Representing the time-evolution operator as a tensor network constitutes a key ingredient in several algorithms for studying quantum lattice systems at finite temperature or in a nonequilibrium setting. For a Hamiltonian composed of strictly short-range interactions, the Suzuki-Trotter decomposition is the main technique for obtaining such a representation. Vanhecke et al. [Phys. Rev. A 103, L020402 (2021)] introduced an alternative strategy—the cluster expansion. This approach naturally preserves internal and lattice symmetries and can more easily be extended to higher-order representations or longer-range interactions. We extend the cluster expansion to two-dimensional fermionic systems and employ it to construct projected entangled-pair operator (PEPO) approximations of Gibbs states. We also discuss and benchmark different truncation schemes for multiplying layers of PEPOs together. Applying the resulting framework to a two-dimensional spinless fermion model with attractive interactions, we resolve a clear phase boundary at finite temperature.

The dual localized-itinerant character of uranium $5f$ electrons governs the electronic and magnetic properties of many actinide materials, yet the microscopic mechanisms controlling their tunable itinerancy remain incompletely understood. Here we investigate the uranium dipnictides $\mathrm{U}{X}_2$ ($X=\mathrm{P},\mathrm{As},\mathrm{Sb}$) using fully charge-self-consistent density functional theory combined with dynamical mean-field theory including spin–orbit coupling (SOC) in the paramagnetic (PM) state at $T=300\mathrm{K}$. The calculations reveal that the uranium $5f$ shell resides in a mixed-valence configuration with occupancies $\langle n_{5f}\rangle \approx 2.6-2.8$, dominated by $5f^2-5f^3$ states. Momentum-resolved spectra and hybridization functions show that decreasing $5f-p$ hybridization along the $\mathrm{P}\to \mathrm{As}\to \mathrm{Sb}$ series enhances correlation effects and strengthens $5f$ localization, whereas hydrostatic pressure increases hybridization and quasiparticle (QP) coherence, driving the system toward greater itinerancy. The Matsubara self-energy indicates coherent Fermi-liquid behavior at 300 K with pronounced spin–orbit-driven orbital differentiation, where the $j=5/2$ manifold is more strongly renormalized than the $j=7/2$ states. Local susceptibilities reveal sizable fluctuating $5f$ moments in the PM phase at room temperature, providing a qualitative—necessarily speculative—connection to magnetic scales inferred from previous static DFT calculations of the antiferromagnetic ground state. Additional calculations for ${\mathrm{UP}}_2$ in its experimentally established tetragonal $I4/mmm$ phase show that the key features identified in the $P4/nmm$ reference structure—including the SOC-split $5f$ manifold, the dominance of $j=5/2$ states near the Fermi level, and pressure-enhanced QP coherence—remain qualitatively preserved, with only moderate quantitative differences arising from the distinct crystallographic environment. Together these results establish a clear microscopic mechanism: ligand chemistry sets the baseline uranium–ligand hybridization and degree of $5f$ localization, while pressure continuously tunes the same control parameter, providing a unified framework for understanding how correlations, SOC, and hybridization govern $5f$ itinerancy in uranium intermetallic compounds.

In the natural chalcopyrite mineral ${\mathrm{Cu}}_{1+x}{\mathrm{Fe}}_{1-x}{\mathrm{S}}_2$ ($x=0.08$), a huge Seebeck effect was reported around room temperature [Ang et al., Angew. Chem. Int. Ed. 54, 12909 (2015)]. In this paper, we suggest that the observed huge Seebeck coefficient is due to antiferromagnetic magnon drag collaborated with an impurity band. First, we show that the temperature dependences of the electrical resistivity and Hall coefficient are in good agreement with the theoretical results based on the self-consistent $t$-matrix approximation, considering the impurity band. Secondly, by deducing the lifetime of the magnon from the experimental result of the thermal conductivity, we evaluate the Seebeck coefficient due to antiferromagnetic magnon drag collaborating with the impurity band by the linear response theory based on the Kubo-Luttinger formalism. Finally, we find that the obtained theoretical result is quantitatively consistent with the experimental one near room temperature.

We theoretically analyze the THz response of an electron-hole pair confined in a semiconductor nanoparticle. We show that the interplay of particle confinement and electron-hole Coulomb interaction leads to significant renormalizations and energy shifts in THz linear conductivity of the nanocrystal. We develop and evaluate models in the strong and weak confinement regime to correctly address the effect of Coulomb interaction. In the weak confinement regime, we find solutions of the problem in a form similar to the Wannier wave function whose spatial extent is reduced as a consequence of the confinement. The resulting states are scalable down to the strong confinement regime, enabling a theoretical description of the exciton response for arbitrarily sized nanoparticles.

