Papers

We explicitly compute and tabulate the suspension map for cohomology operations, applying it to the dimensional reduction of anomalies and higher group structures of generalised symmetries in quantum field theories and lattice systems. In a quantum system with a discrete $p$-form symmetry, we can restrict the symmetry defects to a codimension-$q$ subspace of spacetime, or equivalently confine the gauge field to a slab whose thickness approaches zero. This results in a $(p-q)$-form symmetry on the subspace. We determine the fate of two important properties of symmetries under this process. First, we compute the anomaly of the reduced symmetry, or the higher anomaly of the original symmetry, which acts as an obstruction to higher gauging and onsiteability. Second, for two symmetries forming a higher-group structure, encoded as a Postnikov class, we compute the reduced higher-group structure, which may or may not be trivial. Both cases are captured by the $q$-fold iteration of the cohomology suspension $\Omega$, also known as the loop functor or transgression, in the cohomology of Eilenberg–MacLane spaces. Classical results state that $\Omega$ is an isomorphism in a stable range and annihilates mixed anomalies. To calculate $\Omega$ over a base ring which is not a field, we make use of small models for the chain DGAs of Eilenberg–MacLane spaces, pioneered by Cartan and Moore, whose results we review and extend. The critical added step is the improvement of a mod $p$ chain contraction to the $p$-local integers, obtained via a $p$-adic series. We automate the computations in a software package emcm, and provide extensive tables of the results. Finally, to make contact with explicit cochain formulations of cohomology operations, we demonstrate how to calculate cup products and certain cup-$i$ products in this framework.

We study thermal order in conformal field theories (CFTs) in $d=4-\epsilon$ and $d=3$ dimensions where several scalars are coupled to an $O(N)$ vector field. In $(4-\epsilon)$ dimensions, we consider models coupling a cubic model of $M$ scalars with $\mathbb{Z}_2^M\rtimes S_M$ symmetry (corresponding to sign flips and permutations of the scalars) to an $O(N)$ vector model. For any $M$, we find a window of $N$ in which two Wilson-Fisher-like fixed points exist. We show that the $\mathbb{Z}_2^M\rtimes S_M$ symmetry is spontaneously broken at arbitrary nonzero temperatures for $M=2$ and sufficiently large $N$ within this window, but it remains unbroken for $M>2$. Using the functional renormalisation group to continue these fixed points towards three dimensions, we find that they collide and move into the complex plane well before reaching $d=3$, suggesting that their continuation to $d=3$ does not yield unitary CFTs. We then work directly in three dimensions at large but finite $N$, with $M\ll N$, initially without assuming any permutation symmetry among the $M$ scalars. By studying the RG flow, we show that these models possess a conformal manifold up to the leading nontrivial order in the $1/N$ expansion of the beta functions (which is $\mathcal{O}(1/N)$). At each point on this manifold, the scalars split into two classes that are distinguished by how they couple to the $O(N)$ vector field. We then restrict to a subspace of the conformal manifold where there is an additional symmetry under permutations of the scalars within each class. We prove that in a domain of this subspace, all $M$ scalars acquire thermal expectation values such that the symmetry under sign flips of the scalars is spontaneously broken at all nonzero temperatures. This provides a novel class of large $N$ CFTs that exhibit a rich pattern of persistent symmetry breaking at nonzero temperatures.

Non-commutative sphere regularization of CFT has become a powerful tool for computing conformal data of 3d CFTs and was recently extended to 4d CFTs. In this work we further construct 5d free-scalar CFT and Yang-Lee CFT on a fuzzy 4-sphere. We observe a continuous phase transition and conformal towers in these examples. We obtain the first three scalar primaries of the 5d free-scalar CFT, furthermore, we compute the 5d Yang-Lee $\Delta_\phi,\Delta_{\phi^3}$ with $N_e=10$ fermions using exact diagonalization (ED) and $N_e=20$ fermions using density matrix renormalization group (DMRG), obtaining relatively good agreement with both $\epsilon$-expansion and the Gliozzi truncated bootstrap result.

