The information-geometric origin of fidelity susceptibility and its utility as a universal probe of quantum criticality in many-body settings have been widely discussed. Here, we explore the metric response of quantum relative entropy (QRE), by tracing out all but $n$ adjacent sites from the ground state of spin chains of finite length $N$ as a parameter of the corresponding Hamiltonian is varied. The diagonal component of this metric defines a susceptibility of the QRE that diverges at quantum critical points (QCPs) in the thermodynamic limit, even for small $n$. We study two spin-$1/2$ models as examples, namely, the integrable transverse field Ising model (TFIM) and a nonintegrable Ising chain with three-spin interactions. We demonstrate distinct scaling behaviors for the peak of the QRE susceptibility as a function of $N$ using $n\le 3$: namely, a square logarithmic divergence in TFIM and a power-law divergence in the nonintegrable chain. We further show that this susceptibility diverges even at finite $N$ if the subsystem size, $n$, exceeds a certain value when the Hamiltonian is tuned to its classical limits due to the rank of the corresponding reduced density matrices being finite; unlike the divergence associated with the QCPs, which requires $N\to \infty$.

The vital competition between Zeeman energy, antiferromagnetic (AFM) interchain coupling, and anisotropy energy is studied using angular-dependent and hydrostatic pressure based magnetization techniques in the ${\mathrm{Ca}}_3{\mathrm{Co}}_2{\mathrm{O}}_6$ crystal. It reveals that the critical fields needed for the field-driven three-dimensional (3D) ferrimagnetic (FIM) to 3D ferromagnetic (FM) transition follow the cosine function of angles, which is often described in textbooks. It is rather noteworthy that the equidistant magnetization plateaus in the 3D-FIM to 3D-FM transition adhere to this empirical relation. Moreover, the equidistant nature of the magnetization steps remains unaltered under high-pressure, requiring higher magnetic fields to initiate the field-induced transitions. These hidden aspects of magnetization plateaus imply that the competition between the Zeeman energy and antiferromagnetic interchain coupling gives rise to this remarkable behavior in this Ising ferrimagnet. However, the influence of anisotropy energy leads to a monotonous change in magnetization without showing magnetization plateaus.

In this article, we put forward a practical but generic approach towards constructing a large family of $(3+1)$-dimensional (3D) lattice models which can naturally lead to a single Weyl cone in the infrared limit. Our proposal relies on spontaneous charge $\text{U}\left(1\right)$ symmetry breaking via a pair condensate to evade the usual no-go theorem of a single Weyl cone in a 3D lattice. We have explored three concrete paths in this approach, all involving fermionic topological symmetry protected states (SPTs). Path (a) is to push a gapped SPT in a 3D lattice with time-reversal symmetry (or $T$ symmetry) to a gapless topological quantum critical point (tQCP) which involves a minimum change of topologies, i.e., $\delta N_w=2$ where $\delta N_w$ is the change of winding numbers across the tQCP. Path (b) is to peel off excessive degrees of freedom in the gapped SPT via applying $T$-symmetry breaking fields which naturally result in a pair of gapless nodal points of real fermions. Path (c) is a hybrid of (a) and (b) where tQCPs, with $\delta N_w\ge 2$, are further subject to time-reversal symmetry breaking actions. We identify detailed phase boundaries of emergent single Weyl fermions in these lattice models. The whole family of lattice models with single Weyl fermions here can be effectively encoded in two dual copies of (1, 1) representations of a Spin(4) group. In the infrared limit, all the lattice models with single Weyl fermions studied here are isomorphic to either a tQCP in a DIII class topological superconductor with a protecting $T$ symmetry, or its dual, a $T$-symmetry breaking superconducting nodal point phase, and therefore form an equivalence class. For a generic $T$-symmetric tQCP along path (a), the conserved-charge operators span a six-dimensional linear space while for a $T$-symmetry breaking gapless state along paths (b) and (c), charge operators typically span a two-dimensional linear space instead. Finally, we pinpoint connections between three spatial dimensional lattice chiral fermion models and gapless real fermions that can naturally appear in superfluids or superconductors studied previously.

