$\alpha \text{−}\mathrm{GeTe}\left(111\right)$ is a noncentrosymmetric ferroelectric (FE) material for which a significative lattice distortion combined with a strong spin-orbit interaction gives rise to giant Rashba split states in the bulk and at the surface, which have been intensively probed in the occupied valence states using static angle-resolved photoemission spectroscopy (ARPES). Nevertheless, its unoccupied conduction band structure remains unexplored, in particular the experimental determination of its electronic band gap across momentum space. Using time-resolved ARPES based on high-repetition rate and extreme ultraviolet femtosecond (fs) laser, we unveil the band structure of $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ in the full Brillouin zone, both in the valence and conduction states, as well as the exploration of its out-of-equilibrium dynamics. Our work confirms the semiconducting nature of $\alpha \text{−}\mathrm{GeTe}\left(111\right)$ with a 0.85 eV indirect band gap, which provides an upper limit for comparison to density functional theory calculations. We finally reveal the dominant scattering mechanisms of photoexcited carriers during the out-of-equilibrium dynamics under fs light pulses.

Motivated by a recent experiment that realizes nearest-neighbor dipolar couplings in an optical lattice [C. Lagoin et al., Nature (London) 609, 485 (2022)], we study a one-dimensional version of the two-component extended Bose-Hubbard model via the density-matrix renormalization group method. By using the nearest-neighbor and on-site interaction parameters from the experiment, we start by mapping the quantum phase diagram in the hopping parameter $t_A\text{−}{t}_B$ plane with boson densities ${\rho }_A={\rho }_B=1/2$. In addition to the density-wave phase reported in the experiment, we find several regimes of superfluidity when one or both hopping parameters are large enough, and interestingly there is a supercounterfluid phase at moderate and comparable hopping parameters. The universality classes of these phase transitions are analyzed from the correlation functions, excitation gaps, and entanglement entropy. In particular, a Berezinskii-Kosterlitz-Thouless type is recognized for several gapped-to-gapless transitions. In addition, we also study the quantum phase transitions by varying ${\rho }_B$ from 0 to 1 while keeping ${\rho }_A=1/2$. We identify a supersolid phase in a wide range of $1/2<{\rho }_B<1$. Our work paves the way for realizing exotic many-body phases in cold-atom experiments upon proper tuning of experimental parameters.

Preparing fractional quantum Hall (FQH) states represents a key challenge for quantum simulators. While small Laughlin-type states have been realized by manipulating two atoms or two photons, scaling up these settings to larger ensembles stands as an impractical task using existing methods and protocols. In this work, we propose to use optimal-control methods to substantially accelerate the preparation of small Laughlin-type states, and demonstrate that the resulting protocols are also well suited to realize larger FQH states under realistic preparation times. Our schemes are specifically built on the recent optical-lattice experiment [Léonard et al., Nature (London) 619, 495 (2023)], and consist in optimizing very few control parameters: the tunneling amplitudes and linear gradients along the two directions of the lattice. We demonstrate the robustness of our optimal-control schemes against control errors and disorder, and discuss their advantages over existing preparation methods. Our work paves the way to the efficient realization of strongly correlated topological states in quantum-engineered systems.

The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge (vertex) excitations can be problematic. Therefore, in order to describe all anyon excitations, we study an extended model [Y. Hu et al., Phys. Rev. B 97, 195154 (2018)]. Building on recent methods, we compute the spectral degeneracies of excited states and obtain the exact partition function. In the thermodynamic limit, the latter is dominated by the trivial (vacuum) anyon, so that topological order is destroyed at any nonzero temperature. In contrast, in a finite-size system, order survives up to a finite temperature, revealing a nontrivial scaling between temperature and size similar to that of the one-dimensional classical Ising model. We confirm this scaling by computing the thermal average of several observables such as Wegner-Wilson loops and topological mutual information.

