We investigate the critical behavior and real-time scattering dynamics of the interacting ${\varphi }^4$ quantum field theory in ($1+1$) dimensions using uniform matrix product states (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at $\lambda =0.8$ bounds the critical mass-squared to ${\mu }_c^2\in ]-0.2595,-0.2594[$ and provides a quantitative map of the symmetric, near-critical, and spontaneously broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}\left(E\right)$ and Wigner time delay $\mathrm{\Delta }t\left(E\right)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11}\simeq 0.712, \mathrm{\Delta }t\simeq -158$ for ${\mu }^2=+0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11}\simeq 1, \mathrm{\Delta }t\simeq -108$ for ${\mu }^2=-0.1$ and $P_{11\to 11}\simeq 1, \mathrm{\Delta }t\simeq -177.781$ for ${\mu }^2=-0.5$). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

We study the quantum relaxation dynamics for a lattice version of the one-dimensional $N$-flavor Gross-Neveu model after a Hamiltonian parameter quench. Allowing for a system-reservoir coupling $\gamma$, we numerically describe the system dynamics through a time-dependent self-consistent Lindblad master equation. For a closed ($\gamma =0$) finite-size system subjected to an interaction parameter quench, the order parameter dynamics exhibits oscillations and revivals. In the thermodynamic limit, our results imply that the order parameter reaches its postquench stationary value in accordance with the eigenstate thermalization hypothesis. However, time-dependent finite-momentum correlation matrix elements equilibrate only if $\gamma >0$. Our findings are consistent with the system being described by a pertinent generalized Gibbs ensemble and, accordingly, highlight subtle yet important aspects of the postquench relaxation dynamics of quantum many-body systems.

Correlation functions and correlation lengths are frequently used to describe phase transitions in quantum systems, but they require an explicit choice of observables. The recently introduced information lattice instead provides an observable-independent way to identify where and at which scale information is contained in quantum lattice models. Here, we use it to study the difference between the metallic and insulating regimes of one-dimensional noninteracting tight-binding chains. We find that the information per scale follows a power law in metals at low temperature and that Friedel-like oscillations are visible in the information lattice. At high temperature or in insulators at low temperature, the information per scale decays exponentially. Thus, the information lattice is a useful tool for analyzing the metal-insulator transition.

Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as boson sampling, existing tensor network approaches fail to address the complexity mismatch between tensor contractions and the calculation of photon-counting probability amplitudes. Here, we present an alternative tensor network framework that exploits the input-output relations of quantum optical circuits encoded in the unitary interferometer matrix. Our approach bridges the complexity gap by enabling the computation of the permanent—central to boson sampling—with the same computational complexity as the best known classical algorithm based on a graphical representation of the operator-basis matrix product states that we introduce. Furthermore, we exploit the flexibility of tensor networks to extend our formalism to incorporate partial distinguishability and photon loss, two key imperfections in practical interferometry experiments. This work offers a significant step forward in the simulation of large-scale quantum optical systems and the understanding of their computational complexity.

We explore how the quantum geometric properties of the Bloch wave function, characterized by the Hilbert-Schmidt quantum distance, impact magnetic phases in solid-state systems. To this end, we investigate the spin susceptibility within the random phase approximation, considering the on-site Coulomb interaction. We demonstrate that spin susceptibility can be decomposed into a trivial part, dependent solely on the band dispersion, and a geometric part, where the quantum distance plays a crucial role. Focusing on a model of a quadratic band-touching semimetal, we show that a magnetic phase transition between ferromagnetic and antiferromagnetic orders can be induced solely by tuning the wave function geometry, even while the energy spectrum is held constant. This highlights the versatility of quantum geometry as a mechanism for tuning magnetic properties independent of the energy spectrum. Applying our framework to the Fe pnictide and kagome lattice models, we further show that the geometric contribution is decisive in stabilizing their known antiferromagnetic and ferromagnetic states, respectively. Our work sheds light on the hidden quantum geometric aspects necessary for understanding and engineering magnetic order in quantum materials.

Solving the many-electron problem, even approximately, is one of the most challenging and simultaneously most important problems in contemporary condensed matter physics with various connections to other fields. The standard approach is to follow a divide and conquer strategy that combines various numerical and analytical techniques. A crucial step in this strategy is the derivation of an effective model for a subset of degrees of freedom by a procedure called downfolding, which often corresponds to integrating out energy scales far away from the Fermi level. In this work, we present a rigorous formulation of this downfolding procedure, which complements the renormalization group picture put forward by Honerkamp [Phys. Rev. B 85, 195129 (2012)]. We derive an exact effective model in an arbitrarily chosen target space (e.g., low-energy degrees of freedom) by explicitly integrating out the rest space (e.g., high-energy degrees of freedom). Within this formalism, we state conditions that justify a perturbative truncation of the downfolded effective interactions to just a few low-order terms. Furthermore, we utilize the exact formalism to formally derive the widely used constrained random phase approximation, uncovering underlying approximations and highlighting relevant corrections in the process. Finally, we detail different contributions in the material examples of fcc nickel and the infinite-layer cuprate ${\mathrm{SrCuO}}_2$. Our results open up a pathway to obtain effective models in a controlled fashion and to judge whether a chosen target space is suitable.