Higher-winding skyrmion textures can generate emergent magnetic fields with multiple flux quanta per unit cell. This opens an intriguing route toward fractionalization, allowing fractionalized quantum anomalous Hall states to arise even at integer filling of the microscopic unit cell. We show that, in this setting, increasing lattice-scale inhomogeneity of the emergent magnetic field drives a Berezinskii–Kosterlitz–Thouless (BKT) transition between a fractionalized liquid and a crystalline dielectric state. This transition carries a topological signature: under flux insertion, the many-body polarization defines a quantized winding number that is nonzero in the fractionalized phase and vanishes in the dielectric crystal.

Quantum complexity has emerged as a natural probe of chaos, thermalization, and the black hole interior on timescales long after local observables have equilibrated. However, its time evolution has been studied almost exclusively in subsystems confined to a single connected region. We show, using complementary tools from holography and random quantum circuits, that noncontiguous subsystems composed of multiple disjoint regions give rise to qualitatively new physics compared to the contiguous case. First, at finite temperature, a subsystem occupying less than half of the total system can carry high complexity at late times, even as the complexity of its larger complement remains low. This inversion of the usual hierarchy is intrinsically thermal: it vanishes in the infinite-temperature limit, which is the regime modeled by random quantum circuits. Second, if a subsystem's complexity equilibrates at an early time, then fragmenting it into $m$ disjoint components can further reduce this timescale by a factor of $m$, a phenomenon we exhibit in both holography and random quantum circuits. These results not only sharpen the correspondence between geometric and computational notions of complexity, but also motivate the search for novel complexity phenomena in quantum dynamics.

While correlated insulators are devoid of low-energy quasiparticle poles, their Green functions retain clean momentum structure through zeros. However, precisely what zeros imply is not clear. By studying the extended Hubbard model both analytically and numerically, we establish a new paradigm for strongly correlated matter: the dispersion of Green function zeros is determined by both microscopic spin-spin correlations and defect kinematics. In fact, we find that the dispersion changes discontinuously across the transition between the Mott and the checkerboard charge-density wave phases as is expected for a first-order transition. This physics is robust to the inclusion of further neighbor hopping which simply fine tunes the spin-correlation or charge-defect kinematics. We conclude that it is the dispersion of the Green-function zeros that encode the physics of ordering resultant from the strong correlations.

For mathematicians: In this first in a series of two papers, we give a mathematically rigorous classification of (sufficiently nice) $c=1$ vertex operator algebras (VOAs) and vertex operator superalgebras (VOSAs). We confirm the lore that any such VO(S)A is either a lattice VO(S)A $V_L$ associated to a rank-1 integral lattice $L$, or can be obtained as an orbifold thereof, i.e. a $G$-invariant subalgebra $V_L^G$ for some finite group $G$ of automorphisms. All such $G$ are known, allowing for an explicit enumeration of nice $c=1$ VO(S)As. A key ingredient in our approach is to establish a general criterion for nice VOAs, requiring knowledge only of the vacuum character, for testing when the simple modules with integer conformal dimension span a symmetric fusion subcategory which is braided tensor equivalent to $Rep(G)$. In our companion paper, we calculate the ribbon auto-equivalences of the representation categories of the nice $c=1$ VOAs, and leverage this to obtain the classification of nice bosonic and fermionic $c=1$ full conformal field theories. For physicists: We rigorously classify the chiral algebras that can arise in the holomorphic sector of a bosonic or fermionic rational $c=1$ conformal field theory (CFT) whose non-identity primaries all have positive conformal dimension. Thinking of chiral algebras as gapless boundary conditions of 3D topological quantum field theories (TQFTs), our result says that any such chiral algebra is either a holomorphic boundary of $U(1)_k$ Chern-Simons theory, or can be obtained by passing to the $G$-invariant states thereof for some finite group $G$ of symmetries. We explicitly enumerate these chiral algebras and also discuss their non-invertible symmetries. In a companion paper, we build on these results using techniques from the study of 3D TQFTs to classify full bosonic and fermionic rational $c=1$ CFTs.