The variability of topological states in intrinsic magnetic topological insulators signifies a critical advancement in both fundamental research and technological applications. Employing the tight-binding model, we illustrate that two-dimensional ferromagnetic (FM) second-order topological insulators (SOTIs) with spontaneous valley polarization can display intricate topological phase diagrams through valley modulation. This includes transitions from FM SOTI to quantum anomalous Hall insulator (QAHI), and subsequently to a normal insulator (NI). The synergistic integration of Floquet engineering and static strain modulation enables bidirectional control over the chirality of QAHI edge states, achieved through the combination of time-periodic perturbations and lattice deformation. The reliability of this SOTI-QAHI-NI process is confirmed through the Janus VSNH monolayer by first-principles calculations. The concurrent modulation of strain and Floquet engineering, synergistically coupled with magnetization reversal, supports the realization of directionally tunable, dissipationless topologically protected edge currents in the QAHI phase of the system. Our findings not only establish a broad framework for modulating the topological states but also uncover the potential of Janus topological materials, suggesting possible applications in quantum devices.

Recent experiments have revealed the evidence of band flattening in monolayer graphene utilizing buckled superlattices. However, the fundamental understanding on the atomistic deformation fields in buckled graphene superlattice remains elusive, posing challenges for rationally utilizing such mechanism to access correlated electronic phases and topological properties. In this work, by combining continuum mechanics theory, molecular dynamics simulations, and quantum mechanical calculations, we have developed an analytical model that can accurately describe the postbuckling deformation fields, enabling large-scale computational design on band flattening and pseudomagnetic fields in buckled graphene superlattices. The shear strain gradient is found to be the dominating factor to induce giant pseudomagnetic fields. However, stronger pseudomagnetic fields do not necessarily induce stronger band flattening behavior, which supports recent experimental findings. Our results advance the understanding of flat bands and giant pseudomagnetic fields in monolayer graphene by compressive strain engineering.

Using density-functional theory combined with the many-body perturbation approach, we have studied the evolution of quasiparticle electronic structure, electron-hole excitations, and optical properties in blue phosphorene nanoribbons. In these low-dimensional systems, the unique dielectric screening results in a significant self-energy correction, which remains impactful even in nanoribbons of large width. Density-functional theory calculations show that armchair and zigzag blue phosphorene nanoribbons exhibit distinct scaling law with width due to their substantially anisotropic effective masses. The quasiparticle band gap evolves as $1/w$ with ribbon width $w$ and is insensitive to structural chirality, contrasting with that predicted by density functional theory. In the meantime, the optical properties are dominated by exciton effects. The exciton energy and exciton binding energy evolve as $1/w^{1.5}$ and $1/w^{0.8}$, respectively. The polarizability, evolving as $1/w^{0.4}$, underscores the enhanced electron-electron and electron-hole interaction in these one-dimensional systems. Our findings not only provide deep insight into the many-body effects in the electronic and optical properties of low-dimensional materials, but they also show the tunable band gap over a wide range in blue phosphorene nanoribbons, which could find potential applications in optoelectronics.

Electron-phonon coupling can strongly affect the eigenmodes of nano- and micromechanical resonators. We study the effect of the coupling for $p$-doped semiconductor resonators. We show that the backaction from the strain-induced redistribution of the holes between and within the energy bands can lead to a nonmonotonic dependence of the modes' eigenfrequencies on temperature and to a strong mode nonlinearity that also nonmonotonically depends on temperature. Unexpectedly, we find that the nonlinearity can nonmonotonically depend on the hole density. We also briefly discuss the effect of the coupling to holes on the modes' decay rates. The results are compared with the experiment.

Quantum complexity measures the difficulty of obtaining a given state starting from a typically unentangled state. In this work, we show that complexity, when defined through the minimization of a Riemannian cost functional over the manifold of Gaussian states, provides the same information as quantum fidelity and is therefore capable of detecting quantum phase transitions. However, it does not offer a more refined analysis than entanglement entropy for a given state. We conclude that incorporating a notion of spatial locality into the computation of complexity is essential to uncover new physics beyond what is accessible through entanglement entropy and fidelity.

