We study the phase transitions of three-dimensional (3D) classical $O\left(3\right)$ model and two-dimensional (2D) classical XY model, as well as both the quantum phase transitions of 2D and 3D dimerized spin-1/2 antiferromagnets, using the technique of supervised neural network (NN). Moreover, unlike the conventional approaches commonly used in the literature, the training sets employed in our investigation are neither the theoretical nor the real configurations of the considered systems. Remarkably, with such an unconventional set up of the training stage in conjunction with some semiexperimental finite-size scaling formulas, the associated critical points determined by the NN method agree well with the established results in the literature. The outcomes obtained here imply that certain unconventional training strategies, like the one used in this study, are not only cost-effective in computation but are also applicable for a wide range of physical systems.

Symmetry-protected topological phases (SPTs) have universal degeneracies in the entanglement spectrum in one dimension. Here we formulate this phenomenon in the framework of symmetry-resolved entanglement (SRE) using cohomology theory. We develop a general approach to compute entanglement measures of SPTs in any dimension and specifically SRE via a discrete path integral on multisheet Riemann surfaces with generalized defects. The resulting path integral is expressed in terms of group cocycles describing the topological actions of SPTs. Their cohomology classification allows us to identify universal entanglement properties. Specifically, we demonstrate an equiblock decomposition of the reduced density matrix into symmetry sectors, for all one-dimensional topological phases protected by finite Abelian unitary symmetries.

Multiple-band nature of electronic energy bands leads to novel physical effects in solids. In this paper, we clarify physical properties of a Fermi system with a pair of electron and hole Fermi surfaces (FSs), whose coupling is mediated by a critical U(1) boson field. By using a one-loop renormalization group analysis, we show that when the boson field undergoes a quantum phase transition with broken U(1) symmetry, the multiple-band Fermi system shows a non-Fermi liquid (non-FL) behavior in its thermodynamic and magnetic properties. At a quantum critical point (QCP), Fermi velocities of the two FSs are renormalized into the same critical velocity as a boson velocity, and the fermion's density of states (DOS) shows a pseudogap behavior with a logarithmic energy dependence at the QCP.

We present a derivation of the exact expression for Pulay forces in density-functional theory calculations augmented with extended Hubbard functionals and arising from the use of orthogonalized atomic orbitals as projectors for the Hubbard manifold. The derivative of the inverse square root of the orbital overlap matrix is obtained as a closed-form solution of the associated Lyapunov (Sylvester) equation. The expression for the resulting contribution to the forces is presented in the framework of ultrasoft pseudopotentials and the projector-augmented-wave method and using a plane-wave basis set. We have benchmarked the present implementation with respect to finite differences of total energies for the case of NiO, finding excellent agreement. Owing to the accuracy of Hubbard-corrected density-functional theory calculations—provided the Hubbard parameters are computed for the manifold under consideration—the present work paves the way for systematic studies of solid-state and molecular transition-metal and rare-earth compounds.

We report $\beta \text{−}\mathrm{NMR}$ measurements in ${\mathrm{Bi}}_2{\mathrm{Se}}_3:\mathrm{Ca}$ and ${\mathrm{Bi}}_2{\mathrm{Te}}_3:\mathrm{Mn}$ single crystals using ${}^8\mathrm{Li}^{+}$ implanted to depths on the order of 100 nm. Above $\sim 200\mathrm{K}$, spin-lattice relaxation reveals diffusion of ${}^8\mathrm{Li}^{+}$, with activation energies of $\sim 0.4\mathrm{eV}$ $(\sim 0.2\mathrm{eV})$ in ${\mathrm{Bi}}_2{\mathrm{Se}}_3:\mathrm{Ca}$ $({\mathrm{Bi}}_2{\mathrm{Te}}_3:\mathrm{Mn})$. At lower temperatures, the NMR properties are those of a heavily doped semiconductor in the metallic limit, with Korringa relaxation and a small, negative, temperature-dependent Knight shift in ${\mathrm{Bi}}_2{\mathrm{Se}}_3:\mathrm{Ca}$. From this, we make a detailed comparison with the isostructural tetradymite ${\mathrm{Bi}}_2{\mathrm{Te}}_2\mathrm{Se}$ [McFadden et al., Phys. Rev. B 99, 125201 (2019)]. In the magnetic ${\mathrm{Bi}}_2{\mathrm{Te}}_3:\mathrm{Mn}$, the effects of the dilute Mn moments predominate, but remarkably the ${}^8\mathrm{Li}^{+}$ signal is not wiped out through the magnetic transition at 13 K, with a prominent critical peak in the spin-lattice relaxation that is suppressed in a high applied field. This detailed characterization of the ${}^8\mathrm{Li}^{+}$ NMR response is an important step toward using depth-resolved $\beta \text{−}\mathrm{NMR}$ to study the low-energy properties of the chiral topological surface state in the ${\mathrm{Bi}}_2{\mathrm{Ch}}_3$ tetradymite topological insulator.

