Bipartite charge fluctuations (BCFs) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems) and can be measured experimentally. We study the BCFs in generic one-dimensional ${\mathbb{Z}}_2$ (topological) models including the Kitaev superconducting wire model, the Ising chain, or various topological insulators such as the Su-Schrieffer-Heeger model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCFs probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a subdominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the $XYZ$ model.

Two-dimensional (spin-2) Affleck-Kennedy-Lieb-Tasaki (AKLT) type valence bond solids on a square lattice are known to be symmetry-protected topological (SPT) gapped spin liquids [S. Takayoshi, P. Pujol, and A. Tanaka Phys. Rev. B 94, 235159 (2016)]. Using the projected entangled pair state framework, we extend the construction of the AKLT state to the case of $\text{SU}\left(3\right)$, relevant for cold atom systems. The entanglement spectrum is shown to be described by an alternating $\text{SU}\left(3\right)$ chain of “quarks” and “antiquarks”, subject to exponentially decaying (with distance) Heisenberg interactions, in close similarity with its $\text{SU}\left(2\right)$ analog. We discuss the SPT feature of the state.

We determine the antisymmetric current-current response for a pair of (type-I) tilted Weyl cones with opposite chirality. We find that the dynamical chiral magnetic effect depends on the magnitude of the tilt and on the angle between the tilting direction and the wave vector of the magnetic field. Additionally, the chiral magnetic effect is shown to be closely related to the presence of an intrinsic anomalous Hall effect with a current perpendicular to the tilting direction and the electric field. We investigate the nonanalytic long-wavelength limit of the corresponding transport coefficients.

We employ a weak measurement approach to demonstrate the very existence of the photoexcited interband superposition states in intrinsic graphene. We propose an optical two-beam setup where such measurements are possible and derive an explicit formula for the differential optical absorption that contains a signature of such states. We provide an interpretation of our results in terms of a non-Markovian weak measurement formalism applied to the pseudospin degree of freedom coupled with an electromagnetic wave.

We report an angle-resolved photoemission spectroscopy (ARPES) study of ${\mathrm{Li}}_x{\mathrm{CoO}}_2$ single crystals which have a hole-doped ${\mathrm{CoO}}_2$ triangular lattice. Similar to ${\mathrm{Na}}_x{\mathrm{CoO}}_2$, the Co $3d{a}_{1g}$ band crosses the Fermi level with strongly renormalized band dispersion while the Co $3d{e}_g^{\prime }$ bands are fully occupied in ${\mathrm{Li}}_x{\mathrm{CoO}}_2$ ($x=0.46$ and 0.71). At $x=0.46$, the Fermi surface area is consistent with the bulk hole concentration indicating that the ARPES result represents the bulk electronic structure. On the other hand, at $x=0.71$, the Fermi surface area is larger than the expectation which can be associated with the inhomogeneous distribution of Li reported in the previous scanning tunneling microscopy study by Iwaya et al. [Phys. Rev. Lett. 111, 126104 (2013)]. However, the Co $3d$ peak is systematically shifted towards the Fermi level with hole doping excluding phase separation between hole rich and hole poor regions in the bulk. Therefore, the deviation of the Fermi surface area at $x=0.71$ can be attributed to hole redistribution at the surface avoiding polar catastrophe. The bulk Fermi surface of Co $3d{a}_{1g}$ is very robust around $x=0.5$ even in the topmost ${\mathrm{CoO}}_2$ layer due to the absence of the polar catastrophe.

