Gapless fracton quantum spin liquids are exotic phases of matter described by higher-rank U(1) gauge theories which host gapped and immobile fracton matter excitations as well as gapless photons. Despite well-known field theories, no spin models beyond purely classical systems have been identified to realize these phases. Using error-controlled Green function Monte Carlo, here we investigate a square lattice spin-1 model that shows precise signatures of a fracton quantum spin liquid without indications of conventional ordering. Specifically, the magnetic response exhibits characteristic patterns of suppressed pinch points that accurately match the prediction of a rank-2 U(1) field theory and reveals the existence of emergent photon excitations in 2+1 spacetime dimensions. Remarkably, this type of fracton quantum spin liquid is not only identified in the system's ground state but also in generic low-energy sectors of a strongly fragmented Hilbert space.

Although the generic mechanism behind high-temperature superconductivity remains notoriously elusive, a set of favorable conditions for its occurrence in a given material has emerged: (i) the electronic structure should have a very high density of states near the Fermi level; (ii) electrons need to be susceptible to a sizable interaction with another degree of freedom to ensure pairing themselves; (iii) the ability to fine-tune some of the system properties significantly helps maximising the critical temperature. Here, by means of high-resolution ARPES, we show that all three criteria are remarkably fulfilled in trigonal platinum bismuthide (t-PtBi$_2$). Specifically, this happens on its surface, which hosts topological surface states known as Fermi arcs. Our findings pave the way for the stabilisation and optimisation of high-temperature superconductivity in this topological material.

V-doped (Bi,Sb)$_2$Te$_3$ has a ten times higher magnetic coercivity than its Cr-doped counterpart and therefore is believed to be a superior system for the quantum anomalous Hall effect (QAHE). The QAHE requires the opening of a magnetic band gap at the Dirac point. We do not find this gap by angle-resolved photoelectron spectroscopy down to 1 K. By x-ray magnetic circular dichroism (XMCD) we directly probe the magnetism at the V site and in zerofield. Hysteresis curves of the XMCD signal show a strong dependence of the coercivity on the ramping velocity of the magnetic field. The XMCD signal decays on a time scale of minutes which we conclude contributes to the absence of a detectable magnetic gap at the Dirac point.

We introduce a general corner transfer matrix renormalization group algorithm tailored to projected entangled-pair states on the triangular lattice. By integrating automatic differentiation, our approach enables direct variational energy minimization on this lattice geometry. In contrast to conventional approaches that map the triangular lattice onto a square lattice with diagonal next-nearest-neighbour interactions, our native formulation yields improved variational results at the same bond dimension. This improvement stems from a more faithful and physically informed representation of the entanglement structure in the tensor network and an increased number of variational parameters. We apply our method to the antiferromagnetic nearest-neighbour Heisenberg model on the triangular and kagome lattice, and benchmark our results against previous numerical studies.

The Shockley-Queisser (SQ) limit provides a convenient metric for predicting light-to-electricity conversion efficiency of a solar cell based on the band gap of the light-absorbing layer. In reality, few materials approach this radiative limit. We develop a formalism and a computational method to predict the maximum photovoltaic efficiency of imperfect crystals from first principles. Our scheme includes equilibrium populations of native defects, their carrier-capture coefficients, and the associated recombination rates. When applied to kesterite solar cells, we reveal an intrinsic limit of 20% for $\mathrm{Cu_2ZnSnSe_4}$, which falls far below the SQ limit of 32%. The effects of atomic substitution and extrinsic doping are studied, leading to pathways for enhanced efficiency of 31%. This approach can be applied to support targeted-materials selection for future solar-energy technologies.

The cubic perovskite SrFeO$_3$ was recently reported to host hedgehog- and skyrmion-lattice phases in a highly symmetric crystal structure which does not support the Dzyaloshinskii-Moriya interactions commonly invoked to explain such magnetic order. Hints of a complex magnetic phase diagram have also recently been found in powder samples of the single-layer Ruddlesden-Popper analog Sr$_2$FeO$_4$, so a reinvestigation of the bilayer material Sr$_3$Fe$_2$O$_7$, believed to be a simple helimagnet, is called for. Our magnetization and dilatometry studies reveal a rich magnetic phase diagram with at least 6 distinct magnetically ordered phases and strong similarities to that of SrFeO$_3$. In particular, at least one phase is apparently multiple-$\mathbf{q}$, and the $\mathbf{q}$s are not observed to vary among the phases. Since Sr$_3$Fe$_2$O$_7$ has only two possible orientations for its propagation vector, some of the phases are likely exotic multiple-$\mathbf{q}$ order, and it is possible to fully detwin all phases and more readily access their exotic physics.