Phonon interactions in solid-state photonics systems cause intrinsic quantum decoherence and often present the limiting factor in emerging quantum technology. Due to recent developments in nanophotonics, exciton-cavity structures with very strong light-matter coupling rates can be fabricated. We show that in such structures, a regime emerges where the decoherence is completely suppressed due to decoupling of the dominant phonon process. Using a numerically exact tensor network approach, we perform calculations in this nonperturbative, non-Markovian dynamical regime. Here, we identify a strategy for reaching near-unity photon indistinguishability and also discover an interesting phonon dressing of the exciton-cavity polaritons in the high-$Q$ regime, leading to multiple phonon sidebands when the light-matter interaction is sufficiently strong.

An astroid-shaped loop of exceptional points (EPs), comprising four cusps, is found to spawn from the triple degeneracy point in the Brillouin zone (BZ) of a Lieb lattice with nearest-neighbor hoppings when non-Hermiticity is introduced. The occurrence of the EP loop is due to the realness of the discriminant which is guaranteed by the non-Hermitian chiral symmetry. The EPs at the four cusps involve the coalescence of three eigenstates, which is the combined result of the non-Hermitian chiral symmetry and mirror-T symmetry. The EP loop is exactly an astroid in the limit of an infinitesimal non-Hermiticity. The EP loop expands from the $M$ point with increasing non-Hermiticity and splits into two EP loops at a critical non-Hermiticity. The further increase of non-Hermiticity contracts the two EP loops towards and finally to two EPs at the $X$ and $Y$ points in the BZ, accompanied by the emergence of Dirac-like cones. The two EPs vanish at a larger non-Hermiticity. The EP loop disappears and several discrete EPs are found to survive when next-nearest hoppings are introduced to break the non-Hermitian chiral symmetry. A topological invariant called the discriminant number is used to characterize their robustness against perturbations. Both discrete EPs and those on the EP loop(s) are found to show anisotropic asymptotic behaviors. Finally, the experimental realization of the Lieb lattice using a coupled waveguide array is discussed.

Critical phase transitions contain a variety of deep and universal physics and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or temporal divergences render the thermodynamic limit ill-defined. In this work, we show that a thermodynamic grand potential can still be defined in pseudo-Hermitian Hamiltonians, and can be used to characterize aspects of criticality unique to non-Hermitian systems. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) model as a paradigmatic example, we demonstrate the fractional order of topological phase transitions in the complex energy plane. These fractional orders add up to the integer order expected of a Hermitian phase transition when the model is doubled and Hermitianized. More spectacularly, gap preserving highly degenerate critical points known as non-Bloch band collapses possess fractional order that are not constrained by conventional scaling relations, testimony to the emergent extra length scale from the skin mode accumulation. Our work showcases that a thermodynamic approach can prove fruitful in revealing unconventional properties of non-Hermitian critical points.

Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection have been analyzed to characterize the topology of these systems. While the topological classification of non-Hermitian systems is being developed, little attention has been paid to the impact of the new geometric phases on dynamics and transport. In this work, we derive the full set of semiclassical equations of motion for wave-packet dynamics in a system governed by a non-Hermitian Hamiltonian, including corrections induced by the Berry connection. We show that non-Hermiticity is manifested in the anomalous weight rate and velocity terms that are present already in one-dimensional systems, in marked distinction from the Hermitian case. We express the anomalous weight and velocity in terms of the Berry connections defined in the space of left and right eigenstates and compare the analytical results with numerical lattice simulations. Our work specifies the conditions for observing the anomalous contributions to the semiclassical dynamics and thereby paves the way to their experimental detection, which should be within immediate reach in currently available metamaterials.

As an emerging complex two-dimensional structure, plane fractal has attracted much attention due to its novel dimension-related physical properties. In this paper, we check the feasibility to create an effective Sierpinski carpet (SC), a plane fractal with Hausdorff dimension intermediate between one and two, by applying an external electric field to a square or a honeycomb lattice. The electric field forms a fractal geometry but the atomic structure of the underlying lattice remains the same. By calculating and comparing various electronic properties, we find parts of the electrons can be confined effectively in a fractional dimension with a relatively small field, and representing properties are very close to these in a real fractal. In particular, compared to the square lattice, the external field required to effectively confine the electron is smaller in the honeycomb lattice, suggesting that a graphene-like system will be an ideal platform to construct an effective SC experimentally. Our work paves a way to build fractals from a top-down perspective and can motivate more studies of fractional dimensions in real systems.

