An incommensurate charge-density wave is a periodic modulation of charge that breaks translational symmetry at a momentum that does not coincide with the primitive lattice vectors. Its Goldstone excitation, the phason, comprises collective gapless phase fluctuations. Aiming to unveil the mechanism behind the onset of incommensurate charge order in layered materials, we study a half-filled, four-band tight-binding model on a ladder with a relative shift $\delta =p/q$ between the legs, induced by the dimerization of one of them. The shift results in a moiré supercell comprising $q$ composite cells and a modulated interleg tunneling. The moiré potential compresses the leg bands into flat minibands near the Fermi level, resulting in additional low-energy peaks in the density of states. Including Coulomb interactions, we find an incommensurate charge-density-wave phase in which the charge modulation is out of phase between the legs. The collective excitations of this state are long-lived neutral, acoustic phasons whose speed is controlled by the moiré parameter $\delta$ and the interleg tunneling amplitude. This model sheds light on the role of interlayer incongruities in the formation of excitonic charge-ordered phases in van der Waals and heterostructured materials.

Recently developed artificial Kitaev chains, realized in quantum-dot arrays coupled via superconducting segments, offer a great degree of experimental control over parameters. Motivated by these advances, we study a dimerized Kitaev chain where onsite energies can be independently controlled. The dimerized Kitaev system can be interpreted as two effective Kitaev chains coupled via the onsite energies. We show that interference between Majorana edge modes from each effective chain can be controlled by these energies, resulting in either normal or Andreev transmission dominating the nonlocal conductance across the system. Such effect on the nonlocal conductance is connected to the fermion parity of the chain and, thus, to the system topological invariant. We explain the previous results using an analytical model describing the spatial decay and overlap of the Majorana edge modes from each effective chain.

Motivated by recent reports of ambient-pressure superconductivity in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ films grown on ${\mathrm{LaSrAlO}}_4$, we investigate the superconducting instability in a one-unit-cell (1UC) thin film using ab initio and random-phase approximation techniques. Compared to the high-pressure bulk system, the ratio of interlayer $d_{3z^2-r^2}$ hopping to intralayer $d_{x^2-y^2}$ hopping is suppressed in the 1UC thin film, and the crystal-field splitting of the $e_g$ orbitals is increased. Our calculation indicates that spin-fluctuation-driven pairing correlations are weak for the stoichiometric case at ambient pressure, but increase significantly under hole doping. The leading pairing symmetry is also found to change by hole doping. Specifically, we obtain a leading $d_{x^2-y^2}$ pairing state at moderate hole doping, followed by a $d_{xy}$ state at higher doping. These states are driven by intraband spin-fluctuation scattering within the $\gamma$ hole pocket centered around the $M$ point, and arise primarily from states in the Ni layer farther from the substrate. These results strongly suggest that the thin-film superconducting samples are hole-doped and that pairing in this system predominantly arises in the layer, as opposed to the interlayer pairing in the pressurized bulk system.

Dielectric screening plays a crucial role in shaping the electronic structure of two-dimensional (2D) materials. In 2D semiconductors, screened Coulomb interactions arising from the surrounding dielectric environment are known to induce band renormalization, which is typically understood as a rigid shift of the electronic bands. Here, we experimentally demonstrate that dielectric screening can also give rise to nonrigid, momentum-dependent band renormalization. Using temperature-dependent angle-resolved photoemission spectroscopy, we observe pronounced changes in the electronic band structure of monolayer ${\mathrm{MoS}}_2$ on a highly oriented pyrolytic graphite substrate. The results indicate that temperature-driven variations in the effective interlayer separation modulate the dielectric screening experienced by monolayer ${\mathrm{MoS}}_2$. At room temperature, the screening behavior is well described by a momentum-independent monopole approximation, whereas at liquid-helium temperatures the screening evolves into a multipolelike regime, leading to momentum-dependent band shifts.