Entanglement microscopy reveals the true quantum correlations among the microscopic building blocks of many-body systems [Nat. Commun. 16, 96 (2025)]. Using this approach, we study the multipartite entanglement of the quantum Ising model in 1D, 2D, and 3D. We first obtain the full reduced density matrix (tomography) of subregions that have at most four sites via quantum Monte Carlo, exact diagonalization, and the exact solution in 1D. We then analyze both bipartite and genuine multipartite entanglement (GME) among the sites in the subregion. To do so, we use a variety of measures including the negativity, as well as a true measure of GME: the genuinely multipartite concurrence (or GME concurrence), and its computationally cheaper lower bound $I_2$. We provide a complete proof that $I_2$ bounds the GME concurrence, and show how the symmetries of the state simplify its evaluation. For adjacent sites, we find three- and four-spin GME present across large portions of the phase diagram, reaching a maximum near the quantum critical point. In 1D, we identify the singular scaling of the derivative $d{I}_2/dh$ approaching the critical point. We observe a sharp decrease in GME with increasing dimensionality, consistent with the monogamous nature of entanglement. Furthermore, we find that GME vanishes for subregions consisting of nonadjacent sites in both 2D and 3D, offering a stark illustration of the short-ranged nature of entanglement in equilibrium quantum matter [arXiv:2402.06677]. Finally, we analyze the most collective form of entanglement by evaluating the GME concurrence among all spins in the lattice, which can be obtained from a simple observable: the single-site transverse magnetization. This global concurrence is larger in 1D compared to 2D and 3D, but it is relatively less robust against perturbations such as local measurements.

Simulating strongly correlated quantum systems in continuous space belongs to the most challenging and long-concerned issues in quantum physics. This work investigates the quantum entanglement and criticality of the ground-state wave functions of infinitely many coupled quantum oscillators (iCQOs). The essential task involves solving a set of partial differential equations (Schrödinger equations in the canonical quantization picture) with infinitely many variables, which currently lacks valid methods. By extending the imaginary-time evolution algorithm with translationally invariant functional tensor network, we simulate the ground state of iCQOs with the presence of two- and three-body couplings. We determine the range of coupling strengths where there exists a real ground-state energy (dubbed as physical region). With two-body couplings, we reveal the logarithmic scaling law of entanglement entropy (EE) and the polynomial scaling law of correlation length against the virtual bond dimension $\chi$ at the dividing point of physical and nonphysical regions. These two scaling behaviors are signatures of criticality, according to the previous results in quantum lattice models, but were not reported in continuous-space quantum systems. The scaling coefficients result in a central charge $c=1$, indicating the presence of free boson conformal field theory (CFT). We further show that the presence of three-body couplings, for which there are no analytical or numerical results, breaks down the CFT description at the dividing point. Our work uncovers the scaling behaviors of EE in the continuous-space quantum many-body systems. These results provide solid numerical evidence supporting the high efficiency of TN in representing the continuous-space quantum many-body wave functions in the thermodynamic limit, and meanwhile suggest an efficient approach to study the entanglement properties and criticality in continuous space.

We propose and analyze a deformation of the $3+1\mathrm{d}$ lattice ${\mathbb{Z}}_2$ gauge theory that preserves the noninvertible Wegner duality symmetry at the self-dual point. We identify a frustration-free point along this deformation where there are nine exactly degenerate ground states (on a periodic cubic lattice) even at finite volume. One of these ground states is a trivial product state and the rest are the topologically ordered ground states of the $3+1\mathrm{d}$ toric code, and they are exchanged by the Wegner duality. We also prove that the frustration-free point is gapped in the thermodynamic limit. Our model, therefore, realizes a gapped phase with spontaneously broken Wegner duality symmetry. Furthermore, by imposing the Gauss law constraints energetically, all the above features can be realized on a tensor product Hilbert space. Finally, we discuss a generalization of this deformation to the $3+1\mathrm{d}$ lattice ${\mathbb{Z}}_N$ gauge theory and conjecture the possible phase diagram.