${\mathrm{CeRh}}_2{\mathrm{As}}_2$, a heavy-fermion superconductor discovered in 2021, exhibits two distinct superconducting phases under a $c$-axis magnetic field. This unconventional phase diagram has been attributed to the local inversion symmetry breaking at the $\mathrm{Ce}$ sites. At low magnetic fields, a conventional even-parity spin-singlet superconducting state is realized, whereas at higher fields, an odd-parity spin-singlet superconducting state, in which the order parameter alternates sign between neighboring Ce layers, becomes stabilized. In this study we employ a quasiclassical approach to investigate the vortex states of bilayer superconductors with locally broken inversion symmetry. We calculate the phase diagram and the local density of states (LDOS) in the vortex lattice state and find that the pairing symmetry of different superconducting states is clearly manifested in the peak structure of LDOS at the vortex core. Since LDOS is experimentally observable, our work provides a pathway for experimental verification of the superconducting parity transition in ${\mathrm{CeRh}}_2{\mathrm{As}}_2$.

We consider the intrinsic fluctuation conductivity in metals with multiply sheeted Fermi surfaces approaching a superconducting critical point. Restricting our attention to extreme type-II multicomponent superconductors motivates focusing on the ultraclean limit. Using functional-integral techniques, we derive the Gaussian fluctuation action from which we obtain the gauge-invariant electromagnetic linear response kernel. This allows us to compute the optical conductivity tensor. We identify essential conditions required for a nonzero dissipative part of the longitudinal conductivity in a disorder-free and translationally invariant system. Specifically, this derives indirectly from the multicomponent character of the incipient superconducting order and the parent metallic state. Under these conditions, the enhancement of the DC conductivity due to fluctuations close to the critical point follows the same critical behavior as in the diffusive limit.

The recently discovered superconductor ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has attracted significant attention due to its remarkably high transition temperature ($T_c$) under high pressure. Shortly after this discovery, thin-film ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ was demonstrated to exhibit ambient-pressure superconductivity; however, the corresponding $T_c$ is only about half that of the pressurized bulk material. This striking difference raises questions about the underlying mechanisms governing superconductivity in these two structures. To address this issue, we develop a phenomenological symmetry-based method to investigate the superconducting gap structure in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Using density-functional theory methods ($\mathrm{DFT}+U$), together with the experimentally determined $T_c$ and structural symmetry, we find that both pressurized bulk and thin-film ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ exhibit $s_{\pm }$-wave pairing symmetry and two-gap superconductivity, yet their dominant microscopic pairing configurations are distinct. In the pressurized bulk, superconductivity is dominated by the out-of-plane pairing of the Ni-$d_{z^2}$ orbitals, while in the thin film, the in-plane pairing of the Ni-$d_{x^2-y^2}$ orbitals prevails. Furthermore, the observed reduction in $T_c$ can be attributed to this transition of the dominant pairing type, driven by the decreased ratio of interlayer to intralayer hoppings in the thin film. Our result sheds lights on the microscopic pairing in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ and reveals the significance of the symmetry. This method can potentially be generalized to a broader range of unconventional superconductors.

We investigate the electronic transport properties of a superconductor-quantum dot-superconductor Josephson junction coupled to a ferromagnetic metal reservoir in the presence of an external magnetic field. The device is described by an effective non-Hermitian Hamiltonian, whose complex eigenvalues encode the energy (real part) and the broadening (imaginary part) of the Andreev quasibound states. When extending the Andreev current formula to the non-Hermitian case, a novel contribution arises that is proportional to the phase derivative of the levels broadening. This term becomes particularly relevant in the presence of exceptional points (EPs) in the spectrum, but its experimental detection is not straightforward. We identify optimal Andreev spectrum configurations where this novel current contribution can be clearly highlighted, and we outline an experimental protocol for its detection. We point out that the phase dependence in the levels imaginary part originates from the breaking of a time-reversal-like symmetry. In particular, spectral configurations in the broken phase of the symmetry and without EPs can be obtained, where this novel contribution can be easily resolved. The proposed protocol would allow to probe for the first time a fingerprint of non-Hermiticity in open junctions that is not strictly related to the presence of EPs.

We theoretically investigate a one-dimensional quantum droplet with spin-orbit (SO) coupling and periodically modulated Raman coupling. Using a Floquet approach, we derive an effective time-independent model that reveals a controlled phase diagram. Crucially, the interplay of quantum fluctuations encoded in the Lee-Huang-Yang correction and SO coupling suppresses the plane-wave phase that is typical of mean-field SO-coupled condensates. The ground state is instead restricted to two distinct phases: a stripe phase, with periodic density modulations, and a zero-momentum phase, with a flat-top density profile. The plane-wave droplet is a metastable state of the system. We demonstrate that the boundary between these phases can be dynamically manipulated by tuning the driving parameters. Furthermore, we explore the system's response to quantum quenches, uncovering a wealth of nonequilibrium phenomena, including the dynamical formation of stable, solitonlike structures. Our work establishes periodic driving as a powerful tool for the dynamical control of self-bound quantum matter and elucidates the fundamental role of quantum fluctuations in shaping the phase diagram of SO-coupled droplets.

