We consider lattice Hamiltonians that arise from putting Haldane pseudopotentials into a second quantized or “guiding-center-only” form. These are fascinating examples of frustration-free lattice Hamiltonians. This is so since, even though their highest density zero energy ground states, the Laughlin states, are known to have matrix-product structure (with unbounded bond dimension), the frustration-free character of these lattice Hamiltonians seems obscure, unless one goes back to the original first quantized picture of analytic lowest Landau level wave functions. This step involves putting back additional degrees of freedom associated with dynamical momenta, and one wonders whether the addition of these degrees of freedom is truly necessary to recognize the frustration-free character of the underlying lattice Hamiltonian. Fundamentally, these degrees of freedom have nothing to do with spectrum of a “guiding-center-only” Hamiltonian. Moreover, such constructions are unfamiliar and not available in the study of simpler (finite range) frustration-free lattice Hamiltonians with matrix-product ground states (of finite bond dimension). That the zero mode properties of “lattice versions” of pseudopotentials can be understood from a polynomial-free, intrinsically lattice point of view is also suggested by the fact that these pseudopotentials are constructed from an algebra of reasonably simply looking operators. Here we show that zero mode properties, and hence the frustration-free character, of these lattice Hamitlonians can be understood as a consequence of algebraic structures that these operators are part of. We believe that our results will deepen insights into parent Hamiltonians of matrix-product states with infinite bond dimensions, as could be of use, especially, in the study of fractional Chern insulators.

Monolayer transition-metal dichalcogenides have recently become a playground for spintronics and valleytronics research. Their low-energy spectrum can be described by Dirac cones on the corners of Brillouin zone, but the physical properties are richer than those of graphene since the spin degeneracy is lifted and the optical selection rules are valley dependent. This has been exploited for the optical injection of spin- and valley-polarized currents by the application of static electric fields. In this paper we consider an all-optical method for the injection of charge-, spin-, and valley-polarized currents. The presence of both a fundamental optical field and its second harmonic can lead to the injection of currents due to a nonlinear effect involving the quantum interference between one- and two-photon absorption processes. We analyze how the injected quantities can be controlled through the parameters of the incident light fields, allowing capabilities of control beyond those achieved with static fields, and discuss the conditions for experimental verification of our results.

We study tunneling of quasiparticles through potential barriers in a graphene monolayer with the mass gap using a semiclassical (WKB) approach. The main equations are derived in a way similar to the WKB theory for the Schrödinger equation, which allows for explicit solutions at all orders. The analog of the classical action is used to distinguish types of possible stationary states in the system. The analysis focuses on the resonant scattering and the hole states localized in the vicinity of a barrier that are often overlooked. The scattering coefficients for the physically interesting limits are obtained by matching the WKB approximation with the known solutions at turning points. The localized states demonstrate unconventional properties and lead to alterations of the single particle density of states.

We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a ${120}^{\circ }$ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.

The ludwigite ${\text{Co}}_5\text{Sn}({\mathrm{O}}_2{\text{BO}}_3{)}_2$ was studied using x-ray diffraction, Mössbauer spectroscopy, and magnetic and thermodynamic measurements. This material belongs to a family of oxyborates which presents low-dimensional subunits in the form of three-leg ladders in its structure. The subunits confer to these materials a strong anisotropy in their exchange interactions that provide to the ludwigites several interesting magnetic properties, from partial ordering to spin-glass states. Despite being doped by nonmagnetic ions, ${\text{Co}}_5\text{Sn}({\mathrm{O}}_2{\text{BO}}_3{)}_2$ has long-range magnetic order below 82 K which is, surprisingly, the highest critical temperature found so far in the ludwigites. This record can be explained by the absence of double-exchange interactions, usually present in the ludwigites and that gives rise to strong competition. In this paper we study the magnetic and structural properties of ${\text{Co}}_5\text{Sn}({\mathrm{O}}_2{\text{BO}}_3{)}_2$ and compare our results with those obtained in other cobalt ludwigites.