Kinetically constrained systems, such as those representing Rydberg atom arrays in the blockade regime, have gathered considerable attention due to the presence of atypical eigenstates in their spectrum. The latter manifests itself through the presence of quantum many-body scars as well as unusually large zero-mode (ZM) subspaces which contain analytically tractable eigenstates with various entanglement scalings. In particular, some of the latter are excitable zero-modes (EZMs), meaning that they can be promoted to a non-zero energy for open boundary conditions. In this work, I present an efficient protocol for finding analytical expressions for translation-invariant EZMs in constrained systems, based on the eigendecomposition of the local unconstrained Hamiltonian. I demonstrate the power of this method on a decorated Rydberg chain. In that model, my protocol directly produces a continuous matrix-product-state manifold located entirely in the zero-energy eigenspace for periodic boundary conditions. The span of that manifold grows exponentially with the system, and for odd system sizes it covers the entire zero-momentum eigenspace with zero energy. I then show how the physical structure of the manifold, which is tied to the local eigenbasis, also allows one to derive analytical expressions for ZMs at non-zero momentum and for a polynomial number of exact scars at $E=\pm\sqrt{3}$.

We study the free energy of a critical vector model at large $N$ on $S^{1}\times S^{2}$ with an angular velocity $\hat\mu$ without the singlet constraint. We study the model for which the large $N$ dynamics is controlled by the uniform saddle point of the auxiliary field arising in the Hubbard-Stratanovich transformation. The leading high-temperature behaviour is determined analytically both as an expansion about $\hat\mu r=0$ and $\hat\mu^{2}r^{2}=1$ where $r$ is the radius of the sphere. We supplement the analytic results with a numerical analysis that agrees with both the analytical expansions in their respective regimes and smoothly interpolates between them. The leading high-temperature contribution to the free energy develops a pole at $\hat\mu^{2}r^{2}=1$, in agreement with expectations from the thermal effective field theory. Its residue coincides with that of the massless free theory. Sub-leading terms, however, exhibit non-analytic dependence on the angular velocity and distinguish the critical fixed-point result from the free theory answer. The residue at the pole can also be obtained by placing the model on the pp-wave geometry. We show that the residue agrees with that obtained from the direct computation. The free energy of the model connects the non-trivial fixed point of the $O(N)$ model at $\hat\mu r=0$ to its free fixed point at $\hat\mu^2r^2=1$.

The generalized Bethe ansatz framework formulated in [P. R. Pasnoori, Phys. Rev. B 112, L060409 (2025)] provides a unified framework to find exact solutions to quantum many-body systems with time-dependent coupling strengths with periodic boundary conditions. In this work we extend this framework to the case of open boundary conditions where in addition to the time-dependent interactions in the bulk, the boundary conditions are explicitly time-dependent. We show that for integrable time-dependent bulk coupling strengths, the generalized Bethe ansatz framework provides the time-dependent boundary conditions compatible with integrability and reduces the time-dependent Schrodinger equation to a set of matrix difference equations called the boundary quantum Knizhnik-Zamolodchikov (BqKZ) equations. The solution to the BqKZ equations provides the explicit form of the exact wavefunction. We further show that the RG invariants of the corresponding static model identify with the dynamical invariants in the time-dependent model.