Understanding the response of diamond abrasive grains to mechanical loading remains crucial for optimizing their performance in precision manufacturing. In that context, the role of the initial residual stress and crystallographic orientation of the grains is poorly understood. We investigate synthetic diamond grains in two different grit sizes (D126, D252) subjected to directional loading up to 100 N using x-ray diffraction and spatially resolved Raman spectroscopy. Small grains with preferential (111) orientation show an unexpected stress evolution under contact pressures up to 16 GPa, with Raman shifts increasing from 1331.3 to $1333.0{\mathrm{cm}}^{-1}$, indicating an enhanced local compressive stress state at the probed surface regions. Conversely, large (311)-oriented grains exhibit a heterogeneous stress development with Raman shifts varying from 1331.5 to $1332.6{\mathrm{cm}}^{-1}$, including regions that become more tensile (or less compressive) relative to their initial state. The relationship between the relative Raman shift and a spatially weighted contact pressure follows an empirical power law $\delta E\propto p_{\text{c}}^{\prime \alpha }$ with opposite, orientation-dependent exponents: $\alpha \approx +0.25$ for (111) grains showing progressive compression enhancement and $\alpha \approx -0.35$ for (311) grains exhibiting a trend toward tensile stress components with increasing load. Molecular dynamics simulations reveal that the Schmid factor governs this orientation-dependent response: The low Schmid factor (0.27) for [111] loading restricts dislocation glide, leading to stress retention with high elastic recovery, while the high Schmid factor (0.45) for [311] loading facilitates plastic flow and stress relaxation despite lower peak stress. These findings demonstrate that stress evolution in diamond under directional loading is controlled by the geometric relationship between loading direction and slip systems, providing mechanistic insights for diamond tool design.

The intermediate valence of Ce in ${\mathrm{CeCo}}_5$ challenges standard density functional theory (DFT) and static $\mathrm{DFT}+U$ approaches, which fail to capture its magnetic properties. By combining $\mathrm{DFT}+U$ with exact diagonalization of the Anderson impurity model for the Ce $4f$ shell, we find a substantial reduction of Ce spin and orbital moments, consistent with $\mathrm{DFT}+\mathrm{DMFT}$ (dynamical mean-field theory), arising from ${\mathrm{Ce}}^{4+}-{\mathrm{Ce}}^{3+}$ valence fluctuations. The total magnetic moment of 6.70 ${\mu }_B$ agrees with experiment, and the calculated $4f$ density of states reproduces photoemission and bremsstrahlung isochromat spectra. The uniaxial magnetic anisotropy energy reaches 4.8 meV/f.u. when Coulomb correlations on both Ce $4f$ and Co $3d$ shells are included, in very good agreement with experimental data. These results highlight the importance of dynamical correlations and provide guidance for exploring high-performance, low-rare-earth-content permanent magnets.

We show that a single non-Hermitian defect embedded in an otherwise Hermitian topological lattice can anomalously relocate an edge state into the bulk without altering the topology. Using one- and two-dimensional models, including the Su-Schrieffer-Heeger chain and honeycomb lattices, we demonstrate that tuning an asymmetric coupling or a local parity-time-symmetric perturbation shifts the edge mode to the defect site, where it becomes strongly localized. In two dimensions, the defect further acts as a momentum-bandpass filter, selectively relocating a narrow subset of edge modes from the continuum of boundary states. This relocation is distinct from the non-Hermitian skin effect, which drives collective bulk accumulation, and from trivial defect-induced modes, which lack topological origin. The effect is robust against disorder and system size, enabling programmable, on-demand positioning of topological states for applications in photonic routing, switching, and robust sensing.