Quasiperiodic lattices have recently been shown to be a nontrivial topological phase of matter. Charge pumping—one of the hallmarks of topological states of matter—was recently realized for photons in a one-dimensional off-diagonal Harper model implemented in a photonic waveguide array. However, if the relationship between topological pumps and quasiperiodic systems is generic, one might wonder how to observe it in the canonical and most studied quasicrystalline system in one dimension—the Fibonacci chain. This chain is expected to facilitate a similar phenomenon, yet its discrete nature hinders the experimental study of such topological effects. Here, we overcome this obstacle by utilizing the topological equivalence of a family of quasiperiodic models which ranges from the Fibonacci chain to the Harper model. Implemented in photonic waveguide arrays, we observe the topological properties of this family, and perform a topological pumping of photons across a Fibonacci chain.

Motivated by recent experiments, we consider a generic spin model in the $j_{\mathrm{eff}}=1/2$ basis for the hyperhoneycomb and harmonic-honeycomb iridates. Based on microscopic considerations, the effect of an additional bond-dependent anisotropic spin exchange interaction $\left(\Gamma \right)$ beyond the Heisenberg-Kitaev model is investigated. We obtain the magnetic phase diagrams of the hyperhoneycomb and harmonic-honeycomb $\left(\mathcal{H}\text{−}1\right)$ lattices via a combination of the Luttinger-Tisza approximation, $\text{single}-\mathbf{Q}$ variational ansatz, and classical Monte Carlo simulated annealing. The resulting phase diagrams on both systems show the existence of incommensurate, noncoplanar spiral magnetic orders as well as other commensurate magnetic orders. The spiral orders show counterpropagating spiral patterns, which may be favorably compared to recent experimental results on both iridates. The parameter regimes of various magnetic orders and ordering wave vectors are quite similar in both systems. We discuss the implications of our work for recent experiments and also compare our results to those of the two-dimensional honeycomb iridate systems.

We study fermions and hard-core bosons with long-range dipolar interactions at fractional fillings in a topological checkerboard lattice with short-range hoppings up to next-next-nearest neighbors [T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011)]. We consider the case that the dipoles are aligned in the perpendicular direction by an external field without the complication of anisotropic interaction. Using exact diagonalization, we find clear signatures of fractional quantum Hall (FQH) states at filling factors 1/3 and 1/5 for fermions (1/2 and 1/4 for bosons) in the lowest Chern band with a robust spectrum gap at moderate dipolar interaction strength. The robustness of these FQH states against a long-range interaction tail and band flatness is investigated. When the dipolar interaction decreases, the fermionic FQH states turn into normal states, and the bosonic 1/4 FQH state turns into a superfluid state. The bosonic 1/2 FQH state survives even in the absence of the dipolar interaction, but vanishes when the hard core becomes a soft core with a critical on-site repulsion. In the thin torus limit, the static density structure factors indicate that the FQH state turns into a commensurate charge density wave state.

We present a first-principles theory of dynamical spin excitations in the presence of spin-orbit coupling. The broken global spin rotational invariance leads to a new sum rule. We explore the competition between the magnetic anisotropy energy and the external magnetic field, as well as the role of electron-hole excitations, through calculations for $3d$-metal adatoms on the Cu(111) surface. The spin excitation resonance energy and lifetime display nontrivial behavior, establishing the strong impact of relativistic effects. We legitimate the use of the Landau-Lifshitz-Gilbert equation down to the atomic limit, but with parameters that differ from a stationary theory.

