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 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.

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.

An all-optical method of ultrafast spin rotation is put forward to precisely manipulate the polarization of relativistic charged particle beams of leptons or ions. Laser-driven dense ultrashort beams are manipulated via single-shot interaction with a copropagating temporally asymmetric laser pulse of moderate intensity. Using semiclassical numerical simulations, we show that the initial polarization of a lepton (proton) beam can be rotated to any desired orientation by a flexible control over the phase retardation between the spin precession and the momentum oscillation in a temporally asymmetrical (e.g., half-cycle terahertz or frequency-chirped) laser field. In particular, spin ultrafast rotation from the common transverse to the more valuable longitudinal polarization is feasible in a picosecond scale or less. Moreover, the beam quality, in terms of energy and angular divergence, is improved in the rotation process. This method has potential applications in various areas demanding ultrafast spin manipulation, like laser-plasma, laser-nuclear, and high-energy physics.

Recently, gate-defined Josephson junctions in magic angle twisted bilayer graphene (MATBG) were studied experimentally, and highly unconventional Fraunhofer patterns were observed. In this work, we show that an interaction-driven valley-polarized state connecting two superconducting regions of MATBG would give rise to a long-sought-after purely electric controlled ${\phi }_0$-junction in which the two superconductors acquire a finite phase difference ${\phi }_0$ in the ground state. We point out that the emergence of the ${\phi }_0$-junction stems from the valley-polarized state which breaks time-reversal symmetry, and trigonal warping effects which break intravalley inversion symmetry. Importantly, a spatially nonuniform valley-polarization order parameter at the junction can explain the key features of the observed unconventional Fraunhofer patterns. Our work explores the novel transport properties of the valley-polarized state, and we suggest that gate-defined MATBG Josephson junctions could realize the first purely electric controlled ${\phi }_0$-junctions.

Quantum information processing is a key technology in the ongoing second quantum revolution, with a wide variety of hardware platforms competing toward its realization. An indispensable component of such hardware is a measurement device, i.e., a quantum detector that is used to determine the outcome of a computation. The act of measurement in quantum mechanics, however, is naturally invasive as the measurement apparatus becomes entangled with the system that it observes. This always leads to a disturbance in the observed system, a phenomenon called quantum measurement backaction, which should solely lead to the collapse of the quantum wave function and the physical realization of the measurement postulate of quantum mechanics. Here we demonstrate that backaction can fundamentally change the quantum system through the detection process. For quantum information processing, this means that the readout alters the system in such a way that a faulty measurement outcome is obtained. Specifically, we report a backaction-induced population switching, where the bare presence of weak, nonprojective measurements by an adjacent charge sensor inverts the electronic charge configuration of a semiconductor double quantum dot system. The transition region grows with measurement strength and is suppressed by temperature, in excellent agreement with our coherent quantum backaction model. Our result exposes backaction channels that appear at the interplay between the detector and the system environments, and opens new avenues for controlling and mitigating backaction effects in future quantum technologies.

The electron-phonon $\left(e\text{−}\mathrm{ph}\right)$ coupling system often has a large number of phonon degrees of freedom, whose spectral functions are numerically difficult to compute using matrix product state (MPS) formalisms. To solve this problem, we propose a practical method that combines the Chebyshev MPS and the pseudosite density matrix renormalization group (DMRG) algorithm. The Chebyshev vector is represented by a pseudosite MPS with global $U\left(1\right)$ fermion symmetry, which maps $2^{N_p}$ bosonic degrees of freedom onto $N_p$ pseudosites, each with two states. This approach can handle arbitrary $e$-ph coupling Hamiltonians where pseudosite DMRG performs efficiently. We use this method to study the spectral functions of the doped extended Hubbard-Holstein model in a regime of strong Coulomb repulsion. Key features of the excitation spectra are captured at a modest computational cost. Our results show that weak extended $e$-ph couplings can increase the spectral weight of the holon-folding branch at low phonon frequencies, in agreement with angle-resolved photoemission observations on one-dimensional cuprates.

Recently, the evolution of the Weyl point (WP) caused by the introduction of nonhermiticity into Weyl semimetals has aroused great research interest. We consider elastic flexural wave propagation in a phononic beam containing piezoelectric materials and introduce nonhermiticity through active regulation of external circuits. Considering a synthetic parameter space constituted by the one-dimensional Bloch wave vector and two geometrical parameters, we demonstrate that a double WP (DWP) arises at the band crossing. Then we study its evolution from the hermitic to nonhermitic situation under the effect of the active piezoelectric materials. We find that the DWP in the hermitic case evolves into a Weyl degenerate line and a Weyl hollow ring as concerns the real and imaginary parts of the Weyl frequencies, respectively. The formation mechanisms of the DWPs, lines, and rings are explained through the Hamiltonian of the system. Further, we observe the changes of the DWP and degenerate line in the transmission spectra of finite structures. Finally, we discuss the synthetic Fermi arc interface states through the analysis of the reflected phase vortices. In this paper, we provide insights into the high-dimensional Hermitian and non-Hermitian physics in elastic wave systems using synthetic dimensions.