The method of molecular dynamics and molecular mechanics has been used to numerically simulate the formation of wrinkle systems during compression of a graphene sheet lying on a flat solid substrate. It is shown that under uniaxial compression the nanosheet can transition into several stable wrinkled states: the most energetically favorable one is a linear wrinkle of infinite length. Higher-energy states include wrinkles of finite length aligned along the same line where their ends partially overlap. Under biaxial compression, the graphene nanosheet can contain one linear wrinkle or two linear nonintersecting or intersecting wrinkles corresponding to weak, medium, and strong compression, respectively. There are several nanosheet states with intersecting wrinkles that differ in structure of intersection area. The effect of external hydrostatic pressure on the shape of wrinkles has been studied. It is shown that there is a critical pressure value at which the wrinkle either completely flattens (disappears) or collapses into a vertical two-layer fold (the first scenario is possible only with weak compression of the sheet).

We study the charge and current response functions $P$ and $\mathrm{\Pi }$ in a semi-infinite metal block using the electron surface Green's functions. The surface electrons behave similarly to a two-dimensional Fermi gas, but are strongly damped due to coupling to the bulk. This substantially reduces the region of validity of the Drude model for $P$, which requires the frequency $\omega \gg max(v_{F}q,1/\tau )$, where $v_F$ is the Fermi velocity, $q$ is the wave vector, and $\tau$ is an effective relaxation time. As a consequence, for typical metal in near-field heat transfer, the thermal conductance due to the Coulomb interaction scales as $1/d^4$ with the distance of the vacuum gap instead of the well-known $1/d^2$ result of the Drude model. The current response $\mathrm{\Pi }$ is shown to be highly anisotropic. The Drude model describes well the transverse directions parallel to the surface, but is very different in the normal direction up to about 100 lattice sites away from the surface. These ideas and the residual diamagnetic effect of a nonzero $\mathrm{\Pi }$ on the surface at zero frequency still cannot resolve the Casimir puzzle.

As a layered material, FeSe provides an ideal platform for realizing high-temperature superconductivity and exploring the microscopic pairing mechanisms. Here, we investigate the behavior of superconductivity and orbital-selective pairing of bulk FeSe under different pressuring schemes within first-principles dynamical mean-field theory ($ab$-DMFT). We first confirm that the orthorhombic phase is preferred among the layered structures, and the resultant superconducting transition temperature ($T_{\text{c}}$) is elevated from essentially zero to the experimentally observed order of magnitude only with the inclusion of correlation-enhanced electron-phonon coupling. The vital role of correlation effects is strongly corroborated by our quantitative interpretation of the experimentally observed superconducting dome under hydrostatic pressure. Counter-intuitively, the $T_{\text{c}}$ qualitatively anticorrelates with the correlation strength, as measured by the quasiparticle broadening around the Fermi level. We further investigate the effects of biaxial and uniaxial pressures and predict that uniaxial pressure can induce the emergence of two superconducting domes due to a synergetic effect of structural transitions and a switching of the dominant orbital-selective pairing from $d_{xy}$ to $d_{z^2}$. Collectively, these findings pinpoint the vital role of electron correlations in the phonon-mediated pairing mechanism of bulk FeSe, and the $ab$-DMFT approach for quantitative evaluation of $T_{\text{c}}$ is expected to find broad applicability in other correlated electron systems.

The equation of state (EoS) of a system is vital in multiple fields, including physics, geophysics, and astrophysics. However, the available EoSs of simple metals under pressures of more than 400 GPa are far from adequate for the research under extreme conditions. In this work, we have extended the isothermal EoS of metal tungsten (W) to the most extreme pressures up to ∼527 GPa by employing the modified toroidal diamond anvil cells (mt-DACs), based on the known EoS of gold (Au) according to the synchrotron x-ray-diffractions experiments. Upon compression to the highest pressure of 527 GPa, the structure of W remains unchanged and consistently retains its body-centered-cubic structure. By optimizing the force patterns of the mt-DAC with a modified toroidal process method, the present experiment is capable of producing pressures over 500 GPa, overcoming the 400-GPa limit of the conventional DAC. A minor maximum equivalent stress and maximum principal strain of the mt-DAC in the Boehler-Almax type revealed by the finite-element analysis are crucial for the pressure limit. This result would provide an extensive reference for the pressure calibration in experiments under extreme conditions.