We consider a device which allows one to create and probe single Majorana fermions, in the form of Bogoliubov quasiparticles. It is composed of two counterpropagating edge channels, each put in proximity with a superconducting region where Andreev reflection operates, and which thus converts electrons into Bogoliubov quasiparticles. The edge channels then meet at a quantum point contact where collisions can be achieved. A voltage-biased version of the setup was studied [C. W. J. Beenakker, Phys. Rev. Lett. 112, 070604 (2014)] and showed nonlocal interference phenomena and signatures of Bogoliubov quasiparticle collisions in the high-frequency noise characteristics at the output, constituting an evidence of the Majorana fermion nature of these excitations. Here, voltage-biased leads are replaced by single-electron sources in order to achieve collisions of single Bogoliubov quasiparticles, with the major advantage that zero-frequency noise measurements are sufficient to access the intimate nature of Bogoliubov wave packets. We compute the injection parameters of the source, and go on to investigate the Hanbury-Brown and Twiss and Hong-Ou-Mandel signal at the output, as a function of the mixing angle which controls the electron/hole component of the Bogoliubov wave packet. In particular, information on the internal structure of the Bogoliubov quasiparticle can be recovered when such a quasiparticle collides with a pure electron. Experimental feasibility with singlet or triplet superconductors is discussed.

We revisit the dynamic spin susceptibility $\chi (q,\omega )$ of one-dimensional interacting fermions. To second order in the interaction, backscattering results in a logarithmic correction to $\chi (q,\omega )$ at $q\ll k_F$, even if the single-particle spectrum is linearized near the Fermi points. Consequently, the dynamic spin structure factor $\mathrm{Im}\chi (q,\omega )$ is nonzero at frequencies above the single-particle continuum. In the boson language, this effect results from the marginally irrelevant backscattering operator of the sine-Gordon model. Away from the threshold, the high-frequency tail of $\mathrm{Im}\chi (q,\omega )$ due to backscattering is larger than that due to finite mass by a factor of $k_F/q$. We derive the renormalization group equations for the coupling constants of the $g-\text{ology}$ model at finite $\omega$ and $q$ and find the corresponding expression for $\chi (q,\omega )$, valid to all orders in the interaction but not in the immediate vicinity of the continuum boundary, where the finite-mass effects become dominant.

The lattice dynamics and electronic transitions of $0.93\mathrm{P}\text{b}({\mathrm{Zn}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_3\text{−}0.07\mathrm{PbTiO}{}_3$ (PZN-7%PT) single crystal have been investigated by means of temperature dependence polarized Raman scattering and ellipsometric spectra. The rhombohedral-tetragonal and tetragonal-cubic transformations as well as intermediate temperature are extracted based on the locations, intensity, and linewidths of Raman modes in different geometries. Moreover, the redshift behavior of the electronic transition at about 3.7 eV as a function of temperature follows the Bose-Einstein law. Interestingly, the dramatically different optical responses of PZN-7%PT below 3.7 eV during the phase transitions can be observed experimentally and explained by the first-principles calculations, which reveal the potential application of no-contact optical methods in judging the phase transformations and symmetries of ferroelectric crystals.

We use an atomistic model to consider the effect of shape symmetry breaking on the optical properties of self-assembled InAs/GaAs quantum dots. In particular, we investigate the energy level structure and optical activity of the lowest energy excitons in these nanostructures. We compare between quantum dots with twofold rotational and two reflections $\left(C_{2v}\right)$ symmetry and quantum dots in which this symmetry was reduced to one reflection only $\left(C_s\right)$ by introducing a facet between the quantum dots and the host material. We show that the symmetry reduction mostly affects the optical activity of the dark exciton. While in symmetric quantum dots, one of the dark exciton eigenstates has a small dipole moment polarized along the symmetry axis (growth direction) of the quantum dot, in nonsymmetric ones, the two dark excitons' dipole moments are predominantly cross-linearly polarized perpendicular to the growth direction and reveal pronounced polarization anisotropy. Our model calculations agree quantitatively with recently obtained experimental data.

