We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) and the non-Hermitian Chern insulators. In addition, we find that at a critical point in the PT symmetric SSH model, the entanglement entropy has a logarithmic scaling with corresponding central charge $c=-2$. This critical point then is a free-fermion lattice realization of the non-unitary conformal field theory.

We study the frustrated J1-J2 Heisenberg model with ferromagnetic nearest neighbor coupling J1<0 and antiferromagnetic next-nearest neighbor coupling J2>0 at and close to the z=4 quantum critical point (QCP) at J1/J2=-4. The J1-J2 model plays an important role for recently synthesized chain cuprates as well as in supersymmetric Yang Mills theories. We study the thermodynamic properties using field theory, a modified spin-wave theory as well as numerical density-matrix renormalization group calculations. Furthermore, we compare with results for the classical model obtained by analytical methods and Monte-Carlo simulations. As one of our main results we present numerical evidence that the susceptibility at the QCP seems to diverge with temperature T as chi ~ T^{-1.2} in the quantum case in contrast to the classical model where chi ~ T^{-4/3}.

We present an extensive analytical and numerical study of the antiferromagnetic Heisenberg model on the Cairo pentagonal lattice, the dual of the Shastry-Sutherland lattice with a close realization in the S=5/2 compound Bi2Fe4O9. We consider a model with two exchange couplings suggested by the symmetry of the lattice, and investigate the nature of the ground state as a function of their ratio x and the spin S. After establishing the classical phase diagram we switch on quantum mechanics in a gradual way that highlights the different role of quantum fluctuations on the two inequivalent sites of the lattice. The most important findings for S=1/2 include: (i) a surprising interplay between a collinear and a four-sublattice orthogonal phase due to an underlying order-by-disorder mechanism at small x (related to an emergent J1-J2 effective model with J2 >> J1), and (ii) a non-magnetic and possibly spin-nematic phase with d-wave symmetry at intermediate x.

We report ultrahigh magnetic field Faraday rotation results on the chiral helimagnet Cu2OSeO3, the first Mott insulator showing skyrmion lattice phases and a linear magnetoelectric effect. Between 180 and 300 T, we find signatures of a Bose-Einstein condensation (BEC) of magnons, which can be described as a canted XY ferrimagnet. Due to the magnetoelectric coupling, the transverse magnetic order of the indivual Cu2+ spins is accompanied by a characteristic dome-like electric polarization which is crucial for the observation of the condensate via the Faraday rotation effect.

The term altermagnetism has recently been introduced to describe the N\'eel order of a class of materials whose magnetic sublattices are neither related by translation nor inversion. While these materials arguably have large technological potential, little effort has been devoted to studying the universal distinction of this phase of matter compared to collinear antiferromagnetism. Employing a recently proposed minimal microscopic model, we explicitly derive a nonlinear sigma model describing long-wavelength fluctuations of the staggered magnetization in this system, including quantum effects to leading order. The term that distinguishes the altermagnetic nonlinear sigma model from its antiferromagnetic counterpart is an interaction term that derives directly from the Berry phase of the microscopic spin degrees of freedom. Its effects on the one-loop renormalization group flow in $d=2+\epsilon$ dimensions are examined. Extending the theory to describe the fermionic excitations of the metallic altermagnet, we find an effective low-energy model of $d$-wave spin-split Dirac fermions interacting with the magnetic fluctuations. Using a Dyson-Schwinger approach, we derive the many-body effects on the dynamical critical scaling due to the competition between the long-range Coulomb interaction and the fluctuations of the staggered magnetization.

A DFT-based investigation of rhombohedral (ABC)-type graphene stacks in finite static electric fields is presented. Electronic band structures and field-induced charge densities are compared with related literature data as well as with own results on (AB) stacks. It is found, that the undoped AB-bilayer has a tiny Fermi line consisting of one electron pocket around the K-point and one hole pocket on the line K-$\Gamma$. In contrast to (AB) stacks, the breaking of translational symmetry by the surface of finite (ABC) stacks produces a gap in the bulk-like states for slabs up to a yet unknown critical thickness $N^{\rm semimet} \gg 10$, while ideal (ABC) bulk ($\beta$-graphite) is a semi-metal. Unlike in (AB) stacks, the ground state of (ABC) stacks is shown to be topologically non-trivial in the absence of external electric field. Consequently, surface states crossing the Fermi level must unavoidably exist in the case of (ABC)-type stacking, which is not the case in (AB)-type stacks. These surface states in conjunction with the mentioned gap in the bulk-like states have two major implications. First, electronic transport parallel to the slab is confined to a surface region up to the critical layer number $N^{\rm semimet}$. Related implications are expected for stacking domain walls and grain boundaries. Second, the electronic properties of (ABC) stacks are highly tunable by an external electric field. In particular, the dielectric response is found to be strongly nonlinear and can e.g. be used to discriminate slabs with different layer numbers. Thus, (ABC) stacks rather than (AB) stacks with more than two layers should be of potential interest for applications relying on the tunability by an electric field.