We theoretically investigate a two-dimensional (2D) non-Hermitian generalized Kane-Mele (NH-GKM) model parametrized by an asymmetric intrinsic spin-orbit-coupling (ISOC) scaling parameter $\eta ={\lambda }_{\mathrm{I}}^B/{\lambda }_{\mathrm{I}}^A$, with ${\lambda }_{\mathrm{I}}^{A,B}$ of the sublattice-dependent ISOC strength, and the balanced gain-loss strength $\gamma$. A phase diagram in the parameter space of $(\gamma ,\eta )$ is constructed based on the emergence of the exceptional points along the mirror-symmetry paths. Analogous to the Hermitian Kane-Mele model, under weak gain-loss effects, the NH-GKM model undergoes a quantum phase transition from the non-Hermitian topological-insulator phase to the non-Hermitian Weyl metal (NH-NLWM) phase as $\eta$ varies from positive to negative values. In the NH-NLWM phase, the bulk complex spectra are gapless, and the Weyl points of the Hermitian counterpart deform into the Weyl exceptional rings at the critical condition of $\eta =-1$. By applying the mixed boundary conditions in the nanoribbon configuration, we illustrate distinct topological behavior of the helical and antihelical edge states in two non-Hermitian systems. The distinction primarily manifests as the formation of different types of point gaps that are enclosed by the edge states and the bulk spectra, which leads to distinct spin-dependent hybrid skin-topological effects. In the diamond-nanodisk geometry (the full open boundary conditions), we show that the spin distribution of corner states can be tuned via the interplay between the helical (antihelical) topological edge states and the gain-loss effect. The underlying mechanisms of spin localization are outlined by mapping the boundary of the nanodisk as two sets of one-dimensional zigzag chains with effective gain or loss. Our findings provide a potential platform for the non-Hermitian spin cornertronics devices through the engineering of ISOC and gain-loss distributions.

We study an entanglement phase transition in a class of chaotic non-Hermitian spin chains whose spin-spin coupling terms commute with the non-Hermitian contributions. Two representative models are investigated: the transverse field Ising model with a complex longitudinal field and the non-Hermitian XX model with a transverse field. By analyzing their complex spectra, we find that both models undergo a dissipation-induced gapless-gapped phase transition when the transverse field exceeds a model-dependent threshold. Interestingly, the complex gap does not vary monotonically with the dissipation rate; instead, it exhibits pronounced oscillations before entering the gapped phase. By simulating their nonunitary dynamics, we show that the steady-state entanglement entropy undergoes a transition from volume-law to area-law scaling as the dissipation rate increases. Moreover, several unexpected features emerge within the volume-law regime: a larger complex gap or dissipation rate may lead to a more entangled steady state. We trace these unusual behaviors of the complex gap and the steady-state entanglement to level crossings between the maximal imaginary level and other spectral levels. Our work uncovers an exotic entanglement transition in chaotic non-Hermitian many-body systems.

The evolution of magnetic correlation in strongly correlated electron systems with altermagentic spin splitting remains largely unexplored. Here we investigate how spin splitting generated by spin-dependent next-nearest-neighbor hopping $t^{\prime }$ reshapes the Fermi surface nesting and Van Hove singularities in the two-dimensional square-lattice Hubbard model, leading evolution of magnetic instabilities. Using the constrained-path quantum Monte Carlo method, we find the dominant magnetic correlation as functions of the filling and $t^{\prime }$ by computing the momentum-resolved spin structure factor. The analysis reveals a transition from antiferromagnetic $(\pi ,\pi )$ order in the isotropic, half filled system to noncollinear spiral $(\pi ,q)$ order upon increasing the spin-dependent anisotropy or doping away from half filling, ultimately entering a short-range correlation regime where stripe and spiral correlation coexist. These findings highlight a possible route to realizing spiral correlation in altermagnetic systems, potentially providing a platform for spintronic devices that exploit noncollinear spin textures.