In this work, we investigate the nature of the fractional quantum Hall state in the 1/3-filled second Landau level (SLL) at filling factor $\nu =7/3$ (and 8/3 in the presence of the particle-hole symmetry) via exact diagonalization in both torus and spherical geometries. Specifically, we compute the overlap between the exact 7/3 ground state and various competing states including (i) the Laughlin state, (ii) the fermionic Haffnian state, (iii) the antisymmetrized product state of two composite fermion seas at 1/6 filling, and (iv) the particle-hole (PH) conjugate of the $Z_4$ parafermion state. All these trial states are constructed according to a guiding principle called the bilayer mapping approach, where a trial state is obtained as the antisymmetrized projection of a bilayer quantum Hall state with interlayer distance $d$ as a variational parameter. Under the proper understanding of the ground-state degeneracy in the torus geometry, the $Z_4$ parafermion state can be obtained as the antisymmetrized projection of the Halperin (330) state. Specifically, while unclear at other momentum sectors, all degenerate copies of the $Z_4$ parafermion state can be obtained by antisymmetrizing those of the Halperin (330) state at the zero-momentum sector, where both states occur as the exact ground states of their respective model Hamiltonians with the same degeneracy. Meanwhile, in the spherical geometry, the $Z_4$ parafermion state is shown to be entirely equivalent to the antisymmetrized Halperin (330) state without any ground-state degeneracy issue. Similarly, it is proved in this work that the fermionic Haffnian state can be obtained as the antisymmetrized projection of the Halperin (551) state. The exact 7/3 ground state is obtained as a function of $\delta V_1^{\left(1\right)}$, the variation of the first-moment Haldane pseudopotential $V_1^{\left(1\right)}$ in the SLL with respect to the pure Coulomb interaction. It is shown that, while extremely accurate at sufficiently large positive $\delta V_1^{\left(1\right)}$, the Laughlin state loses its overlap with the exact 7/3 ground state significantly at $\delta V_1^{\left(1\right)}\simeq 0$. At slightly negative $\delta V_1^{\left(1\right)}$, it is shown that the PH-conjugated $Z_4$ parafermion state has a substantial overlap with the exact 7/3 ground state, which is the highest among the above four trial states. Around the Coulomb point, the energy spectrum exhibits an intriguing change from the spectrum with the Laughlin-type magnetoroton structure to that with the specific quasidegeneracy of the ground state, which is characteristic to the PH-conjugated $Z_4$ parafermion state.

We report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at $1/3$ and $2/3$. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for fully spin polarized composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.

The energy spectrum and eigenstates of single-layer black phosphorus nanoribbons in the presence of a perpendicular magnetic field and an in-plane transverse electric field are investigated by means of a tight-binding method, and the effect of different types of edges is examined analytically. A description based on a continuum model is proposed using an expansion of the tight-binding model in the long-wavelength limit. The wave functions corresponding to the flatband part of the spectrum are obtained analytically and are shown to agree well with the numerical results from the tight-binding method for both narrow (10 nm) and wide (100 nm) nanoribbons. Analytical expressions for the critical magnetic field at which Landau levels are formed and the ranges of wave numbers in the dispersionless flatband segments in the energy spectra are derived. We examine the evolution of the Landau levels when an in-plane lateral electric field is applied, and we determine analytically how the edge states shift with magnetic field. For wider nanoribbons, the conductance is shown to have a characteristic staircase shape in combined magnetic and electric fields. Some of the stairs in zigzag and skewed armchair nanoribbons originate from edge states that are found in the band gap.

We investigate the amorphous ${\mathrm{Ge}}_x{\mathrm{S}}_{100-x}$ (with $10\le x\le 40)$ system from ab initio simulations. Results show a very good agreement with experimental findings from diffraction and the topology of the obtained structural models is further analyzed and compared with the selenide analog. Differences emerge, however, from a detailed molecular dynamics analysis showing that the ring statistics and the homopolar defects do not evolve similarly. The findings are also connected to rigidity theory, which provides a topological approach to decoding the physics of network glasses, and the effects of composition and temperature are analyzed.

We focus on a recently experimentally realized scenario of normal-metal–insulator–superconductor tunnel junctions coupled to a superconducting resonator. We develop a first-principles theory to describe the effect of photon-assisted electron tunneling on the quantum state of the resonator. Our results are in very good quantitative agreement with the previous experiments on refrigeration and heating of the resonator using the photon-assisted tunneling, thus providing a stringent verification of the developed theory. Importantly, our results provide simple analytical estimates of the voltage-tunable coupling strength and temperature of the thermal reservoir formed by the photon-assisted tunneling. Consequently, they are used to introduce optimization principles for initialization of quantum devices using such a quantum-circuit refrigerator. Thanks to the first-principles nature of our approach, extension of the theory to the full spectrum of quantum electric devices seems plausible.

We report on the slow magnetization dynamics observed upon the magnetic phase transitions of ${\mathrm{GaV}}_4{\mathrm{S}}_8$, a multiferroic compound featuring a long-ranged cycloidal magnetic order and a Néel-type skyrmion lattice in a relatively broad temperature range below its Curie temperature. The fundamental difference between ${\mathrm{GaV}}_4{\mathrm{S}}_8$ and the chiral helimagnets, the prototypical skyrmion host compounds, lies within the polar symmetry of ${\mathrm{GaV}}_4{\mathrm{S}}_8$, promoting a cycloidal instead of a helical magnetic order and rendering the magnetic phase diagram essentially different from that in the cubic helimagnets. Our ac magnetic susceptibility study reveals slow relaxation dynamics at the field-driven phase transitions between the cycloidal, skyrmion lattice and field-polarized states. At each phase boundary, the characteristic relaxation times were found to exhibit a strong temperature dependence, starting from the minute range at low temperatures, decreasing to the micro- to millisecond range at higher temperatures.