While altermagnetic materials are characterized by a vanishing net magnetic moment, their symmetry in principle allows for the existence of an anomalous Hall effect (AHE). Here we introduce a model with altermagnetism in which the emergence of an AHE is driven by interactions. This model is grounded in a modified Kane-Mele framework with antiferromagnetic (AFM) spin-spin correlations. Quantum Monte Carlo simulations show that the system undergoes a finite temperature phase transition governed by a primary AFM order parameter accompanied by a secondary one of Haldane type. The emergence of both orders turns the metallic state of the system, away from half-filling, to an altermagnet with a finite anomalous Hall conductivity. A mean field ansatz corroborates these results, which pave the way into the study of correlation induced altermagnets with finite Berry curvature.

Altermagnets are fully compensated collinear antiferromagnets that lack the combined time-reversal and translation symmetry. Here we show that their symmetry allows for a switchable ferro-spinetic polarization - the spin analogue of ferroelectricity - in a direction dictated by the lattice symmetry. We demonstrate this effect first in its purest form in an interacting altermagnetic fermion model, in which a many-body chiral symmetry forbids any charge polarization. Our quantum Monte Carlo simulations reveal edge-localized, reversible spin accumulations fully consistent with this symmetry locking. Breaking the chiral symmetry releases the charge sector: a ferroelectric polarization emerges orthogonal to the ferro-spinetic one, yielding mutually perpendicular switchable spin- and charge-polarized responses. We identify Mn-based metal-organic frameworks as realistic hosts for this effect, offering a practical route for experimental verification.

Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this study, we formulate a set of models of Dirac fermions in 2+1 dimensions with SU($N$)$\times$SU(2)$\times$U(1) symmetry that have the potential to host critical points described by field theories with topological terms. For $N=2$ it shows a rich phase diagram containing semimetallic, quantum spin Hall insulating, Kekulé valence bond solid and s-wave superconducting phases and features multiple Landau-Ginzburg-Wilson phase transitions driven by interaction strength. At $N=1$ a deconfined quantum critical point is observed. At $N=2$ one expects the critical theory to correspond to a level 2 Wess-Zumino-Witten theory in 2+1 dimensions. Here the numerical results however show a strong first order transition. Another transition can be governed by a topological $\theta$-term which is rendered irrelevant for even values of $N$ thus leading to Landau-Ginzburg-Wilson behaviour.

The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion method extends well beyond this constraint: It remains valid across the entire complex plane and is thus suitable for arbitrary non-Hermitian matrices. We identify that numerical rounding errors are the primary source of errors encountered when applying the method outside the conventional spectral bounds, and they are not caused by fundamental limitations. By carefully selecting the spectral radius and the time step, we show how these errors can be effectively suppressed, enabling accurate time evolution calculations in non-Hermitian systems. We derive an analytic upper bound for the rounding error, which serves as a practical guideline for selecting time steps in numerical simulations. As an application, we illustrate the performance of the method by computing the time evolution of wave packets in the Hatano-Nelson model.

In quantum optics and condensed matter physics non-Hermitian phenomena are often studied under the assumption of an open physical system. However, there are examples of intrinsically non-Hermitian, though often $\mathcal{PT}$ (parity-time) symmetric, not necessarily open systems, in which case the concept of gain and loss relative to an underlying environment is not primordial. A particularly intriguing example with experimental consequences in the literature is QCD at finite density. Motivated by the existence of such inherently non-Hermitian systems, here we study the critical behavior of a $U(1)$-invariant Lagrangian perturbed by a complex, $\mathcal{PT}$ symmetric $Z_{4}$ anisotropy. We find real critical exponents both in the region of unbroken and broken $\mathcal{PT}$ symmetry. In the former the coupling constants for fixed points or lines are real, whereas in the latter they become complex. Importantly, the most stable fixed point corresponds to the flow at large distances towards an effectively Hermitian $U(1)$ symmetric system. This constitutes an example where both the $U(1)$ and the Hermitian character are emergent features of the theory. This tells us about the importance and physical meaning of some non-Hermitian systems beyond interpretations involving gain and loss.