Tuning the electronic states to understand the interplay between superconductivity and topological states is crucial for realizing topological quantum computation. High pressure provides a unique avenue for tuning both superconducting and topological states. Here, we report the pressure tuning of superconductivity and topological band structures in ${\mathrm{Sn}}_4{\mathrm{P}}_3$. At ambient pressure, The Shubnikov–de Haas oscillations with nonzero Berry phases have been observed, and low-temperature angle-resolved photoemission spectroscopy measurements reveal nontrivial bands across the Fermi level, suggesting the topological character of ${\mathrm{Sn}}_4{\mathrm{P}}_3$. More intriguingly, upon applying pressure, two superconducting domes emerge with a maximum $T_c$ of 3.5 and 8.1 K at 5.6 and 42.1 GPa, respectively. High-pressure synchrotron X-Ray diffraction measurements combined with first-principles calculations show that the first dome is associated with a topological transition from topological insulator to topological semimetal, while the second dome is associated with a structural transition form the $R\overline{3}m$ phase to the $I4$/mmm phase. Our results suggest that ${\mathrm{Sn}}_4{\mathrm{P}}_3$ is a promising candidate as a topological superconductor and a platform for studying the interplay between superconductivity and band topology.

Symmetries are a key tool in understanding quantum systems, and, among many other things, can be exploited to increase the efficiency of numerical simulations of quantum dynamics. Disordered systems usually feature reduced symmetries and additionally require averaging over many realizations, making their numerical study computationally demanding. However, when studying quantities linear in the time-evolved state, i.e., expectation values of observables, one can apply the averaging procedure to the time evolution operator, resulting in an effective dynamical map, which restores symmetry at the level of superoperators. In this work, we develop schemes for efficiently constructing symmetric sectors of the disorder-averaged dynamical map using short-time and weak-disorder expansions. To benchmark the method, we apply it to an Ising model with random all-to-all interactions in the presence of a transverse field. After disorder averaging, this system becomes effectively permutation-invariant, and thus the size of the symmetric subspace scales polynomially in the number of spins, allowing for the simulation of large systems.

We investigate the quantum dynamics generated by quantum quenches (QQs) of the Hamiltonian parameters in many-body systems, focusing on protocols that cross first-order and continuous quantum transitions, both in finite-size systems and in the thermodynamic limit. As a paradigmatic example, we consider the quantum Ising chain in the presence of homogeneous transverse ($g$) and longitudinal ($h$) magnetic fields. This model exhibits a continuous quantum transition (CQT) at $g=g_c$ and $h=0$, and first-order quantum transitions (FOQTs) driven by $h$ along the line $h=0$ ($g<g_c$). In the integrable limit $h=0$, the system can be mapped onto a quadratic fermionic theory; however, any nonvanishing longitudinal field breaks integrability and the spectrum of the resulting Hamiltonian is generally expected to enter a chaotic regime. We analyze QQs in which the longitudinal field is suddenly changed from a negative value $h_i<0$ to a positive value $h_f>0$. We focus on values of $h_f$ such that the spectrum of the post-QQ Hamiltonian $\widehat{H}(g,h_f)$ lies in the chaotic regime, where thermalization may emerge at asymptotically long times. We study the out-of-equilibrium dynamics for different values of $g$, finding qualitatively distinct behaviors for $g>g_c$ (where the chain is in the disordered phase), for $g=g_c$ (QQ across the CQT), and for $g<g_c$ (QQ across the FOQT line).

Continuous monitoring of one-dimensional free fermionic systems can generate phenomena reminiscent of quantum criticality, such as logarithmic entanglement growth, algebraic correlations, and emergent conformal invariance, but in a nonequilibrium setting. However, whether these signatures reflect a genuine phase of nonequilibrium quantum matter or persist only over finite length scales is an active area of research. We address this question in a free fermionic chain subject to continuous monitoring of lattice-site occupations. An unraveling phase $\phi$ interpolates between measurement schemes, corresponding to different stochastic unravelings of the same Lindblad master equation; for $\phi =0$, measurements disentangle lattice sites, while for $\phi =\pi /2$ they act as unitary random noise, yielding volume-law steady-state entanglement. Using replica Keldysh field theory, we obtain a nonlinear sigma model describing the long-wavelength physics. This analysis shows that for $0\le \phi <\pi /2$, entanglement ultimately obeys an area law, but only beyond the exponentially large scale $ln\left(l_{\phi ,*}\right)\sim J/[\gamma cos\left(\phi \right)]$, where $J$ is the hopping amplitude and $\gamma$ the measurement rate. Resolving $l_{\phi ,*}$ in numerical simulations is difficult for $\gamma /J\to 0$ or $\phi \to \pi /2$. However, the theory also predicts that critical-like behavior appears below a crossover scale that grows only algebraically in $J/\gamma$, making it numerically accessible. Our simulations confirm these predictions, establishing the absence of measurement- or unraveling-induced entanglement transitions in this model.