Superconductivity in ${\mathrm{UTe}}_2$ has attracted significant attention, as it is widely recognized as a promising candidate for a spin-triplet superconductor. However, the symmetry of superconductivity and the microscopic origin of spin-triplet pairing remain subjects of debate. Nevertheless, various experiments imply an intimate coupling between magnetism and superconductivity. In this paper, we analyze a multisublattice periodic Anderson model that incorporates spin-orbit coupling allowed in locally noncentrosymmetric crystals to discuss magnetic fluctuations and superconductivity in ${\mathrm{UTe}}_2$. Due to the sublattice-dependent spin-orbit coupling, magnetic fluctuations become anisotropic, and the spin degeneracy of superconducting states is lifted. Our calculations reveal anisotropic antiferromagnetic fluctuations along the $b$ and $c$ axes, anisotropic ferromagnetic fluctuations along the $a$ axis, and their coexistence. These fluctuations can be tuned by the $f$ electron's level. Superconductivity in the $A_u$ representation is predominant for a wide range of parameters, whereas the $B_{2u}$ representation is almost degenerate and can be stabilized. The direction of the $d$ vector changes as we increase the spin-orbit coupling. We discuss the consistency between our results and several experiments.

Electromagnetic wave propagation in time-varying media offers unique possibilities for controlling wave dynamics beyond spatially structured systems. While both nonideal step transitions and the suppression of reflection in the adiabatic limit are well-established phenomena in the WKB framework, these analyses have predominantly relied on the approximation method and assumption of electric displacement ($\mathbf{D}$) continuity. In this work, we provide a comprehensive comparative study of wave scattering by establishing exact analytical solutions for a linear temporal transition under both the standard $\mathbf{D}$-field continuity and the electric field ($\mathbf{E}$) continuity boundary conditions. The latter is explicitly motivated by realistic experimental scenarios such as capacitor switching in transmission lines. By utilizing Bessel functions to construct closed-form solutions, we reveal that while the scattering coefficients in both scenarios exhibit similar trends of damped oscillations as the transition duration increases, their specific amplitudes and momentum-exchange behaviors differ significantly because of the distinct boundary mechanisms. Furthermore, building upon the established WKB framework for soft temporal switching, we derive analytical approximations for both boundary conditions. By benchmarking these results against our exact Bessel-function solutions, we provide a precise quantitative definition of the adiabatic regime through a normalized switching threshold ($\tau /T_0$), thereby elucidating how specific boundary physics dictates the validity range of adiabatic approximations. All analytical derivations are validated against full-wave numerical simulations, demonstrating excellent agreement. This rigorous analysis not only serves as a precise mathematical benchmark for defining the validity range of adiabatic approximations but also elucidates how physical boundary conditions fundamentally dictate the electromagnetic response in time-varying systems.

Twisted bilayer graphene (TBG) emerges as an ideal platform for engineering electronic states owing to its moiré superlattice and tunable electronic structure. Although the intrinsic properties of TBG have been widely studied, its electronic behavior under quantum confinement remains largely unexplored. Here, we create movable TBG quantum dots (QDs) in TBG/$\mathrm{WS}{\mathrm{e}}_2$ heterostructures and observe electronic states induced by the combined effect of moiré modulation and electrostatic confinement. Our experiment shows that the low-energy van Hove singularities (VHSs) in TBG evolve into confined states with different orbitals under the electrostatic potential. In addition, for the QD states formed by electrons with energies above the VHSs, the spatial distribution of these states is significantly modulated by the moiré potential. Furthermore, by moving a TBG QD to a graphene grain boundary, we simultaneously realize the confinement of different types of quasiparticles within the same potential. Our ability to combine moiré and electrostatic potentials advances the design of artificial quantum systems and demonstrates a general method for tailoring quantum states in TBG.

We find that the Berry curvature splits the edge plasmons propagating along the opposite directions in quantum anomalous Hall insulators even with vanishing Chern number. When the bulk is insulating, a single unidirectional edge plasmon survives and becomes acoustic in the long-wavelength limit, which coincides with recent experiments. The group velocity of the chiral edge plasmon would change its sign for a large wave vector and exhibit the unusual negative dispersion, which originates from the $k^2$ correction to the effective mass. The impacts of the Fermi level and the wave vector on the bulk and edge plasmons are discussed. Our work provides a very quantitative explanation of the recent observation of the chiral edge plasmon in quantum anomalous Hall insulators and some insight into the application of realistic topological materials in chiral plasmonics.