The two-dimensional electron gas (2DEG) at oxide interfaces exhibits various exotic properties stemming from interfacial inversion symmetry breaking. In this work, we report the emergence of large nonlinear Hall effects (NHE) in the LaAlO3/KTaO3(111) interface 2DEG under zero magnetic field. Skew scattering was identified as the dominant origin based on the cubic scaling of nonlinear Hall conductivity with longitudinal conductivity and the threefold symmetry. Moreover, a gate-tunable NHE with pronounced peak and dip was observed and reproduced by our theoretical calculation. These results indicate the presence of Berry curvature hotspots and thus a large Berry curvature triple at the oxide interface. Our theoretical calculations confirm the existence of large Berry curvatures from the avoided crossing of multiple 5d-orbit bands, orders of magnitude larger than that in transition-metal dichalcogenides. NHE offers a new pathway to probe the Berry curvature at oxide interfaces, and facilitates new applications in oxide nonlinear electronics.

Energy-loss magnetic chiral dichroism (EMCD) allows for the quantification of magnetic properties of materials at the nanometer scale. It is shown that with the support of simulations that help to identify the optimal conditions for a successful experiment and upon implementing measurement routines that effectively reduce the noise floor, EMCD measurements can be pushed towards quantitative magnetic measurements even on individual nanoparticles. With this approach, the ratio of orbital to spin magnetic moments for the Fe atoms in a single L$1_0$ ordered FePt nanoparticle is determined to be ${m_l}/{m_s} = 0.08 \pm 0.02$. This finding is in good quantitative agreement with the results of XMCD ensemble measurements.

Topoelectrical circuits are meta-material realizations of topological features of condensed matter systems. In this work, we discuss experimental methods that allow a fast and straightforward detection of the spectral features of these systems from the two-point impedance of the circuit. This allows to deduce the full spectrum of a topoelectrical circuit consisting of N sites from a single two-point measurement of the frequency resolved impedance. In contrast, the standard methods rely on $N^2$ measurements of admittance matrix elements with a subsequent diagonalization on a computer. We experimentally test our approach by constructing a Fibonacci topoelectrical circuit. Although the spectrum of this chain is fractal, i.e., more complex than the spectra of periodic systems, our approach is successful in recovering its eigenvalues. Our work promotes the topoelectrical circuits as an ideal platform to measure spectral properties of various (quasi)crystalline systems.

Topology and anomalies lead to edge modes that can interact with critical bulk fluctuations. To study this setup, pertaining to boundary criticality, we consider a model exhibiting a deconfined quantum critical point (DQCP) between a dynamically generated quantum spin Hall state (i.e.a topological Mott insulator) and an s-wave superconductor. For the topological Mott insulator, the bulk Goldstone modes are shown to be irrelevant at the helical Luttinger liquid fixed points. The deconfined quantum critical point is an instance of an emergent anomaly, and we observe a sharp localized edge state at this point. The sharpness of the edge mode is consistent with an ordinary phase in which electronic edge modes decouple from critical edge bosonic fluctuations. At the DQCP, the scaling dimension of the edge electron shows a jump, a feature argued to be a signature of the emergent anomaly. Our results are based on large-scale auxiliary-field quantum Monte Carlo this http URL also carry out calculations for the Kane-Mele-Hubbard model to confirm spectral features of the ordinary and extraordinary-log phases in the vicinity of the bulk critical point.

In frustrated magnetic systems with a subextensive number of classical ground states, quantum zero-point fluctuations can select a unique long-range ordered state, a celebrated phenomenon referred to as \emph{order by quantum disorder} (ObQD). For frustrated spin-$\frac{1}{2}$ systems, unbiased numerical methods able to expose ObQD are necessary. We show that ObQD can be identified from exact diagonalization (ED) calculations through an analysis akin to the Anderson tower of states associated with spontaneous symmetry breaking. By defining an effective quantum rotor model, we describe the competition between ObQD-induced localization of the rotor and its tunneling between symmetry-related ground states, identifying the crossover lengthscale from the finite-size regime where the rotor is delocalized, to the infinite system-size limit where it becomes localized. This rotor model relates the characteristic splittings in the ED energy spectrum to the ObQD selection energy scale, providing an estimate that can be compared to spin wave calculations. We demonstrate the general applicability of this approach in one-, two- and three-dimensional frustrated spin models that exhibit ObQD.