Local constraints govern the low-energy physics of frustrated matter, but familiar ice-type rules constrain flux-like quantities and are insensitive to handedness. Here we show that handedness itself can be imposed as an exact local quantum constraint without selecting an axis in spin space. We construct positive-semidefinite, SU(2)-invariant parent Hamiltonians whose complete zero-energy space on a tetrahedron has a prescribed chirality sign, rather than selecting a particular chiral wave function. For spin-1/2 the local term is a rank-one projector onto a chiral tetrahedral singlet, while for arbitrary spin it factorizes as $B^\dagger B$ through a singlet-annihilation operator, with a completely characterized kernel given by the span of the globally rotated chiral color-ice states. For coherent states, the same zero-energy condition becomes an $S$-independent nonlinear constraint in which three spin directions determine the fourth through a Möbius transformation; compositions of these maps define constraint holonomies on extended lattices. Connecting the same local constraint in different ways produces qualitatively different collective regimes: corner-sharing lattices retain exponentially large quantum ground-state kernels, with rigorous lower bounds exceeding conventional ice benchmarks; edge-sharing lattices support subdimensional plane or line zero modes; while triangular constructions suppress nonuniform coherent deformations and contain the complete Anderson tower of tetrahedral magnetic order at exactly zero energy. Two inequivalent triangular coverings further show that harmonic zero-mode counting does not determine the size of the quantum kernel. These results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled and related directly to the connectivity of the constraint network.

In a slowly varying aperiodic potential $h_i=h\cos(2\pi\beta i^n+\phi)$ with random power-law density interactions $V_{ij}/|i-j|^\alpha$, the resonant-object ensemble changes across $\alpha=2n$, wherever Hartree fragmentation is operative, from isolated two-level bonds to a mixture of fragmented multi-site clusters and isolated wing bonds that survive at finite density, while the pair-resonance scaling $x_{\rm pair}^{4-2n-\alpha}\ln x_{\rm pair}\propto h^2/(Vt_0)$ is unchanged~\cite{letter}. Here we develop the microscopic resonance theory underlying these results, together with its domain of validity. We derive the exact phase-averaged resonance statistics — the supply $N_0\propto L^{2-n}/h$, the correlated common-phase comb, and the closed-form Hartree variance — proving that the interaction leaves the leading supply law unchanged. Exact construction of the resonant Fock-space graph at $L\le18$ shows that the order-one forward-branching scale $h_{\rm FB}\propto L^{2-n}$ carries no giant component: one-step branching and connectivity are inequivalent. We separate the fixed-pair matching law from the shell-averaged $q\ln(1/q)$ law of the bond ensemble and develop the comb into a mesoscopic shell theory; we map the fragmentation domain, with its support threshold $V_*(\alpha)$ and the boundary-healing recursion; and we treat the marginal case $\alpha=2$, where shell and matching marginalities compound into a double logarithm. Three long-range thresholds emerge with distinct meanings — $\alpha=1/2$ (the exact variance threshold of the random Fock-space energy and the square-summability boundary of the leading LIOM-dressing estimate), $\alpha=2n$ (change of the local resonant objects), and $\alpha=2$ (marginality of the long-range shell sum) — none of which is, by itself, a localization transition.

For fermions in a slowly varying aperiodic potential with random interactions $V_{ij}/|i-j|^{\alpha}$, the potential fixes the resonance supply $N_0 \propto L^{2-n}/h$. On crossing ${\alpha}-2n$, wherever Hartree fragmentation is operative, the resonant-object ensemble reconstructs: turning-point runs fragment into clusters whose intrinsic matching law resolves no logarithmic singularity, while isolated wing bonds survive at finite density and restore a reduced logarithm. The scaling $x^{4-2n-{\alpha}}_{pair} ln{x_{pair}} \propto h^2/(V t0)$ is unchanged. Random coefficient fluctuations sustain the $R^{-{\alpha}}$ coupling; uniform ones cancel to $R^{-{\alpha}-2}$.

We extend the functional determinant approach (FDA), previously restricted to static impurities, to the case of finite-mass impurities by using the mass-gap description of Fermi polarons [Phys. Rev. Lett. 135, 193401 (2025)]. The quadratic structure of the mass-gap model enables the exact evaluation of many-body spectra and Ramsey dynamics for mobile impurities. We show that this mass-gap FDA smoothly interpolates between the Fermi-edge singularity for infinitely heavy impurities and the emergence of quasiparticle weight for finite impurity mass. Our results demonstrate that the mass-gap FDA provides a transparent and computationally efficient framework to describe the quantum dynamics of mobile impurities.

