Exploring the relations between coexisting, cooperative, or competing types of ordering is a key to identify and harness the mechanisms governing the mutual interactions between them and to utilize their combined properties. We have experimentally explored the response of the charge density wave (CDW) to various antiferromagnetic, metamagnetic, and field-aligned ferromagnetic states that constitute the magnetic phase diagram of ${\mathrm{TmNiC}}_2$. The high-resolution x-ray diffraction experiment employing synchrotron radiation at low temperature and high magnetic field allowed one to follow the superstructure satellite reflections, being a sensitive probe of CDW. This investigation not only reveals direct evidence that the charge density wave avoids even a partial suppression in the antiferromagnetic ground state, but also proves that this state coexists, without any visible signatures of weakening, in the entire dome of the magnetically ordered phases, including the field-aligned ferromagnetic state. The calculations of the electronic and phonon structures support the experiment, revealing that the dominant contribution to the CDW transition stems from momentum-dependent electron-phonon coupling. We conclude that this mechanism prevents the CDW from vanishing, although the nesting conditions within the magnetically ordered phases deteriorate.

We theoretically investigate the single-particle excitation spectra of a one-dimensional Hubbard model at half filling using an infinite matrix-product state and elucidate the discretized energy spectra emerging under the influence of a dc electric field. In a weak electric-field regime, we observe two kinds of spectral structures in the density of states. With increasing the electric-field strength, the discretized spectra, the period of which is proportional to the strength, become dominant, and the density of states exhibits the Wannier-Stark ladder in their spectra. In addition, we also simulate time- and angle-resolved photoemission spectroscopy using an ultrashort terahertz pump pulse that approximates a dc electric field. Our results represent a significant step forward in understanding the states in strongly correlated electron systems driven by a static electric field.

We propose a scheme for realizing vortex molecules in a nonresonant, incoherently pumped exciton-polariton condensate under finite rounded uniform pumping. These vortex molecules emerge as collective states of multiple vortices, which are stabilized by a balance between the repulsive interactions among vortices and the attractive influence of the pumping boundary. The gain and loss mechanism plays a crucial role in sustaining this attractive effect, making it an intrinsic phenomenon unique to the system. Furthermore, we demonstrate that reducing the boundary width enhances this attractive effect. In addition, the vortices are not confined by uniform pumping, which leads to the formation of vortex molecules that rotate in a regular manner around the pumping center due to vortex-vortex interactions. This behavior is in contrast to the less regular motion observed in a single vortex. The trajectories of these vortex molecules exhibit two distinct patterns. The first pattern consists of regular circular orbits, while the second pattern consists of orbits with periodically varying radii. Within the second category, a special type of trajectory is characterized by helical motion, which we refer to as the spiral trajectory. Moreover, by adjusting the pumping size, exciton diffusion rate, and pumping intensity, it is possible to control different orbital configurations and regulate the average angular velocities of the vortex molecules. This enables the realization of a zero average angular velocity and allows for the reversal of their rotational direction. Our proposed scheme introduces a class of dynamically stable solutions in exciton-polariton condensates, providing insights into interaction mechanisms in nonequilibrium physics. Additionally, vortex molecules offer promising applications in polariton neural networks and quantum communication..

A two-dimensional finite-lattice model is used to facilitate the interpretation and predictive understanding of the vapor-liquid phase behavior of excitons as a function of temperature and laser intensity, in both the classical and quantum Bose-Einstein condensation (BEC) regimes. Classical condensation occurs below a critical temperature determined by the magnitude of the attractive interactions between neighboring excitons. Quantum condensation occurs below a temperature at which the exciton thermal wavelength exceeds its intrinsic size. The resulting laser-intensity-dependent condensation is predicted to have a temperature dependence that is linear in the quantum regime and exponential in the classical regime. Challenges associated with the experimental realization and interpretation of exciton condensation in the classical and quantum regimes, as well as possible implications to interfacial chemical reactivity, are discussed.

Inelastic heat engines are thermodynamic machines governed by inelastic electron-photon scattering processes that promise efficient energy transport and high thermodynamic efficiency. Here we investigate thermodynamic performances and fluctuations in double quantum dots with inelastic electron-photon interactions under strong periodic driving. Using a Floquet-based quantum master equation framework, we analyze both energy conversion efficiency and thermodynamic uncertainty relations in the fast-driving regime. Our study shows that the fast-driving frequency and strong-driving amplitude play crucial roles in optimizing the performances of the inelastic heat engine. The output power and thermodynamic efficiency are greatly improved with respect to the case in absence of Floquet driving by generating multiple incoherent transition channels. They also exceed the counterparts of the elastic engines. Simultaneously, we reveal that periodic driving breaks the thermodynamic uncertainty constraints. Our findings offer a Floquet perspective for optimizing inelastic heat engines.

