustic pulse profile which gives birth to solitons after nonlinear propagation can be retrieved. Such investigations provide a new tool to probe transient properties of highly excited matter through the study of the emitted acoustic pulse after laser excitation.

Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave, which has proved a rather stringent requirement in experiments. Recently, a proposal to seek such transitions in highly tunable systems of cold-atomic gases offers to probe this physics and, at the same time, to investigate the robustness of these transitions to quantum coherent effects. Here, we specifically focus on the interplay between classical and quantum fluctuations in a simple driven open quantum model which, in the classical limit, reproduces a contact process, which is known to undergo a continuous transition in the “directed percolation” universality class. We derive an effective long-wavelength field theory for the present class of open spin systems and show that, due to quantum fluctuations, the nature of the transition changes from second to first order, passing through a bicritical point which appears to belong instead to the “tricritical directed percolation” class.

The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the difference of chemical components and the local atomic relaxation are ignored. However, it has still been difficult to decompose the unfolded band structures into the modes based on the crystallographic symmetry of the underlying structure, and therefore detailed analyses of the unfolded band structures have been restricted. In this study, a procedure to decompose the unfolded band structures according to the small representations (SRs) of the little groups is developed. The decomposition is performed using the projection operators for SRs derived from the group representation theory. The current method is employed to investigate the phonon band structure of disordered face-centered-cubic ${\mathrm{Cu}}_{0.75}{\mathrm{Au}}_{0.25}$, which has large variations of atomic masses and force constants among the atomic sites due to the chemical disorder. In the unfolded phonon band structure, several peculiar behaviors such as discontinuous and split branches are found in the decomposed modes corresponding to specific SRs. They are found to occur because different combinations of the chemical elements contribute to different regions of frequency.