Demonstrating how long-range entangled states are born from product states has gained much attention, which is not only important for quantum technology but also provides an unconventional tool in characterizing and classifying exotic phases of matter. In this paper, we introduce a unified and efficient framework of quantum circuits (i.e., a series of local unitary transformations), termed the seed-entangler-enriched sequential quantum circuit (SEESQC) to construct long-range entangled states (i.e., code states) in the code space of topological error-correcting codes. Specifically, we apply SEESQC to construct code states of tetradigit models—a broad class of long-range entangled stabilizer codes indexed by a four-digit parameter. These models are not rare but encompass toric codes across arbitrary dimensions and subsume the X-cube fracton code as special cases. Featuring a hierarchical structure of generalized entanglement renormalization group, many tetradigit models host spatially extended excitations (e.g., loops, membranes, and exotic nonmanifold objects) with constrained mobility and deformability, and exhibit system-size-dependent ground-state degeneracies that scale exponentially with a polynomial in linear sizes. In this work, we begin with graphical and algebraic demonstration of quantum circuits for the computational basis states, before generalizing to broader cases. Central to this framework is a key ingredient termed the seed-entangler acting on a small number of qubits termed seeds, enabling a systematic scheme to achieve arbitrary code states. Remarkably, the number of available seeds equals the number of logical qubits for the constructed examples, which leaves plenty of room for future investigation in theoretical physics, mathematics and quantum information science. Beyond the critical limitation of prior state-engineering methodologies, which required entirely distinct, model-specific circuit designs for each class of topological order, this framework transcends spatial dimensions, bridges liquid and nonliquid states, and unifies gapped phases governed by distinct entanglement renormalization group schemes. With experimental feasibility via synthetic dimensions in modern quantum simulators, the SEESQC framework offers a pathway toward engineering topological phases, and manipulating logical qubits.

${\mathrm{ZrTe}}_5$ has been extensively studied because of its novel topological properties, which are tunable by subjecting to various parameters like temperature, chemical synthesis conditions, and pressure. In this study, we have investigated and compared the effect of hydrostatic pressure up to ∼20 kbar on the transport properties of ${\mathrm{ZrTe}}_5$ single crystals grown by chemical vapor transport (CVT) and flux methods. With the application of pressure, the electrical resistivity $\rho \left(T\right)$ and thermopower $S\left(T\right)$ of both crystals were found to increase in the whole temperature range unlike the other known thermoelectric materials, such as ${\mathrm{Bi}}_2{\mathrm{Te}}_3$, SnSe etc. This observation is supported by complementary first-principles band-structure calculations, as the application of pressure widens the direct band gap at $\mathrm{\Gamma }$ point. Moreover, the analysis of the pressure-dependent magnetotransport and Shubnikov-de Hass oscillation results revealed an increase in carrier concentration and effective mass along with reduction of mobility as pressure rises. Furthermore, with the application of pressure, the flux-grown ${\mathrm{ZrTe}}_5$ crystals display a transition from unipolar to bipolar charge transport as evidenced by the emergence of a resistivity peak at $T^{*}$ under high pressure, unlike the CVT-grown ${\mathrm{ZrTe}}_5$ crystals where the bipolar charge transport near its characteristic resistivity peak $\left(T_{\mathrm{p}}\right)$ remains unaffected. Our study also reveals a pressure-induced enhancement of $T_{\mathrm{p}}$ and $T^{*}$ for both crystals, suggesting an upward shift of the Fermi level upon compression. Additionally, for the CVT-grown ${\mathrm{ZrTe}}_5$ crystals, the application of pressure nearly doubled the thermoelectric power factor (PF) at 18.2 kbar and room temperature. In contrast, for the flux-grown ${\mathrm{ZrTe}}_5$ crystals, the PF varies weakly as the pressure is raised to 17 kbar. Our results underscore the role of crystal synthesis technique along with the application of pressure as an effective strategy to optimize the magnetotransport and thermoelectric performance of ${\mathrm{ZrTe}}_5$.