Plasmons are bosonic wavelike charge oscillations in solids and the plasmon group velocity ($v_{\mathrm{g}}$), the first derivative of momentum ($q$)-dependent dispersions, depicts the many-body electron motions of critical electronic importance. The profound characteristics of $v_{\mathrm{g}}$ in either three-dimensional (3D) or two-dimensional (2D) electron systems are nonetheless short of quantitative scrutiny. Using $q$-resolved electron energy loss spectroscopy, we tackle the $q$-dependent $v_{\mathrm{g}}$ of π and π + σ plasmons in 3D-bulk and 2D-monolayer (ML) $\mathrm{Mo}{\mathrm{S}}_2$ semiconductors, with the 2D $\mathrm{Mo}{\mathrm{S}}_2$ being the model transition-metal dichalcogenide (TMD) for emergent atomically thin electronics. $v_{\mathrm{g}}$ along with the underlining electronic parameters of the charge density, effective mass, and screening length in 2D for the plasmon dispersions is quantitatively elaborated. 2D $v_{\mathrm{g}}$ is further compared to those evaluated from metallic ML-TMD $\mathrm{Ta}{\mathrm{S}}_2$ and graphene, and the scaling over the single-particle Fermi velocity ($v_{\mathrm{F}}$) unveils a $v_{\mathrm{g}}/v_{\mathrm{F}}$ function generally obeyed by the semiconducting and metallic TMD and graphene of distinctly different massive and relativistic characters, respectively. Beyond the pertinent critical $q$ (on the order of ${10}^{-2}{\AA }^{-1}$) where one observes $v_{\mathrm{g}}=v_{\mathrm{F}}$, electric-field lines connecting the oscillating 2D charges would turn from vacuum into the atomically thin matters, concomitant with the increasing plasmon damping and reducing $v_{\mathrm{g}}$ ($v_{\mathrm{g}}<v_{\mathrm{F}}$). Long-wavelength 2D plasmons below the critical $q$ characterize the field lines largely in vacuum and are persistent and fast ($v_{\mathrm{g}}>v_{\mathrm{F}}$), with high-speed application merits. Conversely, 3D plasmons in bulk $\mathrm{Mo}{\mathrm{S}}_2$ never exceed $v_{\mathrm{F}}$.

We develop a non-Gaussian variational approach that enables us to study both equilibrium and far-from-equilibrium physics of the two-dimensional Fermi polaron. This method provides an unbiased analysis of the polaron-to-molecule phase transition without relying on truncations in the total number of particle-hole excitations. Our results—which include the ground-state energy and quasiparticle residue—are in qualitative agreement with the known Monte Carlo calculations. The main advantage of the non-Gaussian states compared to conventional numerical methods is that they enable us to explore long-time polaron evolution and, in particular, study various spectral properties accessible to both solid-state and ultracold atom experiments. We design two types of radiofrequency spectroscopies to measure polaronic and molecular spectral functions. Depending on the parameter regime, we find that these spectral functions and fermionic density profiles near the impurity either display long-lived oscillations between the repulsive and attractive polaron branches or exhibit fast relaxational dynamics to the molecular state.

We investigate the Nagaoka-Thouless ferromagnetic instability in the strongly interacting $t\text{−}{t}^{\prime }$ Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin polaron when the kinetic frustration $t^{\prime }/t$ exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group simulations reveal a quantum phase transition from the Nagaoka ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite hole density via frustration-induced magnon band deformation.

Topological phases in one-dimensional lattices are usually described by fixed, frequency-independent Hamiltonians, where topology is determined solely by structural parameters. However, in many wave-based systems with internal resonances, effective couplings become intrinsically dispersive and depend on the eigenfrequency itself. Here, we develop an analytical theory of such frequency-dependent topology using a trimer (SSH3) mass-spring lattice as a minimal model. By exactly eliminating the internal sublattice, the three-band SSH3 dynamics are mapped onto an effective two-sublattice Hamiltonian with frequency-dependent inertial and coupling terms. Because the effective parameters depend explicitly on the eigenfrequency, the resulting eigenvalue problem is nonlinear in $\omega$ and self-consistently reproduces the full three-band spectrum despite the two-level representation. This mapping reveals that the resonant effective coupling $G_2\left(\omega \right)$ acts as a bifurcation parameter controlling band inversion, redistribution of integer winding numbers, and the emergence of edge-localized modes. We show that a sign reversal of $G_2\left(\omega \right)$ induces a frequency-selective topological transition accompanied by a winding redistribution $({\nu }_1,{\nu }_2,{\nu }_3)=(-1,2,-1)$ and analytically predictable in-gap edge states governed by closed-form localization criteria. Within this framework, the bulk-edge correspondence is not determined by a fixed Hamiltonian but by the effective Hamiltonian evaluated self-consistently along the bulk dispersion relation. The formulation is further extended to adiabatically modulated lattices, where locally nontrivial Berry curvature and alternating topological charges emerge on the $(q,t)$ torus, while the global Chern number remains neutral. Because dispersive renormalization arising from internal degrees of freedom is ubiquitous in phononic, photonic, and other wave-based lattice systems, the present theory establishes a general analytical framework for topological phases in dispersive multisublattice media beyond conventional static tight-binding descriptions.