The role of layer disorder is important in establishing the topological phases of ${\mathrm{MoTe}}_2$. A rich tapestry of atomic ordering influences the structural phase transitions (SPTs), but there is little understanding of the mechanistic details of the phase transition. An atomistic level study was conducted to investigate the local structure of the $1T^{\prime }$ and $T_d$ phases of ${\mathrm{MoTe}}_2$ by using the pair distribution function (PDF) technique. While the average structure exhibits an SPT and coexistence of phases as a function of temperature, the local structure showed the suppression of SPT. The sample retained its monoclinic structure at all temperatures in short-range order. A sharp PDF peak observed at short distances indicated a strong atom-atom correlation between the Mo and Te atoms within the Mo octahedra. In addition, a large-box modeling of the PDF data indicated a preferential motion of Te atoms towards $c$ axis at all temperatures. Structural defects, such as stacking faults, likely result in the coexistence of phases in the average structure and suppress the local SPT of ${\mathrm{MoTe}}_2$. These results are stepping stones to understand the long-debated origins of structural, vibrational, and electronic properties of ${\mathrm{MoTe}}_2$ and similar transition metal dichalcogenides.

We investigated surface acoustic wave (SAW) propagation and lattice vibrations in two-dimensional (2D) titanium carbide $\left({\mathrm{Ti}}_3{\mathrm{C}}_2{T}_{\mathrm{x}}\right)$ MXene films as a function of surface termination and layer stacking, using atomistic simulations. We found that SAW propagation velocity is highly sensitive to both single-layer properties and interlayer bonding. Surface terminations significantly modulate wave behavior, with oxygen and fluorine terminations producing distinct effects on wave propagation, with oxygen-terminated monolayers exhibiting 20% higher wave speeds than fluorine counterparts due to strengthened intralayer bonds. Key observations include the transition from one to two layers causing wave speed variations, and the development of interlayer modes that generate more dispersed lattice vibrations. As the film layer thickness increases, SAW propagation becomes predominantly confined to the upper surface, with coherence of vibrational modes diminishing in multilayer structures. These findings suggest MXene terminations and layer stacking are crucial parameters for controlling SAW behavior, offering promising avenues for novel acoustic wave device applications.

The structural, dynamic, and electrical properties of a prototypical amorphous electrolyte are examined using a variety of theoretical and experimental techniques. We focus on the $x{\mathrm{Na}}_2\mathrm{S}\text{−}(100\text{−}x){\mathrm{SiS}}_2$ system, which represents a potential application for all-solid-state batteries. First-principles molecular dynamics simulations, x-ray scattering, and conductivity experiments are performed on two select compositions of this binary: ${\mathrm{Na}}_2\mathrm{S}\text{−}{\mathrm{SiS}}_2$ and $2{\mathrm{Na}}_2\mathrm{S}\text{−}{\mathrm{SiS}}_2$. The validation of the model structures, which reproduce with excellent accuracy the measured structure functions permits examining in detail the atomic-scale picture and the effect of alkali addition. Results indicate a complete depolymerization of the network, which is characterized using the $Q^n$ formalism, and at high Na content consists essentially of isolated ${\mathrm{SiS}}_4^{4\ominus }$ tetrahedra typical of the short-range order of the corresponding crystalline compound. As in other modified chalcogenides, the simulation results reveal the presence of homopolar Si-Si and S-S defects, the latter being known to enhance ionic conductivity while the former produces isolated ${\left({\mathrm{Si}}_2{\mathrm{S}}_6\right)}^{6\ominus }$ anions at high Na content. The measured temperature behavior of diffusivity and conductivity suggests typical Arrhenius behavior measured by complex impedance spectroscopy and not fully confirmed theoretically given the reduced ab initio statistics, while measured ionic conduction at room temperature is found to be similar to that of the corresponding thiogermanates. We measured an ionic conductivity of $2.9\times {10}^{-5}{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ at room temperature for the $2{\mathrm{Na}}_2\mathrm{S}\text{−}{\mathrm{SiS}}_2$ glass.