Flat bands can induce strong electron correlation effects that help stabilize both magnetic and superconducting states. Here, we carry out angle-resolved photoemission spectroscopy and density functional theory calculations to study the electronic structure of the Co-pnictides ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ and ${\mathrm{LaCo}}_2{\mathrm{P}}_2$. We find that the $k_z$ Fermi topology of ferromagnetic ${\mathrm{LaCo}}_2{\mathrm{P}}_2$ is markedly two-dimensional, while the antiferromagnetic ${\mathrm{CaCo}}_2{\mathrm{As}}_2$ develops a 3D Fermi surface described by a zigzaglike band dispersion perpendicular to the Co-As plane. Furthermore, the magnetism is driven by the electronic correlations of the flat bands with $d_{xy}$ and $d_{z^2}$ orbital character at the Fermi level. Our results link the electronic dimensionality and the magnetic order and emphasize the critical role of the As-As and P-P bond strength along the $c$ direction to understand the electronic band structure and the rich phase diagram of transition metal pnictides.

We investigate the anomalous Hall effect (AHE) in four ferromagnetic (FM) cerium-based heavy-fermion (HF) compounds. These ferromagnets are distinguished by relatively high Curie temperatures ($T_{\mathrm{C}}$) and large residual resistivity ratios, which allowed us to disentangle the mechanisms of the AHE. Our results reveal a predominant skew-scattering contribution to the AHE within the FM region of all four compounds, with the anomalous Hall conductivity ranging from $100{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ to $1.5\times {10}^4{\mathrm{\Omega }}^{-1}{\mathrm{cm}}^{-1}$ at 2 K. Additionally, skew-scattering AHE also plays a significant role in the paramagnetic state, resulting in a distinct magnetic field dependence of the Hall resistivity when the temperatures are near the $T_{\mathrm{C}}$. We propose that the partially screened $f$ moments serve as scattering centers in the electrical transport of these four compounds.

Since the discovery of unconventional superconductivity in cuprates, unraveling the pairing mechanism of charge carriers in doped antiferromagnets has been a long-standing challenge. Motivated by the discovery of high-$T_c$ superconductivity in nickelate bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ (LNO), we study a minimal mixed dimensional $t-J$ model supplemented with a repulsive Coulomb interaction $V$. When hole doped, previous numerical simulations revealed that the system exhibits strong binding energies, with a phenomenology resembling a BCS-to-BEC crossover accompanied by a Feshbach resonance between two distinct types of charge carriers. Here, we perform a mean-field analysis that enables a direct observation of the BCS-to-BEC crossover as well as microscopic insights into the crossover region and the pairing symmetry for two-dimensional bilayers. We benchmark our mean-field description by comparing it to density-matrix renormalization group simulations in quasi-one-dimensional settings and find remarkably good agreement. For the two-dimensional system relevant to LNO, our mean-field calculations predict a BCS pairing gap with an extended $s$-wave symmetry, directly resulting from the pairing mechanism's Feshbach origin. Our analysis hence gives insights into pairing in unconventional superconductors and, further, can be tested in currently available ultracold atom experiments.

${\mathrm{TiSe}}_2$ is a typical transition-metal dichalcogenide known for its charge-density-wave order. In this study, we report the observation of an unusual anisotropic negative magnetoresistance in exfoliated ${\mathrm{TiSe}}_2$ nanoflakes at low temperatures. Unlike the negative magnetoresistance reported in most other transition-metal dichalcogenides, our results cannot be explained by either the conventional two-dimensional weak localization effect or the Kondo effect. A comprehensive analysis of the data suggests that the observed anisotropic negative magnetoresistance in ${\mathrm{TiSe}}_2$ flakes is most likely caused by the three-dimensional weak localization effect.

Strong evidence of unconventional superconductivity has been very recently reported experimentally in twisted transition metal dichalcogenide bilayer and gathered a significant amount of interest. Here we consider the Hubbard model on a triangular lattice describing the hole-doped moiré superlattice emerging in ${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$ twisted homobilayer in the moderately correlated regime. By applying the density matrix renormalization group, we diagonalize the spin-valley-polarized Hamiltonian and show signatures of coexisting singlet and triplet pairings in the range of hole dopings and displacement fields reported in the experiments. In this view, we show that the superconductivity in the ${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$ twisted homobilayer is likely to be induced by electronic correlations and has a mixed-symmetry character. These predictions can shed light on the nature of the superconducting state observed in the twisted homobilayer of ${\mathrm{WSe}}_2/{\mathrm{WSe}}_2$. We also identify the emerging superconducting orders, which are $d_{xy}(d_{x^2-y^2}\pm i{d}_{xy})$ and $p_y(p_x\mp i{p}_y)$ for the singlet and triplet channels in the cylinder of width three (four), respectively.

