We report an essential improvement of the plain Fourier Monte Carlo algorithm that promises to be a powerful tool for investigating critical behavior in a large class of lattice models, in particular those containing microscopic or effective long-ranged interactions. On tuning the Monte Carlo acceptance rates separately for each wave vector, we are able to drastically reduce critical slowing down. We illustrate the resulting efficiency and unprecedented accuracy of our algorithm with a calculation of the universal elastic properties of crystalline membranes in the flat phase and derive a numerical estimate $\eta =0.795\left(10\right)$ for the critical exponent $\eta$ that challenges those derived from other recent simulations. The large system sizes accessible to our present algorithm also allow us to demonstrate that insufficiently taking into account corrections to scaling may severely hamper a finite size scaling analysis. This observation may also help to clarify the apparent disagreement of published numerical estimates of $\eta$ in the existing literature.

Ground-state and low-energy excitations of the quasi-one-dimensional antiferromagnet CuSe${}_2$O${}_5$ where finite interchain interactions promote long-range antiferromagnetic order below $T_N=17$ K, were experimentally studied using bulk magnetization, neutron diffraction, muon spin relaxation, and antiferromagnetic resonance measurements. The derived spin-canted structure is characterized by the magnetic propagation vector $\mathbf{k}=(1,0,0)$ and the reduced magnetic moment $\mathit{m}=[0.13\left(7\right),0.50\left(1\right),0.00\left(8\right)]{\mu }_B$. The values of the magnetic anisotropies determined from the field and angular dependencies of the antiferromagnetic resonance comply well with a previous electron paramagnetic resonance study and correctly account for the observed magnetic ground state and spin-flop transition.

We investigate the scaling of the bipartite entanglement entropy across Lifshitz quantum phase transitions, where the topology of the Fermi surface changes without any changes in symmetry. We present both numerical and analytical results which show that Lifshitz transitions are characterized by a well-defined set of critical exponents for the entanglement entropy near the phase transition. In one dimension, we show that the entanglement entropy exhibits a length scale that diverges as the system approaches a Lifshitz critical point. In two dimensions, the leading and subleading coefficients of the scaling of entanglement entropy show distinct power-law singularities at critical points. The effect of weak interactions is investigated using the density matrix renormalization group algorithm.

We report a study of a spin-down impurity strongly coupled to a spin-up Fermi sea (a so-called Fermi polaron) with the diagrammatic Monte Carlo (DiagMC) technique. Conditions of zero temperature and three dimensions are considered for an ultracold atomic gas with resonant interactions in the zero-range limit. A Feynman diagrammatic series is developed for the one-body and two-body propagators providing information about the polaron and molecule channel, respectively. The DiagMC technique allows us to reach diagram orders that are high enough for extrapolation to infinite order. The robustness of the extracted results is examined by checking various resummation techniques and by running the simulations with various choices for the propagators and vertex functions. It turns out that dressing the lines in the diagrams as much as possible is not always the optimal choice. We also identify classes of dominant diagrams for the one-body and two-body self-energy in the region of strong interaction. These dominant diagrams turn out to be the leading processes of the strong-coupling limit. The quasiparticle energies and $Z$ factor are obtained as a function of the interaction strength. We find that the DiagMC results for the molecule and polaron properties are very similar to those obtained with a variational ansatz. Surprisingly, this variational ansatz gives very good predictions for the quasiparticle residue even when this residue is significantly less than 1.

We find an exotic spin excitation in a magnetically ordered system with spin orbit magnetism in two dimensions, where the order parameter has a net spin current and no net magnetization. Starting from a Fermi liquid theory, similar to that for a weak ferromagnet, we show that this excitation emerges from an exotic magnetic Fermi liquid state that is protected by a generalized Pomeranchuk condition. We derive the propagating mode using the Landau kinetic equation and find that the dispersion of the mode has a $\sqrt{q}$ behavior in leading order in two dimensions. We find an instability toward superconductivity induced by this exotic mode, and a further analysis based on the forward scattering sum rule strongly suggests that this superconductivity has $p$-wave pairing symmetry. We perform similar studies in the three-dimensional case, with a slightly different magnetic system, and find that the mode leads to a Lifshitz-like instability, most likely toward an inhomogeneous magnetic state in one of the phases.

The electronic orders in Hubbard models on a kagome lattice at van Hove filling are of intense current interest and debate. We study this issue using the singular-mode functional renormalization group theory. We discover a rich variety of electronic instabilities under short-range interactions. With increasing on-site repulsion $U$, the system develops successively ferromagnetism, intra-unit-cell antiferromagnetism, and charge bond order. With nearest-neighbor Coulomb interaction $V$ alone ($U=0$), the system develops intra-unit-cell charge density wave order for small $V$, $s$-wave superconductivity for moderate $V$, and the charge density wave order appears again for even larger $V$. With both $U$ and $V$, we also find spin bond order and chiral $d_{x^2-y^2}+i{d}_{xy}$ superconductivity in some particular regimes of the phase diagram. We find that the $s$-wave superconductivity is a result of charge density wave fluctuations and the squared logarithmic divergence in the pairing susceptibility. On the other hand, the $d$-wave superconductivity follows from bond order fluctuations that avoid the matrix element effect. The phase diagram is vastly different from that in honeycomb lattices because of the geometrical frustration in the kagome lattice.