Transition metal dichalcogenides are a family of quasi-two-dimensional materials that display a high technological potential due to their wide range of electronic ground states, e.g., from superconducting to semiconducting, depending on the chemical composition, crystal structure, or electrostatic doping. Here, we unveil that by tuning a single parameter, the hydrostatic pressure P, a cascade of electronic phase transitions can be induced in the few-layer transition metal dichalcogenide 1T'-WS2, including superconducting, topological, and anomalous Hall effect phases. Specifically, as P increases, we observe a dual phase transition: the suppression of superconductivity with the concomitant emergence of an anomalous Hall effect at P=1.15 GPa. Remarkably, upon further increasing the pressure above 1.6 GPa, we uncover a reentrant superconducting state that emerges out of a state still exhibiting an anomalous Hall effect. This superconducting state shows a marked increase in superconducting anisotropy with respect to the phase observed at ambient pressure, suggesting a different superconducting state with a distinct pairing symmetry. Via first-principles calculations, we demonstrate that the system concomitantly transitions into a strong topological phase with markedly different band orbital characters and Fermi surfaces contributing to the superconductivity. These findings position 1T'-WS2 as a unique, tunable superconductor, wherein superconductivity, anomalous transport, and band features can be tuned through the application of moderate pressures.

We present a detailed investigation of the XXZ Heisenberg model for spin-$1/2$ and spin-$1$ systems on square and honeycomb lattices. Utilizing the density-matrix renormalization group (DMRG) method, complemented by Spiral Boundary Conditions (SBC) for mapping two-dimensional (2D) clusters onto one-dimensional (1D) chains, we meticulously explore the evolution of staggered magnetization and spin gaps across a broad spectrum of easy-axis anisotropies. Our study reveals that, despite the lower site coordination number of honeycomb lattice, which intuitively suggests increased quantum fluctuations in its N\'eel phase compared to the square lattice, the staggered magnetization in the honeycomb structure exhibits only a marginal reduction. Furthermore, our analysis demonstrates that the dependence of staggered magnetization on the XXZ anisotropy $\Delta$, except in close proximity to $\Delta=1$, aligns with series expansion predictions up to the 12th order. Notably, for the $S=1/2$ honeycomb lattice, deviations from the 10th order series expansion predictions near the isotropic Heisenberg limit emphasize the critical influence of quantum fluctuations on the spin excitation in its N\'eel state. Additionally, our findings are numerically consistent with the singular behavior of the spin gap near the isotropic Heisenberg limit as forecasted by spin-wave theory. The successful implementation of SBC marks a methodological advancement, streamlining the computational complexity involved in analyzing 2D models and paving the way for more precise determinations of physical properties in complex lattice systems.

An essential step toward elucidating the mechanism of superconductivity is to determine the sign/phase of superconducting order parameter, as it is closely related to the pairing interaction. In conventional superconductors, the electron-phonon interaction induces attraction between electrons near the Fermi energy and results in a sign-preserved s-wave pairing. For high-temperature superconductors, including cuprates and iron-based superconductors, prevalent weak coupling theories suggest that the electron pairing is mediated by spin fluctuations which lead to repulsive interactions, and therefore that a sign-reversed pairing with an s+-or d-wave symmetry is favored. Here, by using magnetic neutron scattering, a phase sensitive probe of superconducting gap, we report the observation of a transition from the sign-reversed to sign-preserved Cooper-pairing symmetry with insignificant changes in Tc in the S-doped iron selenide superconductors KxFe2-y(Se1-zSz)2. We show that a rather sharp magnetic resonant mode well below the superconducting gap (2delta) in the undoped sample (z = 0) is replaced by a broad hump structure above 2delta under 50% S doping. These results cannot be readily explained by simple spin fluctuation-exchange pairing theories and, therefore, multiple pairing channels are required to describe superconductivity in this system. Our findings may also yield a simple explanation for the sometimes contradictory data on the sign of the superconducting order parameter in iron-based materials.