We present the fingerprints of the dynamic Jahn-Teller effect in resonant inelastic x-ray scattering (RIXS) spectra of ${\mathrm{K}}_2{\mathrm{RuCl}}_6$. We determined the dynamic Jahn-Teller model Hamiltonian of an embedded ${\mathrm{Ru}}^{4+}$ ion using post-Hartree-Fock methods, and derived the vibronic states by numerically diagonalizing the Hamiltonian. With the obtained vibronic states, we reproduced the RIXS spectra. The shape and the temperature dependence of the RIXS spectrum agree well with the experimental data. We found that some peaks emerge due to the dynamic Jahn-Teller effect rather than the crystal-field splitting. Our paper indicates the significance of the Jahn-Teller coupling to adequately interpret RIXS spectra.

We propose and benchmark a Gross-Pitaevskii-like equation for two-component Bose mixtures with competing interactions in 1D. Our approach follows the density functional theory with the energy functional based on the exact quantum Monte Carlo (QMC) simulations. Our model covers, but goes beyond, the popular approach with the Lee-Huang-Yang corrections. We first benchmark our approach against available QMC data in all interaction regimes and then study dynamical properties, inaccessible by ab initio many-body simulations. Our analysis includes a study of monopole modes and reveals the presence of anomalous dark solitons.

The relationship between genotype and phenotype plays a crucial role in determining the function and robustness of biological systems. Here the evolution progresses through the change in genotype, whereas the selection is based on the phenotype, and the genotype-phenotype relation also evolves. The theory for such phenotypic evolution remains poorly developed, in contrast to evolution under the fitness landscape determined by genotypes. Here we provide a statistical-physics formulation of this problem by introducing replicas for genotype and phenotype. We apply it to an evolution model in which phenotypes are given by spin configurations; genotypes are an interaction matrix for spins to give the Hamiltonian, and the fitness depends only on the configuration of a subset of spins called the target. We describe the interplay between the genetic variations and phenotypic variances by noise in this model by our approach that extends the replica theory for spin glasses to include a spin replica for phenotypes and a coupling replica for genotypes. Within this framework we obtain a phase diagram of the evolved phenotypes against the noise and selection pressure, where each phase is distinguished by the fitness and overlaps for genotypes and phenotypes. Among the phases, a robust fitted phase, relevant to biological evolution, is achieved under the intermediate level of noise (temperature), where robustnesses to noise and to genetic mutation are correlated, as a result of replica symmetry. We also find a tradeoff between maintaining a high fitness level of phenotype and acquiring a robust pattern of genes as well as the dependence of this tradeoff on the ratio between the size of the functional (target) part to that of the remaining nonfunctional (non-target) one. The selection pressure needed to achieve high fitness increases with the fraction of target spins.

We investigate four key issues with using a nonzero weak value of the spatial projection operator to infer the past path of an individual quantum particle. First, we note that weak measurements disturb a system, so any approach relying on such a perturbation to determine the location of a quantum particle describes the state of a disturbed system, not that of a hypothetical undisturbed system. Second, even assuming no disturbance, there is no reason to associate the nonzero weak value of an operator containing the spatial projection operator with the classical idea of “particle presence.” Third, weak values are only measurable over ensembles, and so to infer properties of individual particles from values of them is problematic. Finally, weak value approaches to the path of a particle do not provide information beyond standard quantum mechanics (and the classical modes supporting the experiment). We know of no experiment with testable consequences that demonstrates a connection between particle presence and weak values.