Intertwining of spin, charge, and pairing correlations in the repulsive two-dimensional Hubbard model is shown through unrestricted variational calculations, with projected wave functions free of symmetry breaking. A crossover from incommensurate antiferromagnetism to stripe order naturally emerges in the hole-doped region when increasing the on-site coupling. Although effective attractive pairing interactions are identified, they are strongly fragmented in several modes including $d$-wave pairing and more exotic channels related to an underlying stripe. We demonstrate that the entanglement of a mean-field wave function by symmetry restoration can largely account for interaction effects, and that our approach is exact for a two-site cluster.

A thin film of a topological insulator (TI) on a dielectric substrate and a bulk TI–dielectric film–bulk TI structure are considered as natural double-well heterostructures suitable for realizing the counterflow superconductivity. The effect is connected with pairing of electrons and holes belonging to different surfaces of TI and the transition of a gas of electron-hole pairs into a superfluid state. The case of TI heterostructures subjected to a strong perpendicular magnetic field is considered. It is shown that such systems are characterized by two critical temperatures—a mean-field temperature of pairing and a much smaller temperature of the superfluid transition. The dependence of the critical temperatures on the magnetic field is computed. The advantages of TI based structures in comparison with GaAs heterostructures as well as graphene based heterostructures are discussed.

The metallic band structure of the hydrogen-adsorbed SrTiO${}_3$(001) surface is studied by polarization-dependent photoemission spectroscopy measurements. With the dipole-transition selection arguments, we attributed the metallic peaks into the Ti 3$d_{xz}$, 3$d_{yz}$, and 3$d_{xy}$ bands. These $t_{2g}$ bands are partially filled with electrons upon H-induced downward band bending at the surface. Energy splitting of the Ti 3$d$ $t_{2g}$ bands is considered to be induced by a quantum confinement along the surface normal ($z$) direction. The metallic peaks are accompanied by the incoherent states induced by many-body interactions, which likely indicates that the electronic system forms a two-dimensional liquid phase. Also emerged by H exposure are an in-gap state and a $\sigma \left(\mathrm{O}-\mathrm{H}\right)$ state. The possible origin and the feature of these states are discussed from the polarization dependence of the photoemission intensity.

We study the nonlinear dynamics of exciton-polaritons in semiconductor microcavities operating in the strong-coupling regime and driven by a coherent optical pump above the exciton resonance. Provided that the exciton dispersion is accounted for, parametric mixing of polaritons from the upper and the lower polariton branches gives rise to modulational instability of the homogeneous solution. This instability leads to the formation of quasiperiodic patterns. Our analytical analysis shows that there are domains in parameter space where these patterns and stable homogeneous solution may exist simultaneously. This is the prerequisite for the existence of cavity polariton solitons—single-peak solutions on a homogeneous background. Because they originate from parametric mixing of polaritons from both branches of the dispersion relation we term them hybrid parametric cavity solitons. There are two kinds of these resting solitons—stationary and breathing ones. Both types require for stability that the cavity resonance be redshifted to the exciton resonance.

Magnetic states of the electron gas confined in modulation-doped core-shell nanowires are calculated for a transverse field of arbitrary strength and orientation. Magnetoconductance is predicted within the Landauer approach. The modeling takes fully into account the radial material modulation, the prismatic symmetry, and the doping profile of realistic GaAs/AlGaAs devices within an envelope-function approach, and electron-electron interaction is included in a mean-field self-consistent approach. Calculations show that in the low free-carrier density regime, magnetic states can be described in terms of Landau levels and edge states, similar to planar two-dimensional electron gases in a Hall bar. However, at higher carrier density, the dominating electron-electron interaction leads to a strongly inhomogeneous localization at the prismatic heterointerface. This gives rise to a complex band dispersion, with local minima at finite values of the longitudinal wave vector, and a region of negative magnetoresistance. The predicted marked anisotropy of the magnetoconductance with field direction is a direct probe of the inhomogeneous electron gas localization of the conductive channel induced by the prismatic geometry.

State-filling dynamics in self-assembled InAs/GaAs quantum dots (QDs) is studied through their steady-state photoluminescence (PL) using a variant of picosecond excitation-correlation (EC) spectroscopy. Steady-state PL showed an interesting transition from bimolecular recombination at low-excitation fluence to excitonic recombination at higher fluence. As for the EC signal, while the ground-state response is always snubbed when the two excitation pulses are temporally nearly coincident, the excited-state response can either be enhanced or reduced, depending on the excitation fluence. The time evolution of this response is studied for the first three levels in a QD ensemble. A minimal theoretical model, which combines carrier loss kinetics with the principle of detailed balance and the Pauli exclusion principle, quantitatively reproduces the observations.