We present a comprehensive analysis of non-equilibrium fluctuation-dissipation relations connect- ing experimentally accessible chiral-current auto- and cross-correlations to the tunneling-current noise and conductance in Laughlin edge states coupled through a quantum point contact (QPC). We examine their validity for two chiral Laughlin edges held at different temperatures and voltages and show that the relations remain exact for arbitrary tunneling strength, voltage bias, and edge- state temperatures. We further generalize them to spatially extended QPCs and to tunneling am- plitudes with an explicit voltage dependence, and discuss the conditions and limitations associated with these generalizations. Our results establish that the local tunneling-current noise generated at the QPC can be reliably reconstructed from experimentally accessible auto- and cross-correlations measured downstream, providing a robust route to characterize non-equilibrium transport in chiral edge states.

Charge order is conventionally viewed as a static modulation of the electronic density, despite growing experimental capabilities to probe and manipulate its nonequilibrium evolution. In contrast to spin-ordered systems, a microscopic framework for charge-order dynamics and its control under external driving remains largely underdeveloped. Here, starting from an extended Hubbard model, we derive an effective pseudospin model in which the charge-ordered state maps onto staggered pseudospin order. The resulting charge-order dynamics is governed by Landau–Lifshitz–Gilbert-like equations for the pseudospins, closely analogous to those of a bipartite antiferromagnet. We show that an external electric field directly controls the staggered pseudospin order and, above a threshold field, drives coherent reversal of the charge-order polarity by destabilizing collective pseudospin excitations. Our results establish the charge pseudospin as a microscopic dynamical degree of freedom for coherent switching and control of charge order, providing a charge-sector analogue of the well-established framework for spin-order dynamics in spintronics.

In this article, we apply the idea of emergent symmetries to construct holographic representations of a broad class of topological quantum critical points (tQCPs) that appear in fermionic classes in the Bott clock. We show explicitly that around the Bott clock, an emergent symmetry $U_{EM}$ exists at a tQCP between different symmetry protected gapped phases with protecting symmetry $G_p$ in $d$ spatial dimensions. This emergent symmetry can be used to construct a $(d+1)$ spatial dimensional lattice model with a properly upgraded symmetry such as $U_{EM}\times G_p$ or $U_{EM} \rtimes G_p$, etc. By doubling the degrees of freedom of the adjacent topological class in $d$-dimensions, we successfully show that the $(d+1)$-dimensional lattice models constructed in this way have the desired enlarged symmetry groups that precisely belong to the adjacent topological classes, counterclockwise around the Bott clock. Furthermore, $d$-dimensional boundaries of these $(d+1)$ dimensional lattice models of gapped topological classes are shown to exhibit identical infrared dynamics as the corresponding tQCPs in the $d$-dimensional adjacent topological phases in the Bott clock, with lower symmetries.

We report experimental diacovery of superconductivity (SC) in tellurium (Te) polyhydride. The compound was synthesized at high pressure and high temperature conditions using a diamond anvil cell combined with a laser heating system. Subsequent in situ transport measurements at high pressures, performed as a function of temperature and applied magnetic field, revealed a superconducting transition with a critical temperature Tc about 91 K at 263 GPa. The superconducting phase is assigned to TeH4 with characterized face shared TeH12 cage forming quasi molecular H2 units based on synchrotron x-ray diffraction experiments. Analysis of the SC behavior at magnetic fields yielded a Ginzburg Landau (GL) coherence length of approximately 54 angstroms. Tellurium polyhydride thus becomes another chalcogen polyhydride superconductor in addition to the landmark discovery of the first polyhydride high Tc SC SH3.