We report on spectroscopy study of elementary magnetic excitations in an Ising-like antiferromagnetic chain compound SrCo$_2$V$_2$O$_8$ as a function of temperature and applied transverse magnetic field up to 25 T. An optical as well as an acoustic branch of confined spinons, the elementary excitations at zero field, are identified in the antiferromagnetic phase below the Néel temperature of 5 K and described by a one-dimensional Schrödinger equation. The confinement can be suppressed by an applied transverse field and a quantum disordered phase is induced at 7 T. In this disordered paramagnetic phase, we observe three emergent fermionic excitations with different transverse-field dependencies. The nature of these modes is clarified by studying spin dynamic structure factor of a 1D transverse-field Heisenberg-Ising (XXZ) model using the method of infinite time evolving block decimation. Our work reveals emergent quantum phenomena and provides a concrete system for testifying theoretical predications of one-dimension quantum spin models.

Chiral soliton lattices (CSLs) are nontrivial spin textures that emerge from the competition between Dzyaloshinskii-Moriya interaction, anisotropy, and magnetic fields. While well established in monoaxial helimagnets, their role in materials with anisotropic, direction-dependent chirality remains poorly understood. Here, we report the direct observation of a tunable transition from $\pi$ to 2$\pi$ soliton lattices in the non-centrosymmetric Heusler compound Mn1.4PtSn. Using Lorentz transmission electron microscopy, resonant elastic X-ray scattering, and micromagnetic simulations, we identify a $\pi$-CSL as the magnetic ground state, in contrast to the expected helical phase, which evolves into a classical 2$\pi$-CSL under increasing out-of-plane magnetic fields. This transition is governed by a delicate interplay between uniaxial magnetocrystalline anisotropy and magnetostatic interactions, as captured by a double sine-Gordon model. Our analysis not only reveals the microscopic mechanisms stabilizing these soliton lattices but also demonstrates their general relevance to materials with D2d, S4, Cnv, or Cn symmetries. The results establish a broadly applicable framework for understanding magnetic phase diagrams in chiral systems, with implications for soliton-based spintronic devices and topological transport phenomena.

SmB6, a well-known Kondo insulator, has been proposed to be an ideal topological insulator with states of topological character located in a clean, bulk electronic gap, namely the Kondo hybridisation gap. Seeing as the Kondo gap arises from many body electronic correlations, this would place SmB6 at the head of a new material class: topological Kondo insulators. Here, for the first time, we show that the k-space characteristics of the Kondo hybridisation process is the key to unravelling the origin of the two types of metallic states observed directly by ARPES in the electronic band structure of SmB6(001). One group of these states is essentially of bulk origin, and cuts the Fermi level due to the position of the chemical potential 20 meV above the lowest lying 5d-4f hybridisation zone. The other metallic state is more enigmatic, being weak in intensity, but represents a good candidate for a topological surface state. However, before this claim can be substantiated by an unequivocal measurement of its massless dispersion relation, our data raises the bar in terms of the ARPES resolution required, as we show there to be a strong renormalisation of the hybridisation gaps by a factor 2-3 compared to theory, following from the knowledge of the true position of the chemical potential and a careful comparison with the predictions from recent LDA+Gutzwiler calculations. All in all, these key pieces of evidence act as triangulation markers, providing a detailed description of the electronic landscape in SmB6, pointing the way for future, ultrahigh resolution ARPES experiments to achieve a direct measurement of the Dirac cones in the first topological Kondo insulator.

We exploit insights into the geometry of bosonic and fermionic Gaussian states to develop an efficient local optimization algorithm to extremize arbitrary functions on these families of states. The method is based on notions of gradient descent attuned to the local geometry which also allows for the implementation of local constraints. The natural group action of the symplectic and orthogonal group enables us to compute the geometric gradient efficiently. While our parametrization of states is based on covariance matrices and linear complex structures, we provide compact formulas to easily convert from and to other parametrization of Gaussian states, such as wave functions for pure Gaussian states, quasiprobability distributions and Bogoliubov transformations. We review applications ranging from approximating ground states to computing circuit complexity and the entanglement of purification that have both been employed in the context of holography. Finally, we use the presented methods to collect numerical and analytical evidence for the conjecture that Gaussian purifications are sufficient to compute the entanglement of purification of arbitrary mixed Gaussian states.