The bulk-boundary correspondence, which relates topological properties of a material in the bulk to the presence of robust modes localized on the edge, is at the core of the now mature field of topological wave physics. More recently, it was realized that, in crystalline structures, certain types of defects can host localized modes, in which case the bulk-boundary correspondence has to be replaced by a bulk-defect correspondence. These defect-localized modes are expected to have robust properties owing to their topological origin. In this work, we show how to obtain topological defect modes in a lattice possessing both mirror and chiral symmetry. The defect is obtained by endowing a plaquette with a nontrivial gauge flux. We show that the bulk-defect correspondence is satisfied by introducing appropriate topological invariants. Moreover, the topological defect modes are shown to be highly robust to the introduction of symmetry-preserving disorder. The model is then realized in an acoustic system made of a bilayer network of tubes and the presence of topological defect modes is experimentally clearly demonstrated.

The quantum five-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of “theory space” to a complex plane. To study the corresponding complex fixed point on the lattice, the model must be deformed by an additional non-Hermitian term due to its complex coefficient $\lambda$. Although the variational principle breaks down in this case, we demonstrate that tensor network algorithms are still capable of simulating these non-Hermitian theories. We access system sizes up to $L=28$, which enable the observation of the theoretically predicted spiral flow of the running couplings. Moreover, we reconstruct the full boundary CCFT spectrum through the entanglement Hamiltonian encoded in the ground state. Our work demonstrates how tensor networks are the correct approach to capturing the approximate conformal invariance of weakly first-order phase transitions.

We report an extremely rich ground-state phase diagram of two spin-1 Haldane chains frustrated with a three-site exchange and coupled by the antiferromagnetic Heisenberg interaction on a zigzag ladder. A particular feature of the phase diagram is the extended quantum phase transition in the Ashkin-Teller universality class that separates the plaquette phase, which spontaneously breaks translation symmetry, and the uniform disordered phase. The former is connected to the Haldane phase, stabilized by large interchain coupling, via the topological Gaussian transition. Upon decreasing the interchain interactions, this intermediate disorder phase vanishes, giving place to a dimerized phase separated from the plaquette phase on one side via a nonmagnetic Ising transition and from the Haldane phase on the other side by a topological weak first-order transition. Finally, in the limit of two decoupled chains, we recover a quantum critical point that corresponds to two copies of the Wess-Zumino-Witten $\mathrm{SU}{\left(2\right)}_2$ criticality with a total central charge $c=3$.

Ferroaxial ordering, a spontaneous rotational distortion of the atomic arrangement, brings about a cross-product-type spin-orbit coupling (SOC) manifested as an electric toroidal (ET) dipole. We propose the light-induced nonlinear Edelstein effect (NLEE)—a second-order optical response in which a static magnetization is induced by a time-dependent electric field—as a promising probe of ferroaxial ordering. First, we elucidate the relationship between the NLEE tensor and the ET dipole. By decomposing the polarization modes of light, we find that both the linearly and circularly polarized light couple to the ET dipole via distinct mechanisms. We then demonstrate the NLEE using a minimal model that incorporates ferroaxial ordering. Our analysis reveals that effective coupling between orbital magnetization and SOC induces spin magnetization. The spin magnetization is tilted owing to the ET dipole; the tilt angle reflects the ratio between the ferroaxial-origin SOC and the relativistic SOC.

We consider the electronic and magnetic properties of the Hubbard model on a square lattice with the Fermi level near van Hove singularity and the ratio of the next-nearest-neighbor and nearest-neighbor hoppings $t^{\prime }/t=-0.45$, which favors the ferromagnetic instability. We find that a self-consistent consideration of the ferromagnetic fluctuations within the dual triply irreducible local expansion (D-TRILEX) approach results in the splitting of the electronic spectral function at low temperatures. This splitting exhibits only a weak momentum dependence, and only one of the split bands crosses the Fermi level. As a result, the Fermi surface itself remains unsplit but its area increases, reflecting the presence of non-Fermi-liquid electronic excitations. We show that both the self-consistent account of the nonlocal contributions to the electronic self-energy and the proper treatment of electron interaction vertices in D-TRILEX are important to obtain this behavior.