The magnetic structures of $\mathrm{B}{\mathrm{a}}_{3}R\mathrm{R}{\mathrm{u}}_2{\mathrm{O}}_9$ $(R=\mathrm{Tb},\mathrm{Er})$ have been investigated using high-intensity neutron powder diffraction (NPD) supported by dc and ac susceptibility studies. The NPD data reveal antiferromagnetic (AFM) ground states below $T_{\mathrm{N}} \sim 9.8$ and 6 K in $\mathrm{B}{\mathrm{a}}_3\mathrm{TbR}{\mathrm{u}}_2{\mathrm{O}}_9$ and $\mathrm{B}{\mathrm{a}}_3\mathrm{ErR}{\mathrm{u}}_2{\mathrm{O}}_9$, respectively, consistent with the magnetic transitions observed in dc and ac susceptibility measurements. In $\mathrm{B}{\mathrm{a}}_3\mathrm{TbR}{\mathrm{u}}_2{\mathrm{O}}_9$, the magnetic structure is characterized by a propagation vector, $k=(0,0,0)$, where Tb and Ru order ferromagnetically in the $\mathit{ab}$ plane. Neighboring planes of Tb are coupled antiferromagnetically along the $c$ direction as are neighboring planes of Ru, which leads to an AFM order between Tb and Ru as well. In contrast, the magnetic structure of $\mathrm{B}{\mathrm{a}}_3\mathrm{ErR}{\mathrm{u}}_2{\mathrm{O}}_9$ is characterized by $k=(0.5,0,0)$, with Er and Ru moments exhibiting a canted AFM ordering. Interestingly, the collinear (noncollinear) AFM order of Tb (Er) accompanied by the collinear (noncollinear) magnetic order of Ru in $\mathrm{B}{\mathrm{a}}_3\mathrm{TbR}{\mathrm{u}}_2{\mathrm{O}}_9$ ($\mathrm{B}{\mathrm{a}}_3\mathrm{ErR}{\mathrm{u}}_2{\mathrm{O}}_9$) along with the concurrent ordering of the rare earth and Ru in both compounds suggests a strong coupling between $4f$ and $4d$ electrons. Both compounds show weak magnetic ordering above $T_{\mathrm{N}}$ similar to that reported for $\mathrm{B}{\mathrm{a}}_3\mathrm{HoR}{\mathrm{u}}_2{\mathrm{O}}_9$. We have understood this intriguing feature by preparing a $\mathrm{B}{\mathrm{a}}_3\mathrm{ErR}{\mathrm{u}}_2{\mathrm{O}}_9$ sample with 3% excess $\mathrm{Ru}{\mathrm{O}}_2$. Our analysis suggests that the weak magnetic ordering above $T_{\mathrm{N}}$ is strongly dependent on the excess $\mathrm{Ru}{\mathrm{O}}_2$; however, and interestingly, the magnetic structure below $T_{\mathrm{N}}$ is robust against this $\mathrm{Ru}{\mathrm{O}}_2$ surplus. Our detailed study provides insights into the magnetic ground states of these two compounds, thereby enhancing the understanding of magnetic ordering in this fascinating family.

We report a comprehensive study of the structural and magnetic properties of the two-dimensional $S=\frac{5}{2}$ frustrated triangular-lattice antiferromagnet ${\mathrm{Ba}}_3{\mathrm{MnTa}}_2{\mathrm{O}}_9$ using x-ray diffraction, magnetization, electron spin resonance, and heat-capacity measurements on a polycrystalline sample, combined with density-functional band-structure calculations. The magnetic susceptibility and heat-capacity data reveal the onset of antiferromagnetic long-range order at $T_{\mathrm{N}}\simeq 2.6\mathrm{K}$, which is in sharp contrast with the recent report by Mondal et al. [Phys. Rev. B 112, 155153 (2025)] who did not observe magnetic order in this material. The nearest-neighbor exchange coupling $J/k_{\mathrm{B}}\simeq 0.85\mathrm{K}$ is obtained from Monte Carlo fits to the experimental susceptibility data. Combined with the ab initio estimate of the interlayer coupling, this $J/k_{\mathrm{B}}$ value leads to $T_{\mathrm{N}}\simeq 2.7\mathrm{K}$ in a perfect agreement with the experiment. Magnetic isotherms reveal a field-induced transition below $T_{\mathrm{N}}$. The complex $H\text{−}T$ phase diagram features multiple phases as a consequence of magnetic frustration and anisotropy present in the system.