Polymer membranes are typically assumed to be inert and nonresponsive to the flux and density of the permeating particles in transport processes. Here, we study theoretically the consequences of membrane responsiveness and feedback on the steady-state force--flux relations and membrane permeability using a nonlinear-feedback solution-diffusion model of transport through a slab-like membrane. Therein, the solute concentration inside the membrane depends on the bulk concentration, $c_0$, the driving force, $f$, and the polymer volume fraction, $\phi$. In our model, solute accumulation in the membrane causes a sigmoidal volume phase transition of the polymer, changing its permeability, which, in return, affects the membrane's solute uptake. This feedback leads to nonlinear force--flux relations, $j(f)$, which we quantify in terms of the system's differential permeability, $\mathcal{P}_\text{sys}^{\Delta}\propto {\mathrm{d}j}/{\mathrm{d}f}$. We find that the membrane feedback can increase or decrease the solute flux by orders of magnitude, triggered by a small change in the driving force, and largely tunable by attractive versus repulsive solute--membrane interactions. Moreover, controlling the input, $c_0$ and $f$, can lead to steady-state bistability of $\phi$ and hysteresis in the force--flux relations. This work advocates that the fine-tuning of the membrane's chemo-responsiveness will enhance the nonlinear transport control features, providing great potential for future (self-)regulating membrane devices.

Solid matter is classified through symmetry of ordering phenomena. Experimentally, this approach is straightforward, except when distinct orderings occur with identical or almost identical symmetry breaking. Here we show that the cuprate system Y$_{1-x}$Pr$_x$Ba$_2$Cu$_3$O$_{6+y}$ hosts two distinct orderings with almost identical translational symmetry breaking. Only when applying site-sensitive resonant elastic x-ray scattering (REXS), charge ordering can be conclusively differentiated from a super-lattice structure. These two orderings occur with almost the same in-plane symmetry but manifest at different atomic sites and display different temperature dependence. Differentiating these orders provides an important clue to the anomalous behavior of PrBa$_2$Cu$_3$O$_7$ within the 123-series of high-temperature superconductors. We conclude that the symmetry breaking at the Pr-site is unfavorable for superconducting pairing.

Spin waves are the fundamental excitations in magnetically ordered spin systems and are ubiquitously observed in magnetic materials. However, the standard understanding of spin waves as collective spin oscillations in an effective harmonic potential does not consider the possibility of soft modes, such as those due to an effective quartic potential. In this work, we show that such quartic potentials arise under very general conditions in a broad class of isotropic spin systems without a fine-tuning of the interaction parameters. Considering models with spin spiral ground states in two and three spatial dimensions, we numerically demonstrate that quartic amplitude spin oscillations produce a fluctuation-induced spin-wave gap which grows with temperature according to a characteristic power-law. In conjunction with a phenomenological theory, the present work provides a general theoretical framework for describing soft spin modes, extending the previously discussed spin dynamics in the presence of order-by-disorder, and highlighting the important role of finite-size effects. Our predictions of a temperature-dependent gap in spiral spin systems could be tested in inelastic neutron scattering experiments, providing direct spectroscopic evidence for thermal effects arising from soft spin modes in magnetic materials.

Applying angle-resolved photoemission spectroscopy and density functional theory calculations, we present compelling spectroscopic evidence demonstrating the intertwining and mutual interaction between the Kondo and kagome sublattices in heavy-fermion intermetallic compound YbV$_6$Sn$_6$. We reveal the Yb 4$f$-derived states near the Fermi level, along with the presence of bulk kagome bands and topological surface states. We unveil strong interactions between the 4$f$ and itinerant electrons, where the kagome bands hosting the Dirac fermions and van Hove singularities predominate. Such findings are well described using a $c$-$f$ hybridization model. On the other hand, our systematic characterization of magnetic properties demonstrates an unusually enhanced antiferromagnetic ordering, where the kagome-derived van Hove singularities near $E_F$ play a vital role in determining the unconventional nature of the Ruderman-Kittel-Kasuya-Yosida interaction and Kondo coupling. These unique kagome-state-mediated exchange interactions have never been reported before and could lead to a novel phase diagram and various quantum critical behaviors in YbV$_6$Sn$_6$ and its siblings. Our results not only expand the family of exotic quantum phases entangled with kagome structure to the strongly correlated regime, but also establish YbV$_6$Sn$_6$ as an unprecedented platform to explore unconventional many-body physics beyond the standard Kondo picture.