The interlayer quasi-chemical-bonding (QCB) interactions of two-dimensional layered materials advance the research field of interlayer engineering and cause interlayer charge density redistributions (ICDRs). The ICDRs have been reported experimentally and theoretically, showing different redistributions, e.g., accumulation, depletion, or a more complicated behavior. The underlying mechanism for the different ICDRs remains to be elucidated. In the current work, via a systematic theoretical study of the ICDRs of transition metal dichalcogenides with different numbers of $d$ electrons filling ($d^0 {\mathrm{TiS}}_2, d^1 {\mathrm{NbS}}_2$, and $d^2 {\mathrm{MoS}}_2$) in the $T$ and $H$ phases, we reveal three mechanisms based on the coexistence of different types of interlayer QCB interactions. Mechanism (1) is from a competition between two types of interlayer interactions: namely, the interlayer interaction between fully occupied energy levels (in short: o-o interaction) depletes electrons in the overlap region while that between occupied and empty levels (o-e interaction) promotes electron accumulation; the competition between them leads to the $d^0 {\mathrm{TiS}}_2$ tending to electron accumulation in the $T$ phase more than in the $H$ phase. Mechanism (2), the interlayer interaction between half-filled levels (h-h interaction), promotes the electron accumulation of $d^1 {\mathrm{NbS}}_2$. Mechanism (3), the interlayer interaction of multiple filled levels of $d^2 {\mathrm{MoS}}_2$ (namely, the multilevel o-o interaction), leads to a more complicated ICDR. The current study provides a unified understanding of the different ICDRs of van der Waals materials and paves the way for further exploration of their electronic properties and applications.

Recent advances in the scaling of spin qubits have led to the development of sparse architectures where spin qubits are distributed across multiple quantum dots. This distributed approach allows for qubit manipulation through hopping and flopping modes and may enable spin shuttling protocols to entangle spins beyond nearest neighbors. Here, we develop a microscopic theory of a minimal sparse array formed by a hole in a double quantum dot. We show the existence of spin-dependent magnetic corrections to the tunnel couplings that help preserve existing sweet spots, even for quantum dots with different $g$-factors, and introduce new ones that are not accounted for in the simplest models. Our analytical and numerical results explain observed sweet spots in state-of-the-art shuttling and cQED experiments, are relevant to hopping and flopping modes, and apply broadly as corrections to each interdot tunnel link in sparse array encodings of any size.

${\mathrm{Bi}}^{3+}$-doped ${\mathrm{Cs}}_2{\mathrm{AgInCl}}_6$ (${\mathrm{Cs}}_2{\mathrm{AgInCl}}_6:\mathrm{Bi}$) nanocrystals (NCs) have emerged as promising lead-free perovskites. However, the photophysical pathways governing their emission remain to be elucidated. Combining spectroscopic measurements with density functional theory, this work elucidates the role of ${\mathrm{Bi}}^{3+}$ doping in enabling singlet-to-triplet transitions and the origin of the asymmetric photoluminescence (PL) line shape. ${\mathrm{Bi}}^{3+}$ doping in ${\mathrm{Cs}}_2{\mathrm{AgInCl}}_6$ NCs enables triplet self-trapped exciton (STE) emission, evidenced by two distinct microsecond-scale lifetimes, a redshift in the delayed PL spectrum matching the singlet-triplet energy gap, temperature-dependent PL (TDPL) deconvolution resolving two peaks, and integrated intensity analysis yielding two binding energies split by the singlet-triplet gap, as well as transient absorption measurements revealing the intersystem crossing timescale. Theoretical calculations reveal that ${\mathrm{Bi}}^{3+}$ doping introduces strong spin-orbit coupling and breaks local inversion symmetry, which inverts the singlet and triplet energy levels and thereby facilitates the singlet-to-triplet transition. The PL spectrum broadening arises from multiple recombination processes, including free excitons and singlet/triplet self-trapped excitons, as well as ionized impurity and phonon scattering. The spectral asymmetry is mainly attributed to the cumulative emission from long-lived triplet STEs. Additionally, ${\mathrm{Bi}}^{3+}$ doping in ${\mathrm{Cs}}_2{\mathrm{AgInCl}}_6$ NCs induces pronounced phonon-assisted absorption, indicating the presence of strong electron-phonon coupling. The correlation between TDPL broadening and temperature-dependent Raman spectroscopy establishes longitudinal optical phonons as the dominant contributors to electron-phonon coupling. This work unravels the microscopic mechanism underlying triplet emission in ${\mathrm{Cs}}_2{\mathrm{AgInCl}}_6$:Bi NCs, offering a predictive basis for the rational design of luminescent lead-free perovskites.