The Berry phase effect plays a central role in many mesoscale condensed matter and quantum chemical systems that are naturally under the environmental influence of dissipation. We propose and microscopically derive a prototypical quantum coherent tunneling model around a monopole or conical potential intersection in order to address the intriguing but overlooked interplay between dissipation and the topologically nontrivial Berry phase effect. We adopt the instanton approach with both symmetry analysis and accurate numerical solutions that consistently incorporate nonperturbative dissipation and the Berry phase. It reveals a unique and interesting dissipative quantum interference phenomenon with the Berry phase effect. The phase diagram of this tunneling exhibits Kramers degeneracy, nonmonotonic dependence on dissipation, and a generic dissipation-driven phase transition of quantum interference, before which an unconventional dissipation-enhanced regime of quantum tunneling persists.

The strain fields of periodically buckled graphene induce a periodic pseudomagnetic field (PMF) that modifies the electronic band structure. From the geometry, amplitude, and period of the periodic pseudomagnetic field, we determine the necessary conditions to access the regime of correlated phases by examining the band flattening. As compared to twisted bilayer graphene the proposed system has the advantages that (1) only a single layer of graphene is needed, (2) one is not limited to hexagonal superlattices, and (3) narrower flat bandwidth and larger separation between flat bands can be induced. We, therefore, propose that periodically strained graphene single layers can become a platform for the exploration of exotic many-body phases.

We performed angular and temperature-dependent electron-spin-resonance measurements in the quasi-two-dimensional organic conductor $\kappa \text{−}{\left(\text{BEDT-TTF}\right)}_2\mathrm{Cu}[\mathrm{N}{\left(\mathrm{CN}\right)}_2]\mathrm{I}$. The interlayer spin diffusion is much weaker compared to the Cl and Br analogs, which are antiferromagnetic insulator and paramagnetic metal, respectively; $\kappa \text{−}{\left(\text{BEDT-TTF}\right)}_2\mathrm{Cu}[\mathrm{N}{\left(\mathrm{CN}\right)}_2]\mathrm{I}$ behaves insulating when cooled below $T=200\mathrm{K}$. A spin gap ($\mathrm{\Delta }\approx 18\mathrm{K}$) opens at low temperatures leading to a spin-singlet state. Due to intrinsic disorder a substantial number of spins ($\sim 1\%$) remains unpaired. We observe additional signals below $T=4\mathrm{K}$ with a pronounced anisotropy indicating the presence of local magnetic moments coupled to some fraction of those unpaired spins.

We use neutron scattering to investigate spin excitations in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$, which has a $c$-axis incommensurate helical structure of the two-dimensional (2D) in-plane ferromagnetic (FM) ordered layers for $0.013\le x\le 0.25$. By comparing the wave vector and energy dependent spin excitations in helical ordered $\mathrm{Sr}{\left({\mathrm{Co}}_{0.9}{\mathrm{Ni}}_{0.1}\right)}_2{\mathrm{As}}_2$ and paramagnetic ${\mathrm{SrCo}}_2{\mathrm{As}}_2$, we find that Ni doping, while increasing lattice disorder in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$, enhances quasi-2D FM spin fluctuations. However, our band structure calculations within the combined density functional theory and dynamic mean field theory ($\mathrm{DFT}+\mathrm{DMFT}$) failed to generate a correct incommensurate wave vector for the observed helical order from nested Fermi surfaces. Since transport measurements reveal increased in-plane and $c$-axis electrical resistivity with increasing Ni doping and associated lattice disorder, we conclude that the helical magnetic order in $\mathrm{Sr}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$ may arise from a quantum order-by-disorder mechanism through the itinerant electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions.

We discuss the implications that new magnetocaloric, thermal expansion, and magnetostriction data in $\alpha \text{−}{\mathrm{RuCl}}_3$ single crystals have on its temperature-field phase diagram and uncover the magnetic-field dependence of an apparent energy gap structure $\mathrm{\Delta }\left(H\right)$ that evolves when the low-temperature antiferromagnetic order is suppressed. We show that, depending on how the thermal expansion data are modeled, $\mathrm{\Delta }\left(H\right)$ can show a cubic field dependence and remain finite at zero field, consistent with the pure Kitaev model hosting itinerant Majorana fermions and localized ${\mathbb{Z}}_2$ fluxes. Our magnetocaloric effect data provide, below $1\mathrm{K}$, unambiguous evidence for dissipative phenomena at $H_{\mathrm{c}}$, a smoking gun for a first-order phase transition. Conversely, our results show little support for a phase transition from a QSL to a polarized paramagnetic state above $H_{\mathrm{c}}$.