We report on observation of ferroelastic domain structure in single crystals of multiferroic ${\text{CaMn}}_7{\text{O}}_{12}$ at room temperature. Two types of ferroelastic domain wall are found, consistent with the material's rhombohedral symmetry that is reduced from cubic symmetry at higher temperatures. Using Raman spectroscopy along with other measurements, we develop a systematic method to determine the microscopic domain orientation. Moreover, we find a switching behavior of the domains, which allows us to detwin the crystals conveniently at room temperature using a moderate uniaxial compression. Our result paves the way for further spectroscopic study and domain engineering in ${\text{CaMn}}_7{\text{O}}_{12}$.

Bosons interacting repulsively on a lattice with a flat lowest band energy dispersion may, at sufficiently small filling factors, enter into a Wigner-crystal-like phase. This phase is a consequence of the dispersionless nature of the system, which in turn implies the occurrence of single-particle localized eigenstates. We investigate one of these systems—the sawtooth lattice—filled with strongly repulsive bosons at filling factors infinitesimally above the critical point where the crystal phase is no longer the ground state. We find, in the hard-core limit, that the crystal retains its structure in all but one of its cells, where it is broken. The broken cell corresponds to an exotic kind of repulsively bound state, which becomes delocalized. We investigate the excitation spectrum of the system analytically and find that the bound state behaves as a single particle hopping on an effective lattice with reduced periodicity, and is therefore gapless. Thus, the addition of a single particle to a flat-band system at critical filling is found to be enough to make kinetic behavior manifest.

Regular lattices comprising superconducting quantum interference devices (SQUIDs) form magnetic metamaterials exhibiting extraordinary properties, including tunability, dynamic multistability, and negative magnetic permeability. The SQUIDs in a metamaterial interact through nonlocal, magnetic dipole-dipole forces that makes it possible for counterintuitive dynamic states referred to as chimera states to appear; the latter feature clusters of SQUIDs with synchronous dynamics which coexist with clusters exhibiting asynchronous behavior. The spontaneous appearance of chimera states is demonstrated numerically for one-dimensional SQUID metamaterials driven by an alternating magnetic field in which the fluxes threading the SQUID rings are randomly initialized; then, chimera states appear generically for sufficiently strong initial excitations, which exhibit relatively long lifetimes. The synchronization and metastability levels of the chimera states are discussed in terms of appropriate measures. Given that both one- and two-dimensional SQUID metamaterials have been already fabricated and investigated in the laboratory, the presence of a chimera state could in principle be detected with presently available experimental setups.

We analyze the superfluid crossover of harmonically confined bosons with long-range interaction in both two and three dimensions in a broad parameter range from weak to strong coupling. We observe that the onset of superfluidity occurs in three dimensions at significantly lower temperatures compared to that in two dimensions. This is demonstrated to be a quantum degeneracy effect. In addition, the spatial distribution of superfluidity across the shells of the clusters is investigated. It is found that superfluidity is substantially reduced in the outer layers due to increased correlation effects.

A synchrotron x-ray diffraction study of metal-insulator transitions in W-doped ${\text{VO}}_2 \left({\text{V}}_{1-x}{\text{W}}_x{\text{O}}_2\right)$ thin films has been carried out. The insulating phase for $x\le 0.07$ exhibits cell-doubling with the V dimerization similar to bulk ${\text{VO}}_2$, while the insulating phase for $x\ge 0.11$ does not. This result suggests that the electronic structure of the $x\ge 0.11$ insulators should be different from that of the $x\le 0.07$ ones and bulk-insulating phase of ${\text{VO}}_2$. The temperature and $x$ dependence of superlattice reflection as observed casts doubt about the direct relationship between the dimerization of V ions and metal-insulator transition. The temperature dependence of the electrical resistivity rather implies the Mott-Anderson localization nature of the insulating phases. X-ray-induced persistent phase transitions are observed at low temperatures in each insulating phase in the vicinity of the boundary to the metallic phase regardless of the difference in the electronic structure. Gradual peak shift suggests that the x-ray irradiation produces nanometer metallic regions.