Conventional wisdom dictates that the conducting edge states of two-dimensional topological insulators of the ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ family are protected by time-reversal symmetry. However, theoretical bulk calculations and a recent experiment show that the edge states persist in the presence of large external magnetic fields. To address this apparent contradiction, we have developed an analytical description for the edge-state wave function of a semi-infinite sample in a perpendicular magnetic field. Our description relies on the usual bulk Landau levels, together with additional states arising due to the presence of the hard wall, which are unnormalizable in the infinite system. The analytical wave functions agree extremely well with numerical calculations and can be used to directly analyze the behavior of the edge states in a magnetic field.

We extend ferromagnetic resonance (FMR) modulation theory to describe systems in which bulk and boundary states of topological materials coexist, with both appearing at the same energy. As an application of the formulation, we investigate the enhancement of the Gilbert damping constant on the (110) surface of a $d$-wave superconductor where nodal quasiparticles coexist with edge states, which are one-dimensional boundary states, known as surface zero-energy Andreev bound states. We find two characteristic features: a pronounced edge-to-edge excitation peak near zero energy, and an additional edge-to-bulk excitation peak at the superconducting gap energy. We also observe power-law decay at low temperatures and exponential decay at intermediate temperatures in the low-energy regime. These features demonstrate the comparable contributions of the bulk and boundary states to the FMR response. Our theory provides a broadly applicable framework for the analysis of topological materials.

Spin-orbit coupling in two-dimensional materials gives rise to a Rashba spin splitting when inversion and mirror symmetries are broken, yet its microscopic origin and quantitative characterization in transition metal dichalcogenides remain incomplete. Using first-principles calculations, we investigate monolayer ${MX}_2$ transition metal dichalcogenides ($M=\mathrm{Mo}$, W; $X=\mathrm{S}$, Se, Te), and homobilayers lacking inversion and mirror symmetries, exhibiting zero-field Rashba splitting. We determine the field- and momentum-independent Rashba coefficients and intrinsic electric fields of these systems, establishing a direct connection to the Rashba Hamiltonian. Surprisingly, the Rashba effect on the topmost valence band is substantially smaller in bilayers than in monolayers at typical fields. This motivates an analytical microscopic model that identifies the orbital processes responsible for Rashba spin splitting. It confirms that, in bilayers, the effect is governed by the competition between layer-resolved charge deformation and interlayer coupling. To quantify this competition, we introduce the orbital polarization imbalance and orbital polarizability as order parameters and, by combining them with first-principles calculations, identify the dominant microscopic channel responsible for the Rashba splitting.

A quantitative description of the exchange interaction in quantum dots is relevant for modeling gate operations of spin qubits. By measuring the amplitude and frequency of exchange-driven qubit state oscillations, we measure the detuning dependence of the exchange coupling in a GaAs double quantum dot over three orders of magnitude. Both one- and three-dimensional full configuration-interaction simulations can replicate the observed behavior. Extending a Hubbard model by including excited states increases the range of detuning where it provides a good fit, thus elucidating the underlying physics.

Conservation laws are of paramount importance in our understanding of classical and quantum dynamics. Here, we present a general framework for constructing exact quantum integrals of motion with the desired locality and quantum numbers, which will be illustrated for the case of many-body-localization (MBL). The latter has been understood theoretically in terms of the existence of an extensive number of local integrals of motion (LIOMs). Using our approach, we show that one can express the task of finding LIOMs as an optimization problem. For some specifications, this problem surprisingly connects to the question of finding classical ground states of spin-glass models. Our work unifies previous results obtained in the MBL context and reveals intriguing connections between many-body localization, spin-glass physics, and constrained optimization problems.

Topological defects commonly emerge during phase transitions, with their topological charge ($s$) serving as a discrete invariant that dictates defect stability, dynamics, and ordering pathways. Liquid crystals across the nematic-smectic A (N-SmA) transition provide an ideal model for exploring how $s$ constraints govern defect evolution, yet the role of non +1 charges in mediating smectic order remains largely unexplored. Here, we systematically investigate the influence of $s$ on defect evolution during the N-SmA phase transition by combining photoalignment lattices with distinct topological charge distributions and a vertically aligned surface. For $s=+1/2$, cooling from the isotropic to the N phase generates disclination lines. During subsequent thermal cycling across the N-SmA transition, these lines reorient and induce the formation of previously unreported deformed semitoroidal focal conic domains (semi-TFCDs). Landau–de Gennes simulations reveal that the morphological transition in the N phase originates from a geometric transformation of the disclination lines, driven by constraints imposed by the emergence of layered structures. Further analysis indicates that splay deformation promotes TFCD generation. This is confirmed by the observation that reducing the distance between relatively oriented +1/2 alignment singularities diminishes the bending contribution and leads to ordered TFCD formation. In addition, as $s$ increases, the total director rotation within a unit region changes by 2πs, thereby altering the splay-to-bending deformation ratio. At $s=+1$, pure radial splay yields optimal ordered TFCDs. For $s=+3/2$, splay and bending coexist; the unsuppressed bending deformation disrupts layer continuity, resulting in frustrated TFCD arrays. For higher $s$, bending deformation dominates, causing fragmentation and disorder of SmA textures, and irregular TFCDs form at positions dominated by splay deformation. In this work, we advance the understanding of topological defect-mediated phase transitions by revealing the rich morphological diversity arising from the interplay between topological constraints and molecular deformations. We also offer broader insights into soft matter physics, where topological defects serve as fundamental building blocks for hierarchical self-assembly, pattern formation, and the design of functional materials.