First-principles calculations are performed on magnetic multidomain structures in the $\mathrm{SmFe}{\mathrm{O}}_3$ rare-earth orthoferrite compound. We focus on the magnetic symmetry breaking at (001)-oriented antiphase domain walls, treating magnetism in the simplest (collinear) approximation without any relativistic (spin-orbit coupling) effects. We found that the number of $\mathrm{Fe}{\mathrm{O}}_2$ layers inside the domains determines the electrical nature of the whole system: multidomains with odd number of layers are paraelectric, while multidomains with even number of layers possess an electric polarization aligned along $b$ axis and a resulting multiferroic $Pmc{2}_1$ ground state. Our ab initio data and model for ferroelectricity induced by spin order reveal that this polarization is of the improper type and originates from an exchange striction mechanism that drives a polar displacement of the oxygen ions located at the magnetic domain walls. Additional calculations ratify that this effect is general among magnetic perovskites with an orthorhombic $\mathrm{SmFe}{\mathrm{O}}_3\text{−}\mathrm{like}$ structure.

Several recent experiments in atomic, molecular, and optical systems motivated a huge interest in the study of quantum long-range systems. Our goal in this paper is to present a general description of their critical behavior and phases, devising a treatment valid in $d$ dimensions, with an exponent $d+\sigma$ for the power-law decay of the couplings in the presence of an $\text{O}\left(N\right)$ symmetry. By introducing a convenient ansatz for the effective action, we determine the phase diagram for the $N$-component quantum rotor model with long-range interactions, with $N=1$ corresponding to the Ising model. The phase diagram in the $\sigma \text{−}d$ plane shows a nontrivial dependence on $\sigma$. As a consequence of the fact that the model is quantum, the correlation functions are anisotropic in the spatial and time coordinates for $\sigma$ smaller than a critical value, and in this region the isotropy is not restored even at criticality. Results for the correlation length exponent $\nu$, the dynamical critical exponent $z$, and a comparison with numerical findings for them are presented.

Through a direct comparison of specific heat and magnetoresistance, we critically asses the nature of superconducting fluctuations in the same nanogram crystal of SmFeAs(O,F). We show that although the superconducting fluctuation contribution to conductivity scales well within the two-dimensional lowest Landau level (2D-LLL) scheme, its predictions contrast with the inherently 3D nature of SmFeAs(O,F) in the vicinity of $T_c$. Furthermore, the transition seen in specific heat cannot be satisfactory described either by the LLL or the $XY$ scaling. Additionally we have validated, through comparing $H_{c2}$ values obtained from the entropy conservation construction ($H_{c2//ab}=-19.5\mathrm{T}/\mathrm{K}$ and $H_{c2//c}=-2.9\mathrm{T}/\mathrm{K})$, the analysis of fluctuation contribution to conductivity as a reasonable method for estimating the $H{}_{c2}$ slope.

We present resistivity and magnetization measurements on proton-irradiated crystals demonstrating that the superconducting state in the doped topological insulator ${\mathrm{Nb}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ ($x=0.25$) is surprisingly robust against disorder-induced electron scattering. The superconducting transition temperature $T_c$ decreases without indication of saturation with increasing defect concentration, and the corresponding scattering rates far surpass expectations based on conventional theory. The low-temperature variation of the London penetration depth $\mathrm{\Delta }\lambda \left(T\right)$ follows a power law $[\mathrm{\Delta }\lambda \left(T\right)\sim T^2]$ indicating the presence of symmetry-protected point nodes. Our results are consistent with the proposed robust nematic $E_u$ pairing state in this material.

Various nonlinear optical (NLO) responses, like shift current and second harmonic generation (SHG), are revealed to be closely related to topological quantities involving the Berry connection and Berry curvature. First-principles prediction of NLO responses is of great importance to fundamental research and device design, but efficient computational methods are still lacking. The main challenge is that the calculations require a very dense $k$-point sampling that is computationally expensive and a proper treatment of the gauge problem for topological quantities. Here we present a Wannier interpolation method for first-principles calculation of NLO responses, which overcomes the challenge. This method interpolates physical quantities accurately for any desired $k$ point with little computational cost and constructs a smooth gauge by the perturbation theory. To demonstrate the method, we study shift current of monolayer GeS and ${\mathrm{WS}}_2$ as well as SHG of bulk GaAs, getting good agreements with previous results. We show that the traditional sum rule method converges slowly with the number of bands, whereas the perturbation way does not. Moreover, our method is easily adapted to build tight-binding models for the following theoretical investigations. Last but not least, the method is compatible with most first-principles approaches, including density functional theory and beyond. With these advantages, Wannier interpolation is a promising method for first-principles studies of NLO phenomena.