We study conditions of the appearance of $U\left(1\right)\times {\mathbb{Z}}_2$ superconducting states that spontaneously break time-reversal symmetry (BTRS) on a square lattice as a function of applied strain. Calculations show that if critical temperatures coincide at zero strain, they exhibit a linear kink and no kink otherwise for uniaxial and isotropic strain. Linear kink is absent for shear strain. We find that in general, the microscopic calculations show a complex phase diagram, for example, nonmonotonic behavior of BTRS transition. Another beyond-Ginzburg-Landau theory result is that $U\left(1\right)$ critical temperature can decrease under compressional [100] uniaxial strain for small Poisson ratio materials. In the second part of the paper, we consider the effects of boundaries and finiteness of the sample on the strain-induced splitting of $T_c^{U\left(1\right)}$ and $T_c^{{\mathbb{Z}}_2}$ transitions. A finite sample has BTRS boundary states with persistent superconducting currents over a wide range of band filling. Overall, the BTRS dome occupies a larger band-filling-temperature phase space region for a mesoscopic sample with [110] surface compared to an infinite system. Hence, the presence of boundaries helps to stabilize the BTRS phase.

There are a few exact results for the Hubbard model on bipartite lattices of spatial dimension $d>1$. Nevertheless, the Hubbard model with transfer integral $t$ and onsite repulsion $U$ on bipartite lattices with $N_a$ sites, such as the square, honeycomb, cubic, body-centered cubic, face-centered cubic, and diamond lattices, provides the simplest toy model for describing electronic correlations in many condensed-matter systems and is therefore a quantum problem of considerable physical interest. Most previous studies have assumed that, for finite onsite repulsion $U>0$, the global symmetry of the model is $\mathrm{SO}\left(4\right)=[\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)]/{\mathbb{Z}}_2$. However, the actual global symmetry is larger and given by $[\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)\times \mathrm{U}\left(1\right)]/{\mathbb{Z}}_2^2$, which may equivalently be written as $[\mathrm{SO}\left(4\right)\times \mathrm{U}\left(1\right)]/{\mathbb{Z}}_2$ or as $\mathrm{SO}\left(3\right)\times \mathrm{SO}\left(3\right)\times \mathrm{U}\left(1\right)$. The main goal of this paper is to extract physical insight, including further exact results for the Hubbard model on bipartite lattices with spatial dimension $d>1$, from its full global symmetry. The hidden U(1) symmetry beyond SO(4), which has been ignored in most previous studies, becomes an explicit symmetry within an exact quasiparticle representation of the model for $u=U/t>0$. The generator of this symmetry has eigenvalues $S_{\tau }\in \{0,\frac{1}{2},1,\frac{3}{2},2,...,\frac{N_a}{2}\}$. Importantly, this exact quasiparticle representation naturally leads to the emergence of $N_s=(N_a-2S_{\tau })$ physical spins $1/2$ and $N_{\eta }=2S_{\tau }$ physical $\eta$-spins $1/2$, associated with the two SU(2) symmetries in $[\mathrm{SU}\left(2\right)\times \mathrm{SU}\left(2\right)\times \mathrm{U}\left(1\right)]/{\mathbb{Z}}_2^2$. The spin and $\eta$-spin multiplet and singlet configurations of the $4^{N_a}$ exact energy and momentum eigenstates are generated from the vacuum by quasiparticle creation and annihilation operators. Seven exact theorems that provide new physical insight into the model are established. Overall, the exact framework based on physical spins and physical $\eta$-spins for the Hubbard model on bipartite lattices of spatial dimension $d>1$ offers a robust foundation for future studies of the model, as well as of the condensed-matter materials, such as cuprate superconductors, graphene and graphene-derived systems, and other quantum systems, that it describes.