Lead-free halide vacancy-ordered double perovskites ${\mathrm{Cs}}_{2}B{X}_6$ have recently attracted significant attention due to their intrinsically ultralow lattice thermal conductivity (${\kappa }_{\mathrm{L}}$), which is highly desirable for thermal insulation and thermoelectric applications. In this work, we systematically investigate the anharmonic lattice dynamics and thermal transport properties of ${\mathrm{Cs}}_{2}B{X}_6$ ($B$ = Zr, Pd, Sn, Te, Hf, and Pt; $X$ = Cl, Br, and I) using state-of-the-art first-principles calculations, based on a unified theory of thermal transport for crystals and glasses. All studied compounds are found to exhibit ultralow ${\kappa }_{\mathrm{L}}$ below 1.0 ${\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ at room temperature and large derivation from the conventional $T^{-1}$ temperature dependence. Our analysis combined with the machine-learning approach show that sound velocities (1100 – 1600 m ${\mathrm{s}}^{-1}$), which originate from the intrinsically weak chemical bonding, are strongly correlated with ${\kappa }_{\mathrm{L}}$ in these compounds. Furthermore, the influence of $B$- and $X$-site elements on phonon dispersion, anharmonicity, and scattering phase space is clarified. Our results provide microscopic insights into the origin of ultralow ${\kappa }_{\mathrm{L}}$ in ${\mathrm{Cs}}_{2}B{X}_6$ and offer guiding principles for the rational design of halide-based materials with tailored thermal transport properties.

The novel class of collinear compensated magnets, dubbed altermagnets, has attracted immense research attention by the property of nonrelativistic spin splitting. More recently, the properties of altermagnets caused by relativistic spin-orbit coupling (SOC) became the topic of many investigations. The aim of the paper is to contribute to a deeper understanding of the formation of relativistic effects in altermagnets. The focus of the paper is on the phenomena of weak ferromagnetism (WFM) and relativistic modification of the electron states including the interplay of these phenomena. The main tools of the study are various types of relativistic calculations based on density functional theory combined with the symmetry analysis on the basis of spin space groups. The consideration is performed on two different levels. On the first level, the atomistic magnetic structure of weak ferromagnetic state is calculated and discussed. Both spin and orbital atomic moments are taken into account. We study the dependence of the WFM moment on the strength of the SOC and obtain a peculiar nonmonotonous type of dependence. We separate the contributions of the SOC of the metal and ligand atoms to WFM. A very interesting result is obtained in quasisymmetry (QS) calculation where only the component of the SOC collinear to the Néel vector is taken into account. In QS calculation the spin WFM is absent while the orbital WFM is present. This result reveals a principal difference in the formation of the spin and orbital magnetic moments. On the second level, the study is focused on the properties of individual electron states. We introduce the notion of the magnetic structure of the electron state (MSES). It is shown how the nonrelativistic collinear spin-MSES of both metal and ligand moments and nonrelativistic compensated orbital-MSES of the ligand moments transform into complex noncollinear three-dimensional MSESs of both spin and orbital nature giving large contributions to WFM. An important role in the formation of MSESs is played by the relativistic splitting of the accidental spin degeneracies at general k points filling the volume of the Brillouin zone. The formation of the regions of avoided crossings in the relativistic band structure is related to the nonmonotonous dependence of the WFM moment as the function of the SOC strength. The importance of the metal-ligand hybridization in the formation of the AM properties is discussed and illustrated by means of the comparison of the local density approximation (LDA) and $\mathrm{LDA}+U$ calculations. Most of the calculations are performed for MnTe, a prototypical material for the class of altermagnets.

We theoretically demonstrate squeezed light generation in a compact, electrically driven device utilizing the nonlinear light-matter interaction of Cooper pair recombination in a hybrid superconductor-semiconductor structure. On the basis of second-order perturbation theory, we developed an effective Hamiltonian which incorporates the electronic component of the interaction as a photon coupling strength coefficient, enabling a model to describe the quadrature squeezing effect of Cooper pair recombination on the photonic state. We find the squeezing strength to be proportional to the superconducting energy gap squared and device length, as well as increasing with applied voltage. For a practical device length, materials, and voltage bias, we calculated squeezing values comparable to those of existing squeezed light generation methods when operating below the critical temperature. This theoretically developed concept shows viability for electrically pumped squeezed light generation and can pave the way towards the realization of squeezing in compact integrated structures.