The synchronization of oscillator ensembles is pervasive throughout nonlinear science, from classical or quantum mechanics to biology, to human assemblies. Traditionally, the main focus has been the identification of threshold parameter values for the transition to synchronization as well as the nature of such transition. Here, we show that considering an oscillator lattice as a discrete growing interface provides unique insights into the dynamical process whereby the lattice reaches synchronization for long times. Working on a generalization of the celebrated Kuramoto model that allows for odd or non-odd couplings, we elucidate synchronization of oscillator lattices as an instance of generic scale invariance, whereby the system displays space-time criticality, largely irrespective of parameter values. The critical properties of the system (like scaling exponent values and the dynamic scaling Ansatz which is satisfied) happen to fall into universality classes of kinetically rough interfaces with columnar disorder, namely, those of the Edwards-Wilkinson (equivalently, the Larkin model of an elastic interface in a random medium) or the Kardar-Parisi-Zhang (KPZ) equations, for Kuramoto (odd) coupling and generic (non-odd) couplings, respectively. From the point of view of kinetic roughening, the critical properties we find turn out to be quite innovative, especially concerning the statistics of the fluctuations as characterized by their probability distribution function (PDF) and covariance. While the latter happens to be that of the Larkin model irrespective of the symmetry of the coupling, in the generic non-odd coupling case the PDF turns out to be the Tracy-Widom distribution associated with the KPZ nonlinearity. This brings the synchronization of oscillator lattices into a remarkably large class of strongly-correlated, low-dimensional (classical and quantum) systems with strong universal fluctuations.

Digital quantum simulation of electron-phonon systems requires truncating infinite phonon levels into $N$ basis states and then encoding them with qubit computational basis. Unary encoding and binary encoding are the two most representative encoding schemes, which demand $O\left(N\right)$ and $O(logN)$ qubits as well as $O\left(N\right)$ and $O(NlogN)$ quantum gates, respectively. In this paper, we propose a variational basis state encoding algorithm that reduces the scaling of the number of qubits and quantum gates to both $O\left(1\right)$ for systems obeying the area law of entanglement entropy. The cost for the scaling reduction is a constant amount of additional measurement. The accuracy and efficiency of the approach are verified by both numerical simulation and realistic quantum hardware experiments. In particular, we find using one or two qubits for each phonon mode is sufficient to produce quantitatively correct results across weak and strong coupling regimes. Our approach paves the way for practical quantum simulation of electron-phonon systems on both near-term hardware and error-corrected quantum computers.

We study one-dimensional lattices with imaginary-valued Aubry-André-Harper (AAH) potentials. Such lattices can host edge states with purely imaginary eigenenergies, which differ from the edge states of the Hermitian AAH model and are stabilized by a non-Hermitian particle-hole symmetry. The edge states arise when the period of the imaginary potential is a multiple of four lattice constants. They are topological in origin, and can manifest on domain walls between lattices with different modulation periods and phases, as predicted by a bulk polarization invariant. Interestingly, the edge states persist and remain localized even if the gap in the real spectrum closes. These features can be used in laser arrays to select topological lasing modes under spatially extended pumping.

Donor electron spin qubits hosted within nanoscale devices have demonstrated seconds-long relaxation times at magnetic fields suitable for the operation of spin qubits in silicon of $B=1.5\mathrm{T}$. The relaxation rates of these qubits have been shown at milliKelvin temperatures to be mediated by spin-orbit coupling with a $B^5$ dependency on magnetic field for $B>3\mathrm{T}$ with a transition to a $B^3$ dependency at magnetic fields below ($B\le 3\mathrm{T}$). This deviation has been observed in many spin qubit systems but is particularly notable in multidonor quantum dot qubits. The reason for this has remained a mystery. In this paper we show that for these multidonor low noise, crystalline qubits this deviation at low magnetic fields can be explained by a hyperfine mediated relaxation mechanism of the electron spin through a quantitative model of the relaxation rates. This model identifies the importance of donor nuclear spin flips which are more apparent in multidonor systems in which the larger numbers of donor nuclei creates stronger confinement potentials and enhanced hyperfine couplings. We show theoretically that with atomic precision engineering of the locations of the donor nuclei in these multidonor quantum dot qubits, and/or nuclear spin control, we can minimize the hyperfine mediated relaxation allowing $T_1$ to extend to $\sim 200$ seconds ($B=1.5\mathrm{T}$).