Ptychography is a scanning coherent diffraction imaging technique successfully applied in the electron, visible and x-ray regimes. One of the distinct features of ptychography with respect to other coherent diffraction techniques is its capability of dealing with partial spatial and temporal coherence via the reconstruction algorithm. Here we focus on the temporal and clarify theoretically and with simulations the constraints which affect the energy resolution limits of the ptychographic algorithms. Based on this, we design and perform simulations for a broadband ptychography in the hard x-ray regime, which enables an energy resolution down to 1 eV. We benchmark the simulations against experimental ptychographic data from a nickel test sample, by extracting the x-ray absorption near edge spectrum with energy resolution of 5 eV using a continuum spectrum of 20 eV bandwidth. We review the results, discuss the limitations, and provide guidelines for future broadband ptychography experiments, its prospective applications and potential impact on achieving diffraction limited resolutions.

Spontaneous symmetry-breaking quantum phase transitions play an essential role in condensed matter physics. The collective excitations in the broken-symmetry phase near the quantum critical point can be characterized by fluctuations of phase and amplitude of the order parameter. The phase oscillations correspond to the massless Nambu$-$Goldstone modes whereas the massive amplitude mode, analogous to the Higgs boson in particle physics, is prone to decay into a pair of low-energy Nambu$-$Goldstone modes in low dimensions. Especially, observation of a Higgs amplitude mode in two dimensions is an outstanding experimental challenge. Here, using the inelastic neutron scattering and applying the bond-operator theory, we directly and unambiguously identify the Higgs amplitude mode in a two-dimensional S=1/2 quantum antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$ near a quantum critical point in two dimensions. Owing to an anisotropic energy gap, it kinematically prevents such decay and the Higgs amplitude mode acquires an infinite lifetime.

Spin currents which allow for a dissipationless transport of information can be generated by electric fields in semiconductor heterostructures in the presence of a Rashba-type spin-orbit coupling. The largest Rashba effects occur for electronic surface states of metals but these cannot exist but under ultrahigh vacuum conditions. Here, we reveal a giant Rashba effect ({\alpha}_R ~ 1.5E-10 eVm) on a surface state of Ir(111). We demonstrate that its spin splitting and spin polarization remain unaffected when Ir is covered with graphene. The graphene protection is, in turn, sufficient for the spin-split surface state to survive in ambient atmosphere. We discuss this result along with evidences for a topological protection of the surface state.

By means of powder neutron diffraction we investigate changes in the magnetic structure of the coplanar non-collinear antiferromagnet Mn$_3$Ge caused by an application of hydrostatic pressure up to 5\phantom{ }GPa. At ambient conditions the kagomé layers of Mn atoms in Mn$_3$Ge order in a triangular 120$^{\circ}$ spin structure. Under high pressure the spins acquire a uniform out-of-plane canting, gradually transforming the magnetic texture to a non-coplanar configuration. With increasing pressure the canted structure fully transforms into the collinear ferromagnetic one. We observed that magnetic order is accompanied by a noticeable magnetoelastic effect, namely, spontaneous magnetostriction. The latter induces an in-plane magnetostrain of the hexagonal unit cell at ambient pressure and flips to an out-of-plane strain at high pressures in accordance with the change of the magnetic structure.

Confinement is a process by which particles with fractional quantum numbers bind together to form quasiparticles with integer quantum numbers. The constituent particles are confined by an attractive interaction whose strength increases with increasing particle separation and as a consequence, individual particles are not found in isolation. This phenomenon is well known in particle physics where quarks are confined in baryons and mesons. An analogous phenomenon occurs in certain magnetic insulators; weakly coupled chains of spins S=1/2. The collective excitations in these systems is spinons (S=1/2). At low temperatures weak coupling between chains can induce an attractive interaction between pairs of spinons that increases with their separation and thus leads to confinement. In this paper, we employ inelastic neutron scattering to investigate the spinon confinement in the quasi-1D S=1/2 XXZ antiferromagnet SrCo2V2O8. Spinon excitations are observed above TN in quantitative agreement with established theory. Below TN the pairs of spinons are confined and two sequences of meson-like bound states with longitudinal and transverse polarizations are observed. Several theoretical approaches are used to explain the data. A new theoretical technique based on Tangent-space Matrix Product States gives a very complete description of the data and provides good agreement not only with the energies of the bound modes but also with their intensities. We also successfully explained the effect of temperature on the excitations including the experimentally observed thermally induced resonance between longitudinal modes below TN ,and the transitions between thermally excited spinon states above TN. In summary, our work establishes SrCo2V2O8 as a beautiful paradigm for spinon confinement in a quasi-1D quantum magnet and provides a comprehensive picture of this process.