Disorder in moiré superlattices simultaneously degrades flat-band localization and induces Anderson localization, yet how these two regimes interact has remained unclear. Here, we introduce a combined framework linking localization‐length scaling with differential probability density analysis to map localization transitions in partially disordered one‐dimensional silicon moiré lattices. It is found that flat bands confined within the interband gap keep their strong localization even as disorder grows. In contrast, flat bands intersecting dispersive bands exhibit rich behaviors: the low‐frequency branch undergoes an inverse Anderson transition, while the high‐frequency branch supports coexisting flat-band and Anderson localization at strong disorder. Our results deliver direct evidence of competing localization mechanisms in disordered moiré systems and offer guiding principles for engineering robust, nonideal moiré photonic devices.

Long coherence times rank among the most important performance measures for many different types of quantum technology. In the electron-nuclear spin system of NV centers of diamond, the nuclear spins provide particularly long dephasing times. However, since initialization and readout require assistance from the electron spin, the apparent dephasing times can be reduced by the electron spin lifetime. Here we propose and implement schemes for measuring and extending the dephasing times of nuclear spins, resulting in dephasing times that are longer than the longitudinal relaxation time $T_1$ of the electron spin.

The frequency-dependent complex optical conductivity $\widehat{\sigma }\left(f\right)$ reflects key properties of superconductors, such as the energy gap $2\mathrm{\Delta }$ in the density of states (DOS) and the superfluid density $n_{\mathrm{s}}$. For disordered superconductors, $\widehat{\sigma }\left(f\right)$ often can be described within Bardeen-Cooper-Schrieffer (BCS) theory, while in corresponding tunneling experiments, deviations in the observed DOS typically require modeling by the phenomenological Dynes formula. The implications of such Dynes DOS for optics have been rarely discussed so far. Here we probe the terahertz $\widehat{\sigma }\left(f\right)$ of superconducting NbN thin films with thicknesses ranging from 4.5 to 20 nm, which were grown by atomic layer deposition. Our frequency range from 0.3 to 2.1 THz covers energies below and above $2\mathrm{\Delta }$. For 20-nm-thick NbN, we find in $\widehat{\sigma }\left(f\right)$ distinct deviations from the BCS model, including a steplike characteristic in the absorption at ${\mathrm{\Delta }}_0$, i.e., half the zero-temperature spectral gap. These observations can be fully captured by introducing a small and temperature-independent Dynes pair-breaking rate $\mathrm{\Gamma }\sim 0.036{\mathrm{\Delta }}_0$. For the other films, we also observe signs of Dynes-type DOS and we discuss the evolution of $2{\mathrm{\Delta }}_0, n_{\mathrm{s}},0$, and $\mathrm{\Gamma }$ as a function of film thickness.

Two-dimensional ferroelectrics provide a unique platform for exploring symmetry breaking and electromechanical coupling at the atomic limit. Using first-principles calculations, we investigate the shear piezoelectric response of a black-phosphorus-like bismuth monolayer. Bismuthene exhibits a giant shear piezoelectric coefficient of $d_{26}=311.1$ pC/N, placing it among the highest values reported for two-dimensional materials. We show that this exceptional response originates from shear-strain-induced polarization rotation between symmetry-equivalent in-plane ferroelectric states, enabled by an intrinsically flat potential-energy landscape with a rotational barrier of only $\sim 10\mathrm{meV}$. This flat landscape also gives rise to an anomalous barrier inversion, where the in-plane switching barrier is lower than the conventional out-of-plane barrier. These findings establish that multiaxial ferroelectricity and an intrinsically flat potential-energy landscape are the two essential physical ingredients for giant shear piezoelectricity, providing a symmetry-guided computational strategy for discovering high-performance low-dimensional piezoelectric materials.

In this study, we use time- and angle-resolved photoelectron spectroscopy to investigate electron relaxation dynamics in an epitaxially grown graphene monolayer on SiC. Our findings reveal significantly faster relaxation of photoexcited electrons in non-hydrogen-intercalated epitaxial graphene compared to that for previously reported hydrogen-intercalated graphene structures. The differences in relaxation time are modeled by a combination of density function theory in conjunction with ab initio nonadiabatic molecular dynamics, providing a comprehensive explanation of electron relaxation pathways. This study highlights the critical influence of substrate interactions on the relaxation mechanisms in graphene, offering different perspectives for tailoring graphene electronic properties through controlled intercalation techniques.