The ${\mathrm{Ising}}_h^2$ integrable field theory emerges when two quantum critical Ising chains are weakly coupled. This theory possesses eight types of relativistic particles, among which the lightest one ($B_1$) has been predicted to be a dark particle, which cannot be excited from the ground state through (quasi)local operations. The stability on the one hand highlights its potential for applications, and on the other hand makes it challenging to be observed. Here, we point out that the mass of the $B_1$ dark particle $m_{B_1}$ appears as a thermally activated gap extracted from local spin dynamical structure factors at low frequency ($\omega \ll m_{B_1}$) and low temperatures ($T\ll m_{B_1}$). We then further propose that this gapped behavior can be directly detected via the NMR relaxation rate measurement in a proper experimental setup. Our results provide a practical criterion for verifying the existence of dark particles.

We study a mechanical oscillator coupled to a two-level system driven by a blue-detuned coherent source in the resolved sideband regime. For weak mechanical damping, we find dynamical instabilities leading to limit cycles. They are signaled by strong fluctuations in the number of emitted photons, with a large Fano factor. The phonon-number fluctuations exhibit strikingly similar behavior. When the coupling strength becomes comparable to the mechanical frequency, nonclassical mechanical states appear. We demonstrate that these properties can be detected by measuring the photon-emission spectrum, which enables the reconstruction of the Wigner function. We then discuss the relation with cavity optomechanical systems. Candidates for observing these effects include superconducting qubits, NV centers, and single molecules coupled to oscillators.

We theoretically study photoinduced magnetic phase transitions and their dynamical processes in the double-exchange model on a cubic lattice. It is demonstrated that light irradiation gives rise to magnetic phase transitions from the ground-state ferromagnetic state to a three-dimensional antiferromagnetic state as a nonequilibrium steady state in the photodriven system. This phase transition occurs as a consequence of the formation of pseudo-half-filling band occupation via the photoexcitation and relaxation of electrons, where all the electron states constituting the lower band separated from the upper band by an exchange gap are partially but nearly uniformly occupied. We also find that several types of antiferromagnetic correlations, e.g., A-type and C-type antiferromagnetic correlations, appear in a transient state of the dynamical phase transition. By calculating magnon spectra for the photodriven system, we argue that the instability to the A-type or C-type antiferromagnetic state occurs in the ferromagnetic ground state as a softening of the magnon band dispersion at corresponding momentum points depending on the light polarization. Our findings provide important insights into the understanding of photoinduced magnetic phase transitions in the three-dimensional double-exchange magnets.

Recent work has shown that the triangular lattice spin-$\frac{1}{2} J_1-J_2$ Heisenberg and XXZ antiferromagnets may exhibit coplanar or supersolid orders proximate to a gapless Dirac spin-liquid phase. We explore a distinct $\text{SU}\left(2N\right)\times \text{SU}\left(M\right)$ fermionic parton approach, complemented by variational Monte Carlo calculations for the spin-$\frac{1}{2}$ model, to study the phase diagram of these models. We also calculate their dynamical spin response including parton interactions within a random-phase approximation, and discuss implications for neutron scattering on triangular lattice cobaltates ${\mathrm{Ba}}_3{\mathrm{CoSb}}_2{\mathrm{O}}_9, {\mathrm{Na}}_2\mathrm{BaCo}{\left({\mathrm{PO}}_4\right)}_2, {\mathrm{K}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_2, {\mathrm{Rb}}_2\mathrm{Co}{\left({\mathrm{SeO}}_3\right)}_2$, and Yb-based magnet ${\mathrm{KYbSe}}_2$.

We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto $Z_2$ gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as ${\mathrm{Zr}}_{0.5}{\mathrm{Ru}}_{0.5}{\mathrm{Cl}}_3$. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.

The superconducting order parameter at the ${\mathrm{KTaO}}_3$ interfaces and its dependence on interface orientation remains a subject of debate. The superconductivity at these interfaces exhibits strong resilience against in-plane magnetic field and violates Pauli limit. The interface orientation dependence of critical field and violation of Pauli limit, however, have not been investigated. To address this problem, we grew epitaxial ${\mathrm{LaMnO}}_3/{\mathrm{KTaO}}_3$ heterostructures using molecular beam epitaxy. We show that superconductivity is extremely robust against the in-plane magnetic field. The critical field to the Pauli limiting field coincides with the (111) interfaces for the same carrier density. This suggests that the orientation of the surface does not play a critical role in determining the ratio, despite the strong impact on the critical temperature. These results offer opportunities to engineer superconductors which are resilient against magnetic field.

Although the appearance of vortex-localized states with zero energy in first-order topological superconductors is well known, their possibility to form in the higher-order topological phase of two-dimensional (2D) systems has not been completely uncovered yet. Here we demonstrate the coexistence of zero-energy vortex modes and Majorana corner modes in the model of a 2D second-order topological superconductor. The model describes an interface between a normal layer supporting the topological insulating phase and a superconducting layer, for which different symmetries of the spin-singlet superconducting order parameter are considered. We show that the gapless vortex modes can appear under certain conditions in the superconducting state with a vortex if the bulk energy spectrum of the normal (nonsuperconducting) state is gapless and has Dirac cones. The number of pairs of such vortex modes corresponds to the number of Dirac cones. It is essential that if the normal bulk spectrum becomes gapped and the system is in the state of a topological insulator, then the zero-energy vortex modes cannot be realized, while Majorana corner modes hold in the superconducting state. The interaction of the vortex modes with the edge and topological corner modes is studied when the vortex appears near the boundaries.