Interfaces between topological insulators and superconductors (SCs) are promising platforms for realizing Majorana zero modes (MZMs) via the superconducting proximity effect. We introduce a bilayer model consisting of the surface states of a three-dimensional topological insulator (3DTI) coupled to an $s$-wave superconductor and systematically study the role of interlayer tunneling strength ($t_{\perp }$) motivated by the recent growth of the $\mathrm{Fe}\left(\mathrm{Te},\mathrm{Se}\right)/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ heterostructure. We find that increasing $t_{\perp }$ shifts the proximity-induced (PrI) gap minimum away from the $\mathrm{\Gamma }$ point, giving rise to momentum-selective interference patterns that manifest as spatial oscillations in the in-gap states. We introduce an antidot with a magnetic vortex in the model and investigate the resulting in-gap states, including MZMs and Caroli–de Gennes–Matricon (CdGM) modes. With increasing hybridization strength, the energy separation between MZMs and CdGM states increases, enhancing the isolation of MZMs. Importantly, in the strong hybridization limit, the leading CdGM separation remains large in spite of the decrease in the PrI gap. Spin- and spatially resolved wavefunction analysis reveals angular momentum asymmetries absent in conventional $s$-wave systems. A direct comparison with a standalone $s$-wave superconductor confirms the emergence of distinct $p$-wave-like features in the bilayer geometry. Our results provide experimentally relevant predictions for tuning the stability of MZMs and their differentiation from the CdGM modes in SC-3DTI heterostructures and offer a theoretical framework for probing unconventional superconductivity in engineered topological systems.

We introduce an active-space embedding framework for core-level spectroscopies that connects localized atomic multiplets to continuum resonances within a plane-wave density functional theory/projector augmented-wave description. The approach is complementary to widely used core-level Bethe-Salpeter implementations based on a two-particle (core-exciton) picture with typically static screening: Here, a correlated multiplet manifold of the absorber (including the core hole and open-shell configurations) is coherently coupled to a plane-wave photoelectron, enabling a unified treatment of localized multiplet structure and continuum lineshapes. Spectra are computed in a general time-domain formulation equivalent to Fermi's golden rule: A transition operator tailored to the specific spectroscopy technique is applied to the correlated ground state to generate an excited wave packet, and the corresponding wave packet autocorrelation function is evaluated without explicit real-time propagation, using Lanczos tridiagonalization or the kernel polynomial method; the spectral intensity follows from its Fourier representation. We validate the method at the Ce $N_{4,5}$ edges, reproducing in quantitative agreement with experiment both high-$Q$ multiplet features and the low-$Q$ giant dipole resonance continuum, including a characteristic low-energy shoulder relevant for robust Ce valence assignments. The implementation is available open source within the quantum espresso xspectra package (xspectruplet mode), together with reproducible inputs and scripts.

We study a fourfold symmetric dispersion relation of a quantum material, which exhibits a single high-order Van Hove singularity of $X_9$ type at the Fermi energy. First, we analyze in detail its form, type, and density of states when the energy dispersion is in its canonical form. Subsequently, we study the possibility of a superconducting state when Hubbard repulsive interactions are taken into account. By solving the gap equation, it is shown that triplet state superconductivity with power-law dependence of the critical temperature $T_c$ on the interaction strength can be formed when a single singularity is present in the Brillouin zone. We discuss the effects of fluctuations and provide an upper bound of a possible superconducting critical temperature for the ruthenate ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$, which has been shown to exhibit this type of singularity.

This paper presents the technical details and commissioning results of a newly upgraded platform for ion-irradiation experiments under multi-GPa static pressure conditions at the GSI Helmholtz Center for Heavy Ion Research (Darmstadt, Germany), now accessible to external users. The GSI SIS18 accelerator provides heavy ions with tens of GeV kinetic energies, capable of penetrating through diamond anvil cells and depositing extremely high energy densities within the pressurized samples. This energy deposition triggers ultrafast, localized structural and phase transformations at the nanoscale. The platform integrates online optical microscopy and Raman spectroscopy, providing real-time monitoring of material modifications during stepwise fluence accumulation. By enabling controlled studies of structural responses and phase transitions under coupled extreme conditions, this setup opens unprecedented opportunities for research across condensed-matter physics, materials science, geoscience, high-pressure chemistry, and planetary science.

Circularly polarized phonons conventionally carry an angular momentum and a magnetic moment arising from circular motions of the atoms. Here, we present three anomalous cases that lead to phonon magnetic moments, which cannot be described in the conventional framework: rotationless axial phonons, which exhibit magnetic responses despite only carrying pseudoangular momentum, divergent gyromagnetic ratios of phonons, in which a magnetic moment is produced despite vanishing angular momentum, and anisotropic gyromagnetic ratios of phonons, which make the phonon angular momentum and magnetic moment noncollinear. Our results shed light on the origin and nature of phonon magnetism and suggest the existence of phononomagnetic hidden order.