We have studied the magneto-optical response of $\mathrm{Co}\left(t_1\right)/\mathrm{Pt}\left(d\right)/\mathrm{Co}\left(t_2\right)$ trilayer structures, in which the total Co thickness $(t_1+t_2)$ was held constant, but the split between the top and bottom layer made variable to investigate the impact of the Co layer thickness asymmetry $a_t=\left(t_1-t_2\right)/\left(t_1+t_2\right)$ as well as the influence of the Pt interlayer thickness $d$. The optical and magneto-optical properties of these films were measured using generalized magneto-optical ellipsometry. A set of specifically designed inverted double-wedge structures were characterized to determine the influence of $d$ and especially of $a_t$, which should be significant if quantum-well states are relevantly modified by the Co layer thickness asymmetry. In addition to a Co/Pt interface proximity effect that leads to an overall enhancement of the magneto-optical response, we do not find the expected quadratic $a_t$ effect, but instead observe a strong linear $a_t$ effect. We also compare our experimental results to a classical optics description based upon the transfer matrix method, but we can achieve agreement in between these calculations and our experimental data only if we assume massively anomalous optical wave attenuation in Pt. This perceived anomalous attenuation of Pt is not observed for Co/Pt/Co trilayer structures with much thicker Co films, in which quantum-well states should not be relevant anymore. Thus, the origin of the unexpected strong linear $a_t$ effect in ultrathin Co/Pt/Co trilayers cannot be a local materials modification, but instead must be associated with the collective nature of quantum-mechanical electronic states in asymmetric trilayers.

We perform extensive auxiliary-field quantum Monte Carlo (AFQMC) calculations for the three-band Hubbard (Emery) model in order to study the ground-state properties of copper-oxygen planes in the cuprates. Employing cutting-edge AFQMC techniques with a self-consistent gauge constraint in auxiliary-field space to control the sign problem, we reach supercells containing $\approx 500$ atoms to capture collective modes in the charge and spin orders and characterize the behavior in the thermodynamic limit. The self-consistency scheme interfacing with generalized Hartree-Fock calculations allows high accuracy in AFQMC to resolve small energy scales, which is crucial for determining the complex candidate orders in such a system. We present detailed information on the charge order, spin order, momentum distribution, and localization properties as a function of charge-transfer energy for the the underdoped regime. In contrast with the stripe and spiral orders under hole doping, we find that the corresponding $1/8$ electron-doped system exhibits purely antiferromagnetic order in the three-band model, consistent with the asymmetry between electron and hole doping in the phase diagram of cuprates.

Rogue waves, first discovered in the ocean, are extraordinarily large amplitude waves which can form in relatively calm environments. Magnetic materials also support waves, but with a completely different set of underlying physics. We demonstrate the possibility of generating magnetic rogue waves by applying an abstract form of time reversal. Magnetic systems have important differences from the other media which admit rogue waves; they are inherently anisotropic and have many tunable parameters such as the magnitude and direction of an applied field. We investigate the role of anisotropy and these tunable parameters in the formation and properties of magnetic rogue waves. Through analytic calculations, we identify the important wave vectors and frequencies, typically ranging from 10 to 25 GHz, of the spin waves involved in the creation of magnetic rogue waves. We then correlate this information with the overall efficiency of the rogue wave generation process.

A detailed understanding of ultrathin film surface properties is crucial for the proper interpretation of spectroscopic, catalytic, and spin-transport data. We present x-ray magnetic circular dichroism (XMCD) and x-ray resonant magnetic reflectivity (XRMR) measurements on ultrathin ${\mathrm{Fe}}_3{\mathrm{O}}_4$ films to obtain magnetic depth profiles for the three resonant energies corresponding to the different cation species ${\mathrm{Fe}}_{\mathrm{oct}}^{2+}$, ${\mathrm{Fe}}_{\mathrm{tet}}^{3+}$, and ${\mathrm{Fe}}_{\mathrm{oct}}^{3+}$ located on octahedral and tetrahedral sites of the inverse spinel structure of ${\mathrm{Fe}}_3{\mathrm{O}}_4$. By analyzing the XMCD spectrum of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ using multiplet calculations, the resonance energy of each cation species can be isolated. Performing XRMR on these three resonant energies yields magnetic depth profiles that each correspond to one specific cation species. The depth profiles of both kinds of ${\mathrm{Fe}}^{3+}$ cations reveal a $\left(3.9\pm 1.0\right)\text{−}\AA$-thick surface layer of enhanced magnetization, which is likely due to an excess of these ions at the expense of the ${\mathrm{Fe}}_{\mathrm{oct}}^{2+}$ species in the surface region. The magnetically enhanced ${\mathrm{Fe}}_{\mathrm{tet}}^{3+}$ layer is additionally shifted about $2.9\pm 0.4\AA$ farther from the surface than the ${\mathrm{Fe}}_{\mathrm{oct}}^{3+}$ layer.