We study the symmetry requirements for topologically protected spin-polarized Dirac points in 2D altermagnets. The topology is characterized by a quantized $\pi$-Berry phase and the degeneracy is protected by spin-space group symmetries. Gapped phases with finite Chern and/or spin/chirality Chern numbers emerge under different symmetry-breaking mass terms. We investigate the surface and transport properties of these gapped phases using representative electronic tight-binding and magnonic linear spin-wave models. In particular, we calculate the electronic and magnonic Hall currents and discuss implications for experiments.

The van der Waals (vdW) two-dimensional (2D) material copper chromium thiophosphate ($\mathrm{CuCr}{\mathrm{P}}_2{\mathrm{S}}_6$) exhibits robust magnetoelectric (ME) coupling with coexisting type-I and II multiferroic characteristics, suggesting significant potential for ME applications. Nevertheless, the weak coupling strength has limited its potential for applications. Here, we systematically investigate the magnetic and electrical properties of the V-doped $\mathrm{CuCr}{\mathrm{P}}_2{\mathrm{S}}_6$ solid solution $\mathrm{CuC}{\mathrm{r}}_{1-x}{\mathrm{V}}_x{\mathrm{P}}_2{\mathrm{S}}_6$ combining experiments and density functional calculations. Substitution of V for Cr induces a gradual transition from A-type antiferromagnetic (AFM) to ferromagnetic (FM) ordering, accompanied by a progressive reduction in Néel temperature. The $\mathrm{CuV}{\mathrm{P}}_2{\mathrm{S}}_6$ manifests characteristics of a quasi-2D Heisenberg FM, exhibiting weak magnetic anisotropy and weak interlayer FM interactions. Dielectric characterization reveals that V substitution suppresses the antiferroelectric (AFE) ground state (space group $\mathit{Pc}$) of pristine $\mathrm{CuCr}{\mathrm{P}}_2{\mathrm{S}}_6$, inducing a paraelectric state (space group C2/$c$) with enhanced dielectric relaxation and polar fluctuations across characteristic temperature ranges. Strikingly, a pronounced magnetodielectric response emerges near saturation fields ($H_s$) in V-doped AFM compositions. Through Landau free energy analysis, we establish that the quadratic coupling between the FM order parameter ($M$), AFM order parameter ($A$), and polarization ($P$) plays a key role in mediating the observed magnetodielectric phenomena.

Here, we present experimental evidence of the pseudodoublet ground state of the non-Kramers compound ${\mathrm{SrTm}}_2{\mathrm{O}}_4$, based on specific heat, magnetic entropy, and electron paramagnetic resonance. We demonstrate that the two crystallographic ${\mathrm{Tm}}^{3+}$ sites give rise to distinct single-ion anisotropies, and by extension, ${\mathrm{SrTm}}_2{\mathrm{O}}_4$ hosts two magnetic sublattices. Inelastic neutron scattering reveals low-lying dispersing crystal-field excitations, which we modeled using an effective charge model and mean-field random phase approximation. The extracted magnetic exchange interactions are both antiferromagnetic and frustrated for both sublattices. The magnetic exchange interactions between the different sublattices are negligible. The strength of the magnetic exchange interactions in relation to the size of the crystal-field energy gaps, together with the frustration and low dimensionality, force the system to remain paramagnetic down to the lowest experimentally reachable temperature despite the pseudodoublet nature of its ground state.

We study the three-body Fermi liquid effects in the SU($N$) Anderson impurity model within the strong interaction limit $U\to \infty$, where the occupation number $N_d^{}$ of the impurity levels varies over the range of $0<N_d^{}<1$. The three-body correlations arise among the impurity electrons when the electron-hole symmetry, the time-reversal symmetry, or both are broken by external fields or potentials. They play a key role in low-energy transport, particularly in the next-to-leading-order terms of power expansion with respect to temperature $T$ and bias voltage $eV$. Using the numerical renormalization group approach, we calculate the differential conductance and nonlinear current noise through quantum dots, as well as the thermal conductivity of both quantum dots and magnetic alloys. Specifically, we focus on the SU(2) and SU(4) cases, demonstrating how the three-body correlations evolve in the strong interaction limit across the $1/N$-filling Kondo regime at $N_d^{}\simeq 1.0$ and the valence fluctuation regime where the occupation number $N_d^{}$ varies rapidly with the position ${\epsilon }_d^{}$ of the impurity levels. We also show that the three-body correlations strongly couple with asymmetries in the tunnel couplings between quantum dots and reservoirs. For $N=4$, this coupling significantly affects the order ${\left(eV\right)}^3$ nonlinear current through the quarter-filling Kondo state, where the electron-hole symmetry is broken. In particular, in the $U\to \infty$ limit, the expansion coefficients exhibit clear plateau structures associated with the Kondo effect at $N_d^{}\simeq 1.0$. Our formulation and analysis pave the way for deducing the three-body correlations from the low-energy experiments on the next-to-leading-order transport.