We study four-dimensional fractional quantum Hall states on ${\mathbb{CP}}^2$ geometry from microscopic approaches. While in 2d the standard Laughlin wave function, given by a power of Vandermonde determinant, admits a product representation in terms of the Jastrow factor, this is no longer true in higher dimensions. In 4d, we can define two different types of Laughlin wave functions, the determinant-Laughlin and Jastrow-Laughlin states. We find that they are exactly annihilated by, respectively, two-particle and three-particle short-ranged interacting Hamiltonians. We then mainly focus on the ground state, low-energy excitations, and the quasihole degeneracy of determinant-Laughlin state. The quasihole degeneracy exhibits an anomalous counting, indicating the existence of multiple forms of quasihole wave functions. We argue that these are captured by the mathematical framework of “commutative algebra of $N\mathrm{points}$ in the plane.” The microscopic wave functions and Hamiltonians studied in this work pave the way for a systematic study of a high-dimensional topological phase of matter that is potentially realizable in cold atom and optical experiments.

We study the effect of thermal fluctuations on a sourced quench in a system with $Z_2$ symmetry. By ignoring the fluctuation of finite momentum modes and tracing the dynamics of zero momentum mode driven by a spatially homogeneous source near the critical point, we map out a phase diagram for the quench dynamics. The phase diagram consists of three different phases. Phase I occurs for large fluctuations with the relaxation time set by fluctuation-induced inverse effective mass square. Phase II occurs for small fluctuation and slow quench rate. The dynamics is characterized by a modified Kibble-Zurek scaling. Phase III corresponds to small fluctuations and rapid quench rate. The relaxation time tends to a finite value in the rapid quench limit. We also estimate the fluctuations of finite momentum modes, finding significant enhancement of the effective mass square. We speculate the qualitative features of the phase diagram may remain the same, but enhanced fluctuations can lead to shrinkage of phase II and III.

Active fluids demonstrate complex collective behavior and self-organization often resulting in the emergence of localized vortices. We report on a combined experimental and computational study of the spontaneous formation of globally correlated vortex lattices formed in active roller fluids. The vortices are comprised of active ferromagnetic rollers placed on a patterned substrate promoting localization of self-organized vortices in a lattice with square symmetry. Each individual vortex spontaneously selects its chiral state (clockwise or counterclockwise). Nevertheless, confined to a square lattice, an ensemble of interacting active vortices is capable of developing correlations between chiral states of neighboring vortices. We show that such ensembles of active vortices can spontaneously evolve towards a globally correlated state with the antiferromagnetic ordering of their vorticities. We explore the correlations between chiral states of neighboring vortex pairs in response to changes in the geometry of the confining lattice. The results are supported by numerical simulations based on phenomenological coarse grained particle dynamics coupled to shallow water Navier-Stokes hydrodynamics. We show that these ordered vortex lattices formed by magnetic rollers have the ability to self-heal the antiferromagnetic order and stabilize individual vortical states in the activity regimes beyond optimal conditions for the collective vortex states. The results provide insights into the collective behavior of active magnetic roller fluids in the presence of geometrical confinement.

The two-time measurement scheme is well studied in the context of quantum fluctuation theorem. However, it becomes infeasible when the random variable determined by a single measurement trajectory is associated with the von Neumann entropy of the quantum states. We employ the one-time measurement scheme to derive a Jarzynski-like equality of nonequilibrium information production by proposing an information production distribution based on the quantum cross-entropy. The derived equality further enables one to explore the roles of the quantum cross-entropy in quantum communications, quantum machine learning, and quantum thermodynamics.

The spectrum of a non-Hermitian system generically forms a two-dimensional complex Riemannian manifold with a distinct topology from the underlying parameter space. This spectral topology permits eigenvalue trajectories to braid into knots. In this paper, through the analyses of encircling loops, exceptional points, and their topology, we uncover the necessary considerations for constructing eigenvalue knots and establish their relation to the spectral topology. Using an acoustic system with two periodic synthetic dimensions, we experimentally realize several knots with braid index 3. In addition, by highlighting the role of branch cuts on the eigenvalue manifolds, we show that eigenvalue knots produced by homotopic parametric loops are isotopic such that they can deform into one another by type-II or III Reidemeister moves. Our results not only provide a general recipe for constructing eigenvalue knots but also expand the current understanding of eigenvalue knots by showing that they contain information beyond that of the spectral topology.