We gain quantitative insights on effects of light-matter interactions on correlated quantum matter by quantum Monte Carlo simulations. We introduce a wormhole algorithm for the paradigmatic Dicke-Ising model which combines the light-matter interaction of the Dicke model with Ising interactions. The quantum phase diagrams for ferro- and antiferromagnetic interactions on the chain and the square lattice are determined. The occurring superradiant phase transitions are in the same universality class as the Dicke model, leading to a well-known peculiar finite-size scaling that we elucidate in terms of scaling above the upper critical dimension. For the ferromagnetic case, the transition between the normal and the superradiant phase is of second order with Dicke criticality (first order) for large (small) longitudinal fields separated by a multicritical point. For antiferromagnetic interactions, we establish the light-matter analog of a lattice supersolid with off-diagonal superradiant and diagonal magnetic order and determine the nature of all transition lines. Our achievements allow to quantitatively enter the domain of mesoscopic light-matter systems, which is an increasingly prominent topic at the interface of quantum optics and condensed matter physics.

We examine the magnetic and electrical transport properties of the hexagonal ${\mathrm{EuIn}}_2{\mathrm{As}}_2$ compound, combining experimental and theoretical results. This compound is predicted to be an axion insulator from an electronic point of view and an altermagnet in the collinear magnetic phase. However, experiments indicate that the Fermi level lies within the valence band rather than in the topological gap, potentially leading to the dominance of magnetic properties. Our detailed studies on magnetization and electrical transport support the presence of a broken-helix antiferromagnetic state, which was previously identified by x-ray and neutron diffraction experiments. Notably, we observed within that state a field-induced metamagnetic transition marked by a large hysteresis in magnetoresistance, which turns into a sharp upturn for the magnetic field tilted by ${15}^{\circ }$ from the $c$ axis of the crystal. Combined with theoretical calculations, it is explained that the application of a magnetic field changes the low-resistivity antiferromagnetic domain walls to the high-resistivity domain walls due to the reduction in the Fermi surface sheets interaction area in the domain walls, originating from $p$ orbitals of As. ${\mathrm{EuIn}}_2{\mathrm{As}}_2$, therefore, presents a new case study that broadens the understanding of complex magnetic structures and their influence on electrical transport.

Magnetic topological semimetals $\mathit{Ln}\mathrm{SbTe}$ ($\mathit{Ln}=\text{lanthanide elements}$) provide a platform to study the interplay of structure, magnetism, topology, and electron correlations. Varying Sb and Te compositions in $Ln\mathrm{S}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{2-x}$ can effectively control the electronic, magnetic, and transport properties. Here, we report the evolution of transport properties with Sb and Te contents in $\mathrm{NdS}{\mathrm{b}}_x\mathrm{T}{\mathrm{e}}_{2-x}$, ($0<x<1$). Our work reveals nonmonotonic evolution in magnetoresistance with varying composition stoichiometry. Specifically, reducing Sb content $x$ leads to strong negative magnetoresistance up to 99.9%. Such a strong magnetoresistance, which is likely attributed to the interplay between structure, magnetism, and electronic bands, establishes this material as a promising platform for investigating topological semimetal for future device applications.

We demonstrate theoretically that double angle resolved photoemission spectroscopy (2eARPES) can directly probe the existence of Cooper pairs away from the Fermi surface, and can thus provide insight into the characteristic energy scale around the Fermi surface, the Debye energy, in which electrons are bound into Cooper pairs. To this end, we compute the photoelectron counting rate $P^{\left(2\right)}$ in two different types of unconventional superconductors, a $d_{x^2-y^2}$-wave superconductor, and a topological superconductor with a broken time-reversal symmetry. We show that $P^{\left(2\right)}$ provides insight into the relative strength of intra- and interband pairing in multiband systems, as well as into the spin polarization of the bands.