We report the first numerical examination of symmetric mass generation (SMG) for domain-wall fermions. Our simulation on a two-dimensional Euclidean lattice computes the path-integral of the Fidkowski-Kitaev Majorana chain with two boundaries, corresponding to the two (physical and mirror) walls. We demonstrate by evaluating the lattice Dirac operator eigenvalue spectrum that the local four-Fermi interaction selectively gaps the edge fermions on the mirror wall while leaving the physical wall intact. We further identify a characteristic signature of SMG in the path-integral: the gap of the Dirac operator opens along the imaginary axis of the complex spectrum, in contrast to the standard mass shift in the real direction. The conventional hybrid Monte Carlo algorithm remains practical with reweighting the complex phase of the Pfaffian, which is found to be remarkably small throughout the simulation. These results provide a practical nonperturbative framework for interaction-induced mirror-fermion decoupling of lattice domain-wall fermions.

We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called $S^1$-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such $S^1$-family classifications by the exotic symmetry interplay: (i) nontrivial mixed anomalies, (ii) semi-direct product relation between the spontaneously broken and the unbroken symmetries, and (iii) symmetry with noninvertible operators. We find that such structures lead to the novel $S^1$-family classifications inaccessible by earlier classifications based on “independent” symmetries. Furthermore, we construct lattice realizations of these $S^1$-families and explicitly demonstrate their novel algebraic structures.

The recent discovery of long-sought dice flat band in layered YCl electride has opened up rich possibilities of correlation and topological physics in dice lattice systems [Nature Communications 17, 2213 (2026), arXiv:2509.05958]. Here, we reveal a plethora of distinctive correlated topological phases in a generic layered dice lattice system at band filling of $\nu =4$ under on-site Hubbard interactions: (i) the system is an intrinsic sublattice anti-ferromagnetic (AFM) quantum spin-valley Hall insulator; (ii) a circularly polarized light (CPL) drives the AFM spin-valley insulator into a Floquet odd-parity $f$-wave altermagnet(AM) insulator; (iii) a vertical displacement field turns the Floquet $f$-wave AM insulator into a spin-valley-layer-polarized Chern insulator, with the sign of spin, valley and Chern number all controlled by the direction of the displacement field. Our results not only establish the layered dice lattice as a versatile platform for electrically switchable magnetic and topological phases, but also provide an all-electrical scheme for integrated spin-valley-layertronics for non-volatile information storage and processing.

Thermal transport offers a bulk probe of charge-neutral excitations in frustrated magnets. It remains challenging, however, to determine whether such transport can distinguish different parton mean-field structures of the same spin system. This question is particularly relevant on the honeycomb lattice, where distinct $0$-flux, $\pi$-flux, and chiral $\pi/2$-flux sectors have been proposed. In this paper, we compare self-consistent saddle-point solutions in these three sectors for a frustrated $J_1-J_2$ Heisenberg model with a next-nearest-neighbor Dzyaloshinskii-Moriya interaction and a perpendicular magnetic field. Using finite-temperature Schwinger-boson mean-field theory and the Kubo formula for bosonic Bogoliubov-de Gennes systems, we evaluate the intrinsic spinon thermal Hall conductivity. At a common parameter point where all three branches remain gapped, the $0$-flux response is positive and the $\pi$-flux response is negative for $D>0$ and $h>0$ under the sign conventions used in this paper, whereas the $\pi/2$-flux response changes sign with increasing temperature. We further show that a projective symmetry combining a sixfold rotation with time reversal forces the zero-field response of a fixed chiral $\pi/2$-flux domain to vanish. Within the mean-field regime examined in this paper, the sign and temperature dependence of $\kappa_{xy}/T$ therefore provide a flux-sensitive transport signature.