The recent experimental discovery of several families of kagome materials has boosted the interest in electronic correlations on a kagome lattice. As an initial step to understand the observed complex phenomena, it is helpful to know the correspondence between the simple forms of interactions and the induced correlated states on a kagome lattice. Considering the lack of such studies, here we systematically investigate the attractive kagome-lattice Hubbard model using the mean-field approach and determinant quantum Monte Carlo (DQMC). A charge-density-wave order satisfying the triangle rule is predicted by the mean-field treatment, and subsequent DQMC simulations provide indirect evidence for its existence. The $s$-wave superconductivity is found to be stabilized at low temperatures, and to exist in dome regions of the phase diagrams. We then determine the superconducting critical temperature quantitatively by finite-size scaling of the pair structure factor. These results may be helpful in understanding the observed superconductivity in kagome materials.

Dispersionless flat bands can be classified into two types: (1) non-singular flat bands whose eigenmodes are completely characterized by compact localized states, and (2) singular flat bands that have a discontinuity in their Bloch eigenfunctions at a band touching point with an adjacent dispersive band, thereby requiring additional extended states to span their eigenmode space. In this study, we design and numerically demonstrate two-dimensional thin-plate phononic metamaterials in which tunable flat bands of both kinds can be achieved. Non-singular flat bands are achieved by fine tuning the ratio of the global tension and the bending stiffness in triangular and honeycomb lattices of plate resonators. A singular flat band arises in a kagome lattice due to the underlying lattice geometry, which can be made degenerate with two additional flat bands by tuning the plate tension. A discrete model of the continuum thin-plate system reveals the interplay of geometric and mechanical factors in determining the existence of flat bands of both types. The singular nature of the kagome lattice flat band is established via a metric called the Hilbert-Schmidt distance calculated between a pair of eigenstates infinitesimally close to the quadratic band touching point. We also simulate a phononic manifestation of a robust boundary mode arising from the singular flat band and protected by real-space topology in a finite system. Our theoretical and computational study establishes a framework for exploring flat-band physics in a tunable classical system, and for designing phononic metamaterials with potentially useful sound manipulation capabilities.

Real eigenvalues of pseudo-Hermitian matrices, such as real matrices and $\mathcal{PT}-\mathrm{symmetric}$ matrices, frequently split into complex conjugate pairs. This is accompanied by the breaking of certain symmetries of the eigenvectors and, typically, also a drastic change in the behavior of the system. In this paper, we classify the eigenspace of pseudo-Hermitian matrices and show that such symmetry breaking occurs if and only if eigenvalues of opposite kinds collide on the real axis of the complex eigenvalue plane. This enables a classification of the disconnected regions in parameter space where all eigenvalues are real—which correspond, physically, to the stable phases of the system. These disconnected regions are surrounded by exceptional surfaces, which comprise all the real-valued exceptional points of pseudo-Hermitian matrices. The exceptional surfaces, together with the diabolic points created by their intersections, comprise all points of pseudo-Hermiticity breaking. In particular, this clarifies that the degeneracy involved in symmetry breaking is not necessarily an exceptional point. We also discuss how our study relates to conserved quantities and derive the conditions for when degeneracies caused by external symmetries are susceptible to thresholdless pseudo-Hermiticity breaking. We illustrate our results with examples from photonics, condensed matter physics, and mechanics.

Chromosomal loci in bacterial cells show a robust subdiffusive scaling of the mean square displacement, $\text{MSD}\left(\tau \right)\sim {\tau }^{\alpha }$, with $\alpha <0.5$. On the other hand, recent experiments have also shown that DNA-bridging nucleoid associated proteins (NAPs) play an important role in chromosome organization and compaction. Here, using polymer simulations we investigate the role of DNA bridging in determining the dynamics of chromosomal loci. We find that bridging compacts the polymer and reproduces the subdiffusive elastic dynamics of monomers at timescales shorter than the bridge lifetime. Consistent with this prediction, we measure a higher exponent in a NAP mutant compared to the wild type. Furthermore, bridging can reproduce the rare but ubiquitous rapid movements of chromosomal loci that have been observed in experiments. In our model the scaling exponent defines a relationship between the abundance of bridges and their lifetime. Using this and the observed mobility of chromosomal loci, we predict a lower bound on the average bridge lifetime of around five seconds.