We study theoretically a large quantum dot in the fractional quantum Hall regime that is strongly coupled to $\mathcal{M}$ leads via single-mode quantum point contacts. In the case $\mathcal{M}=2$, when the system is mapped onto the two-channel charge Kondo problem, we predict a universal expression for the conductance in the vicinity of a strong-coupling fixed point. The power of the leading temperature correction to the maximal conductance is determined by the fractional filling factor $\nu =1/m$. For $\mathcal{M}>2$, we examine the case in which $\mathcal{M}-1$ quantum point contacts are fully open, reproducing a single-channel circuit coupled to a dissipative Ohmic environment. The system is treated as a Luttinger liquid with an impurity, whose effective interaction parameter is defined as $K=\nu (\mathcal{M}-1)/\mathcal{M}$. Conductance scaling in the weak and strong tunnel regimes is used to discuss the low-temperature transport behavior of multichannel single- and double-charge Kondo devices.

We investigate the nonequilibrium dynamics of the $S=1$ quantum spin chain subjected to a time-dependent external drive, where the driving frequency is adiabatically decreased as a function of time (Floquet adiabatic evolution). We show that, when driving the rhombic anisotropy term (known as the two-axis countertwisting in the context of squeezed spin states) of a Néel antiferromagnet, we can induce an overall enhancement in the quadrupole polarization, while at the same time suppressing the staggered magnetization order. The system evolves into a new state with a net quadrupole moment and antiferroquadrupolar correlations. This state remains stable at long times once the driving frequency is kept constant. On the other hand, we find that we cannot achieve a quadrupole polarization for the symmetry-protected Haldane phase, which remains robust against such driving.

We present a systematic study of the dynamical phase diagram of a periodically driven BCS system as a function of drive strength and frequency. Three different driving mechanisms are considered and compared: oscillating density of states, oscillating pairing interaction, and oscillating external paring field. We identify the locus in parameter space of parametric resonances and four dynamical phases: Rabi-Higgs, gapless, synchronized Higgs, and time-crystal phases. We demonstrate that the main features of the phase diagram are quite robust to different driving protocols and discuss the order of the transitions. By mapping the BCS problem to a collection of nonlinear and interacting classical oscillators, we shed light on the origin of time-crystal phases and parametric resonances appearing for subgap excitations.

We generalize the dynamical phase diagram of a Bardeen-Cooper-Schrieffer condensate, considering attractive to repulsive, i.e., critical quenches (CQs) and a nonconstant density of states (DOS). We show that different synchronized Higgs dynamical phases can be stabilized, associated with singularities in the DOS and different quench protocols. In particular, the CQ can stabilize an overlooked high-frequency Higgs dynamical phase related to the upper edge of the fermionic band. For a compensated Dirac system we find a Dirac-Higgs mode associated with the cusp singularity at the Fermi level, and we show that synchronized phases become more pervasive across the phase diagram. The relevance of these remarkable phenomena and their realization in ensembles of fermionic cold atoms confined in optical lattices is also discussed.

We study the interplay of disorder and Heisenberg interactions in the Kitaev model on a honeycomb lattice. The effect of disorder on the transition between Kitaev spin liquid and magnetic ordered states as well as the stability of magnetic ordering is investigated. Using Lanczos exact diagonalization we discuss the consequences of two types of disorder: (i) random-coupling disorder and (ii) singular-coupling disorder. They exhibit qualitatively similar effects in the pure Kitaev-Heisenberg model without long-range interactions. The range of spin-liquid phases is reduced and the transition to magnetic ordered phases becomes more crossoverlike. Furthermore, the long-range zigzag and stripy orderings in the clean system are replaced by their three domains with different ordering direction. Especially in the crossover range the coexistence of magnetically ordered and Kitaev spin-liquid domains is possible. With increasing the disorder strength the area of domains becomes smaller and the system goes into a spin-glass state. However, the disorder effect is different in magnetically ordered phases caused by long-range interactions. The stability of such magnetic ordering is diminished by singular-coupling disorder and, accordingly, the range of the spin-liquid regime is extended. This mechanism may be relevant to materials like $\alpha \text{−}{\mathrm{RuCl}}_3$ and ${\mathrm{H}}_3{\mathrm{LiIr}}_2{\mathrm{O}}_6$ where the zigzag ground state is stabilized by weak long-range interactions. We also find that the flux gap closes at a critical disorder strength and vortices appears in the flux arrangement. Interestingly, the vortices tend to form kinds of commensurate ordering.