We investigate the dynamical emergence of a state driven by the interplay between antiferromagnetism (AFM) and singlet $d$-wave superconductivity (SC) within a slave-rotor mean-field framework. By decomposing the electron into charge and spin degrees of freedom, the formalism captures strong-correlation effects beyond conventional mean-field approaches. A PDW order is found to emerge dynamically in the coexistence region of AFM and SC. The AFM-SC coexistence region is significantly modified with correlation, leading to a systematic shift of the tetra-critical point. The doping and temperature evolution of the AFM, SC, and PDW order parameters, together with the rotor condensate amplitude $\phi$, which characterizes charge coherence, shows a crossover from a coherent to an incoherent metal with the suppression of coherent quasi-particle spectral weight. Moreover, in the AFM + $(\phi \neq 0)$ region, coherent quasi-particle bands coexist with incoherent Hubbard-like excitations, whereas only incoherent spectral features survive in the AFM + $(\phi = 0)$ regime. The SC phase exhibits nodal quasi-particles consistent with $d$-wave pairing.

We report single-shot terahertz time-domain spectroscopy of Cr$_2$O$_3$ in pulsed magnetic fields up to 30 T. Well above the spin-flop field, in the 20-30 T range, the resonance frequency exhibits a nearly linear field dependence with a slope of ~22 GHz/T, smaller than the 28 GHz/T reported from low-field measurements. This reduction is insensitive to temperature and to a 15{\deg} field tilt, suggesting an intrinsic high-field property.

Two ultra-narrow absorption peaks around 1.5 eV, which are widely believed to originate from a transition from a spin-orbital entangled triplet to a singlet state, in the two-dimensional van der Waals crystal NiPS$_3$, have attracted considerable attention because of their pronounced spin-dependent character. An interesting question is whether ultrahigh magnetic fields modify an interaction-driven hybridization between those two peaks. In this work we perform systematic magneto-optical measurements of NiPS$_3$ in pulsed magnetic fields of up to 178 T and observe a pronounced mutual repulsion between the two sharp exciton peaks accompanied by a redistribution of oscillator strength, while the band edge shows no detectable field-induced shift within our experimental resolution. We construct a minimal two-level interaction model and compare it semi-quantitatively with the experimental data. Our results reveal a magnetic-field-tunable exciton-exciton coupling as the dominant high-field response of NiPS$_3$, and clarify this material as a new experimental platform for exploring strongly correlated exciton physics in magnetic van der Waals insulators.

Controlling intertwined electronic orders in two-dimensional superconductors offers an effective route to answering fundamental questions and engineering new quantum devices. However, tuning the balance between competing orders typically requires complex chemistry, strain, or interface engineering. Here, we show that a pristine alternative is the dimensional reduction of the unconventional superconductor FeSe. Exfoliation suppresses the bulk electronic nematic response and switches the superconducting symmetry from bulk s-wave to d-wave-dominant. Transport, electron microscopy, and Raman spectroscopy establish the substantial weakening of nematic order in thin flakes. To probe superconductivity, we perform angle-dependent Andreev reflection spectroscopy on pristine crystal edges. As the junction's orientation is rotated, the spectra evolve from zero-energy bound states to coherence peaks. The injection angle, field, and temperature dependence, along with theoretical modeling, confirm that exfoliation switches the superconducting symmetry. Our results suggest a versatile superconducting platform for engineering quantum orders and provide fresh insights into the underlying pairing mechanisms.

Nabokoite family compounds ACu$_7$(TeO$_4$)(SO4)$_5$X (A=Na, K, Rb, Cs; X=Cl, Br) host frustrated 2D square kagom'{e} lattice layers decorated by additional inter-layer magnetic ions. We study magnetic order in nabokoites with multi-frequency electron spin resonance spectroscopy and thermodynamic measurement (specific heat, magnetization and dielectric permittivity). Our study reveals that the choice of the low-temperature ground state is qualitatively different in light-alkali-ion (K, Na) and heavy-alkali-ion (Rb, Cs) compounds. Heavy-alkali-ion nabokoites order in conventional collinear antiferromagnetic pattern with easy-axis anisotropy. The parameters of the ordered antiferromagnetic state are very close for all heavy-alkali-ion subfamily. Light-alkali-ion members of nabokoite family demonstrate much more complicated route to the ordered state: firstly, a ferroelectric transition at 25-90K lifts the frustration and thus pre-cooks the low-temperature ordering; secondly, an unusual noncollinear magnetic order develops via two-step phase transition with first transition temperature $T_{c1}\simeq 5-6$K and the second transition at $T_{c2}\simeq 3-4$K. Noncollinear order is evidenced by observation of characteristic non-Larmor antiferromagnetic resonance mode. Spin dynamics of light-alkali-ion nabokoites is characterized by three zero-field magnon gaps and two spin-reorientation fields, the values of magnon gaps and critical fields are quite different for different compounds. The finite-size cluster modeling of pyramidal structural block of nabokoite structure combined suggests that the critical closeness of the nabokoite exchange coupling parameters to the border-line between the different quantum ground state of pyramidal building block of nabokoite structure could be the clue to the choice of qualitatively different ordered state in light- and heavy-alkali-ion nabokoites.