The experimental quest for high-temperature and room-temperature superconductivity (SC) at ambient pressure has been a long-standing research theme in physics. It has also been desired to construct reliable microscopic mechanisms that may achieve high-temperature SC. Here, we systematically explore SC in the Su-Schrieffer-Heeger (SSH) electron-phonon coupling (EPC) models by performing numerically exact quantum Monte Carlo simulations. Our results reliably showed that the superconducting $T_c$ of the SSH models is high, remarkably higher than those in the Holstein models, particularly in the strong EPC regime. This is mainly because SSH phonons can not only induce strong pairing between electrons but also help the phase coherence of Cooper pairs, thus realizing higher $T_c$. As the mechanism of the higher $T_c$ of the SSH models could be potentially relevant to realistic materials, it paves a promising way to find higher-temperature SC in the future.

In this study, we present a range-separated thermal hybrid exchange-correlation (XC) functional, termed RS-KDT0, which provides highly accurate band-gap predictions at elevated temperature while reducing the computational cost relative to thermal global hybrid functionals. At zero temperature, RS-KDT0 recovers the widely used ground-state range-separated hybrid functional HSE06. To assess its performance across temperature regimes, we conducted static calculations of electronic pressure, band gaps, and band structures. RS-KDT0 exhibits the same level of accuracy as HSE06 in the low-temperature regime and demonstrates improved agreement with finite-temperature GW calculations at elevated temperatures when compared to other thermal XC functionals such as the generalized gradient approximation (GGA)-level KDT16 and the global hybrid KDT0.

We investigate a hole-doped Mott insulator in a slab geometry using the dynamical cluster approximation. We show that the enhancement of the correlation strength at the surface results in the remarkable evolution of the layer-projected Fermi surface, which exhibits holelike pockets in the superficial layers, but gradually evolves into a single electronlike surface in the innermost layers. We further analyze the behavior of the Friedel oscillations induced by the surface and identify distinct signatures of the Fermi surface reconstruction as function of hole doping. In addition, we introduce a computationally tractable quantity that diagnoses the same Fermi surface variation by the concurrent breakdown of Luttinger's theorem. Both the latter quantity and the Friedel oscillations serve as reliable indicators of the change in Fermi surface topology, without the need for any periodization in momentum space.

$M$-type hexaferrite is an optically active transition-metal oxide, characterized by a tunable band gap within the semiconducting range, along with inherent perpendicular magnetic and optical anisotropy. However, the nature of the optical band gap and associated transitions remains unclear due to its complex crystal structure. Here, we investigate the optical properties and electronic structure of ${\mathrm{SrFe}}_{12}{\mathrm{O}}_{19}$ (SrM) $M$-type hexaferrite using a combination of UV-visible diffuse reflectance spectroscopy, x-ray absorption spectroscopy (XAS), and first-principles calculations. The optical band gap, determined from derivative absorption spectra fitting, is consistent with generalized gradient approximation plus $U_{\text{eff}}$ calculations $(U_{\text{eff}}=3.7\mathrm{eV})$, whereas HSE06 overestimates the gap. Maximally localized Wannier functions constructed from O $2p$ and Fe $3d$ orbitals reveal site-dependent crystal-field splitting and mixed $t_{2g}\text{−}{e}_g$ hybridization. The electronic structure near the Fermi level $\left(E_F\right)$ is dominated by hybridized O $2p$ and Fe $3d$ states, which govern the optical transitions. Simulated O $K$- and Fe $L_{2,3}$-edge spectra reproduce experimental XAS, with O $K$ preedge features confirming covalency of O $2p/\mathrm{Fe}$ $3d$ hybridization. X-ray magnetic circular dichroism measurements further demonstrate the magnetic polarization of O $2p$ states induced by $\text{Fe-3}d$ hybridization, with site-specific contributions from inequivalent Fe sites. These results demonstrate that the optical transitions and electronic structure of SrM are primarily governed by O $2p/\mathrm{Fe}$ $3d$ hybridization and site-resolved crystal-field effects.

We consider plasmon-assisted electron tunneling in a quantum twisting microscope (QTM). The dependence of the differential conductance on the two control parameters of the QTM—the twist angle and bias—reveals the plasmon spectrum as well as the strength of plasmon-electron interactions in the sample. We perform microscopic calculations for twisted bilayer graphene (TBG) to predict the plasmon features in the tunneling spectra of TBG close to the magic angle for different screening environments. Our work establishes a general framework for inelastic tunneling spectroscopy of collective electronic excitations using the quantum twisting microscope.