We demonstrate that the local nonfreeness, an unbiased measure of correlation between electrons at a single lattice site, can be computed as the mutual information between local natural spin orbitals. This leads us to prove a general result: local electron correlations in Hubbard-type models that conserve the orbital- and spin-resolved electron number are fully classical since the local reduced density matrix is separable in the natural basis and no quantum correlations beyond entanglement are present. Finally, we compare different theoretical descriptions of magnetic and nonmagnetic states, showing that local classical correlations are drastically influenced by nonlocal processes. These results confirm the relation between local classical correlations within an open system and nonlocal entanglement and they provide a clear path for the study of the relationship between traditional quantum resources and the nonfreeness in terms of experimentally accessible quantities.

We study current flow around a density inhomogeneity in a two-dimensional electron gas in the presence of a strong magnetic field. The inhomogeneity is parametrized by a power-law tail with an exponent $\beta >2$. We show that current and electrochemical potential are exponentially suppressed inside a surrounding area much larger than the geometric size of the perturbation. The corresponding “no-go” radius grows as a certain power of the magnetic field. Residual current and potential exhibit spiraling patterns inside the no-go region. Outside of it, they acquire corrections inversely proportional to the distance, which is known as the Landauer resistivity dipole. The Landauer dipole is rotated by the angle $\pi (1-1/\beta )$ with respect to the average electric field. The rotation direction depends on whether the local density is raised or lowered. We also consider the effect of electron viscosity and show that the variation of the no-go radius with magnetic field becomes more rapid if viscosity is large enough. The Landauer dipole size is set by the Gurzhi length, which is much larger than the no-go radius, which is in turn much larger than the geometric size of the perturbation. Our results may be useful for interpreting nanoimaging of current distribution in graphene and other two-dimensional systems.

Ferroelectric multiple polarization states offer higher information storage density and promising opportunities for neuromorphic computing, making them an important frontier in next-generation ferroelectric research. Reorientable ferroelectrics provide an alternative pathway to realize multiple polarization states. In this work, we report that two-dimensional graphitic carbon nitride ($g\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$) exhibits this reorientable ferroelectric behavior, originating from its distinctive internal structure. First-principles calculations reveal that both $Pca{2}_1$-triazine and $Pca{2}_1$-heptazine $g\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ exhibit spontaneous polarization with three equivalent ferroelectric states, each separated by 120°. Unlike conventional ferroelectrics, they do not exhibit antiparallel polarization and therefore cannot undergo polarization flipping. Instead, they possess several polarization states oriented along different directions. The piezoelectric coefficients $d_{22}$ of the $Pca{2}_1$-triazine and $Pca{2}_1$-heptazine $g\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ are 1.33 and 0.97 pm/V. Such novel properties highlight $g\text{−}{\mathrm{C}}_3{\mathrm{N}}_4$ as a promising candidate for future miniaturized and integrated multifunctional electronic devices.

Localized $5d^2$ electrons in a cubic crystal field possess multipoles such as electric quadrupoles and magnetic octupoles. We studied the cubic double perovskite ${\mathrm{Ba}}_2{\mathrm{CaOsO}}_6$ containing the ${\mathrm{Os}}^{6+}$ ($5d^2$) ions, which exhibits a phase transition to a ‘‘hidden order’’ below $T^{*}\sim$ 50 K, by x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) at the Os $L_{2,3}$ edge. The cubic ligand-field splitting between the $t_{2g}$ and $e_g$ levels of Os $5d$ was deduced by XAS to be $\sim 4\mathrm{eV}$. Ligand-field multiplet calculation under fictitious strong magnetic fields indicated that the exchange interaction between nearest-neighbor octupoles should be as strong as $\sim 1.5\mathrm{meV}$ if a ferro-octupolar order is stabilized in the hidden-ordered state, consistent with the exchange interaction of $\sim 1\mathrm{meV}$ previously predicted theoretically using model and density functional theory calculations. The temperature dependence of the XMCD spectra is consistent with a $\sim 18\mathrm{meV}$ residual cubic splitting of the lowest $J_{\mathrm{eff}}=$ 2 multiplet state into the non-Kramers $E_g$ doublet ground state and the $T_{2g}$ triplet excited state.