The square kagomé lattice (SKL) offers a model platform for investigating geometric frustration in 2D systems. Nabokoite-family compounds \nabok{A}{X} (A=Na, K, Cs, Rb and X=Cl, Br) extend this physics to a 3D network, where 2D SKL layers are decorated by interlayer spins. Using electron paramagnetic resonance (EPR), we demonstrate a dramatic splitting of this complex exchange network into two virtually decoupled spin subsystems: absolute calibration of the electron paramagnetic resonance (EPR) absorption reveals that only a fraction of all copper spins in nabokoites is EPR-active and this fraction of the spins orders at the Néel point. Comparison of the EPR absorption and static susceptibility indicates that contribution of the EPR-silent spin subsystem to total magnetic susceptibility decreases on cooling. This direct observation of coexisting magnetic order and possible spin-liquid dynamics within a single compound challenges conventional models of unified exchange networks in decorated frustrated lattices.

We use inelastic neutron scattering (INS) to determine the crystal electric field (CEF) excitations of Yb$^{3+}$ in the rare-earth hyperkagome magnet Yb$_3$Sc$_2$Ga$_3$O$_{12}$. Three nearly dispersionless magnetic excitations are observed near 58, 68, and 74~meV, corresponding to transitions from the ground-state Kramers doublet to the three excited doublets of the $J=7/2$ multiplet. A Stevens-operator analysis constrained by the local $222$ ($D_2$) symmetry reproduces the excitation energies and spectral weights and yields an Ising-type ground-state $g$ tensor. The first excited doublet lies approximately 58~meV above the ground state, establishing a well-isolated effective $J_{\mathrm{eff}}=1/2$ degree of freedom over the low-temperature regime relevant to collective magnetism. Notably, the directly measured CEF spectrum substantially revises the level scheme previously inferred from bulk measurements, while preserving the essential low-energy pseudospin description. Two independent fitting protocols give consistent excitation energies, ground-doublet wave functions, and $g$ tensors, despite the nonuniqueness of the individual CEF parameters. The resulting single-ion model also reproduces the characteristic susceptibility, magnetization, and field evolution of the Schottky anomaly in specific heat. These results establish the microscopic single-ion basis needed to construct an effective exchange Hamiltonian and to interpret future measurements of low-energy collective excitations in Yb$_3$Sc$_2$Ga$_3$O$_{12}$.

AV$_3$Sb$_5$ kagome metals are characterized by intertwined electronic and structural orders, which motivated extensive studies in recent years. Yet the details of the electronic state preceding the superconducting phase remain poorly understood. Here we extend our previous investigation [Phys. Rev. Research 7, L032046 (2025)] of RbV$_3$Sb$_5$ using avoided level crossing (ALC) muon-spin spectroscopy to the $A$ = Cs and K systems. Consistent with our previous study, we identify a second transition whose origin cannot be attributed solely to an internal magnetic field, indicating the involvement of an additional electronic mechanism that subtly modifies the charge distribution within the V plane. In particular, the ALC results point towards an additional charge modulation taking place within the charge density wave (CDW) phase and occurring at $T^{*}<T_{CDW}$ for $A$ = Cs and Rb, or in the vicinity of $T_{CDW}$ for $A$ = K.