Orbital magnetism is studied for graphene flakes with various shapes and edge configurations using the tight-binding approximation. In the low-temperature regime where the thermal energy is much smaller than the energy-level spacing, the susceptibility rapidly changes between diamagnetism and paramagnetism as a function of Fermi energy, in accordance with the energy-level structure. The susceptibility at the charge neutral point is generally larger in armchair flake than in zigzag flake, and larger in hexagonal flake than in triangular flake. As the temperature increases, the discrete structures due to the quantum confinement are all gone, and the susceptibility approximates the bulk limit independently of the atomic configuration. The diamagnetic current circulates entirely on the graphene flake at zero temperature, while in increasing temperature it is localized near the edge with the characteristic depth proportional to $1/T$. We predict that the diamagnetism of graphene can be observed using the alignment of graphene flakes in a feasible range of magnetic field.

Random hyperfine fields are essential to mechanisms of low-field magnetoresistance in organic semiconductors. Recent experiments have shown that another type of random field—fringe fields due to a nearby ferromagnet—can also dramatically affect the magnetoresistance. A theoretical analysis of the effect of these fringe fields is challenging, as the fringe field magnitudes and their correlation lengths are orders of magnitude larger than that of the hyperfine couplings. We extend a recent theory of organic magnetoresistance to calculate the magnetoresistance with both hyperfine and fringe fields present. This theory describes several key features of the experimental fringe-field magnetoresistance, including the applied fields where the magnetoresistance reaches extrema, the applied field range of large magnetoresistance effects from the fringe fields, and the sign of the effect.

We report a striking in-plane anisotropy of the spin-flip Raman signals observed for dilute magnetic Cd${}_{1-x}$Mn${}_x$Te quantum wells containing a two-dimensional electron gas. The effect depends upon electron concentration, which can be varied within a single sample via secondary above-barrier illumination. The experimental results are described in a simple, single-electron picture by a model of the conduction band Hamiltonian that includes contributions from Dresselhaus, Rashba, and Zeeman terms.

We present a rotationally invariant Hirsch-Fye quantum Monte Carlo algorithm in which the spin rotational invariance of Hund's exchange is approximated by averaging over all possible directions of the spin quantization axis. We employ this technique to perform benchmark calculations for the two- and three-band Hubbard models on the infinite-dimensional Bethe lattice. Our results agree quantitatively well with those obtained using the continuous-time quantum Monte Carlo method with rotationally invariant Coulomb interaction. The proposed approach is employed to compute the electronic and magnetic properties of paramagnetic $\alpha$ iron and nickel. The obtained Curie temperatures agree well with experiment. Our results indicate that the magnetic transition temperature is significantly overestimated by using the density-density type of Coulomb interaction.

Real-space renormalization-group techniques for quantum systems can be divided into two basic categories: those capable of representing correlations following a simple boundary (or area) law, and those which are not. I discuss the scaling of the accuracy of gapped systems in the latter case and analyze the resultant spatial anisotropy. It is apparent that particular points in the system, that are somehow “central” in the renormalization, have local quantities that are much closer to the exact results in the thermodynamic limit than the system-wide average. Numerical results from the tree-tensor network and tensor renormalization-group approaches for the two-dimensional transverse-field Ising model and three-dimensional classical Ising model, respectively, clearly demonstrate this effect.

We study the effect of electron-electron interaction on the charge and spin structures at the edge of integer quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems indicates that the low-energy excitations of the $\nu =1$ ferromagnetic state are bosonic edge spin waves. Instabilities of the ferromagnetic state with altering confinement strength result from the softening of these edge spin waves and formation of edge spin textures. In the $\nu \lesssim 2$ regime, exact diagonalization on edge electron systems indicates that compact Hartree-Fock states with different total spin always become ground states in some regions of parameter space, and the ground states appearing between two compact states are their edge spin waves. The initial $\nu =2$ instability is toward the compact state with total spin 1. Larger systems are studied using a microscopic trial wave function, and some quantitative predictions on the edge instabilities for a certain type of confining potential are reached in the thermodynamic limit.

The effect of on-site electron-electron repulsion $U$ in a band insulator is explored for a bilayer Hubbard Hamiltonian with opposite sign hopping in the two sheets. The ground-state phase diagram is determined at half-filling in the plane of $U$ and the interplanar hybridization $V$ through a computation of the antiferromagnetic (AF) structure factor, local moments, single-particle and spin wave spectra, and spin correlations. Unlike the case of the ionic Hubbard model, no evidence is found for a metallic phase intervening between the Mott and band insulators. Instead, upon increase of $U$ at large $V$, the behavior of the local moments and of single-particle spectra give quantitative evidence of a crossover to a Mott insulator state preceding the onset of magnetic order. Our conclusions generalize those of single-site dynamical mean-field theory, and show that including interlayer correlations results in an increase of the single-particle gap with $U$.

High-order optical phonon modes in wurtzite ZnO and MgZnO nanocrystals were investigated using resonant Raman spectroscopy. The Raman modes in ZnO showed agreement with a harmonic model, consistent with prior work. MgZnO, in contrast, exhibited a large degree of anharmonic behavior. The strength of the anharmonicity increases upon application of hydrostatic pressure. These results suggest a harmonic-to-anharmonic phase transition, which could be related to the anisotropy ($c$/$a$ ratio) of the crystal structure.