We present a new strategy for contracting tensor networks in arbitrary geometries. This method is designed to follow as strictly as possible the renormalization group philosophy, by first contracting tensors in an exact way and, then, performing a controlled truncation of the resulting tensor. We benchmark this approximation procedure in two dimensions against an exact contraction. We then apply the same idea to a three-dimensional quantum system. The underlying rational for emphasizing the exact coarse graining renormalization group step prior to truncation is related to monogamy of entanglement.

By means of time-dependent density-matrix renormalization-group calculations, we study topological quantum pumping in a strongly interacting system. The system under consideration is described by the Hamiltonian of a one-dimensional extended Bose-Hubbard model in the presence of a correlated hopping which breaks lattice inversion symmetry. This model has been predicted to support topological pumping [E. Berg, M. Levin, and E. Altman, Phys. Rev. Lett. 106, 110405 (2011)]. The pumped charge is quantized and of a topological nature. We provide a detailed analysis of the finite-size scaling behavior of the pumped charge and its deviations from the quantized value. Furthermore, we also analyze the nonadiabatic corrections due to the finite frequency of the modulation. We consider two configurations: a closed ring where the time dependence of the parameter induces a circulating current and a finite open-ended chain where particles are dragged from one edge to the opposite edge, due to the pumping mechanism induced by the bulk.

Effective field theories that describe the dynamics of a conserved U(1) current in terms of “hydrodynamic” degrees of freedom of topological phases in condensed matter are discussed in general dimension $D=d+1$ using the functional bosonization technique. For noninteracting topological insulators (superconductors) with a conserved U(1) charge and characterized by an integer topological invariant [more specifically, they are topological insulators in the complex symmetry classes (class A and AIII), and in the “primary series” of topological insulators, in the eight real symmetry classes], we derive the BF-type topological field theories supplemented with the Chern-Simons (when $D$ is odd) or the $\theta$ (when $D$ is even) terms. For topological insulators characterized by a ${\mathbb{Z}}_2$ topological invariant (the first and second descendants of the primary series), their topological field theories are obtained by dimensional reduction. Building on this effective field theory description for noninteracting topological phases, we also discuss, following the spirit of the parton construction of the fractional quantum Hall effect by Block and Wen, the putative “fractional” topological insulators and their possible effective field theories, and use them to determine the physical properties of these nontrivial quantum phases.

Far-infrared (FIR) cyclotron resonance of a high-mobility two-dimensional electron gas (2DEG) in a GaAs/(Al,Ga)As single heterojunction is detected by resonant modulation of the photoluminescence. This optically detected cyclotron resonance (ODCR) of the 2DEG occurs in two photoluminescence (PL) bands originating from spatially separated sample regions: The exciton emission from the wide GaAs buffer layer is enhanced, while the photoluminescence of the 2D electrons with itinerant holes is suppressed when the 2D electrons resonantly absorb FIR radiation. The ODCR mechanism is attributed to the interaction of excitons with ballistically propagating acoustic phonons (phonon wind) emitted upon energy relaxation of 2D electrons heated by FIR. The interaction results in an effective long-range 2DEG-exciton repulsion that hinders dissociation of free excitons in the 2DEG vicinity. We show that the FIR ODCR lineshape is well described in the frame of the Drude model accounting for FIR reflection from the 2DEG. The significant difference between this FIR-induced ODCR and previously studied microwave-induced ODCR is discussed.

In this experimental study of single InGaAs/GaAs quantum dots (QDs) the photoluminescence intensity of the second order LO-phonon replica of the excitonic interband recombination was measured along with the intensities of the first and zeroth orders. The results show that the intensity of the second-order replica is three to four times stronger than expected from the adiabatic Huang-Rhys theory, indicating that the neglected nonadiabaticity plays an important role for the understanding of the exciton-phonon coupling in QDs.

We report on measurement of the electron-hole effective $g$-factors ($g_{\mathrm{eff}}^{*}$) depending on electron filling factors $\nu$ from magnetophotoluminescence spectroscopy at low magnetic fields $B<1$ T in low electron density regime in a GaAs/Al${}_{0.33}$Ga${}_{0.67}$As-gated quantum well. Enhancement of $g_{\mathrm{eff}}^{*}$ at odd $\nu$ is observed. The oscillatory behavior of $g_{\mathrm{eff}}^{*}$ is compared with results of a theory that takes into account the lowest-order exchange interaction of the screened Coulomb interaction. Good agreement of the observed $g_{\mathrm{eff}}^{*}$ with theoretical results is obtained except $\nu$ at around 3. The enhancement of $g_{\mathrm{eff}}^{*}$ at even $\nu$ with decrease in electron density has not been observed.

Dirac electrons in two-dimensional continuum space subject to $\delta$-function impurities, which have inherent ultraviolet divergence, fail to be gauge-invariant if regularized by the standard momentum (Brillouin-zone) cutoff. A regularization scheme which respects gauge invariance is proposed here based on the cutoff in the impurity-potential range. The relation to a lattice model, which has no ultraviolet divergence, is also discussed.

Au(001) surfaces that have been prepatterned into a rippled morphology develop one-dimensional nanodot arrays (nanobeads) selectively along the ripples when bombarded with energetic ions at an angle that is normal to the average surface orientation. By quantifying the shape and morphology of these arrays, we show experimentally and by numerical simulations of an extended Kuramoto-Sivashinsky equation that the degree of one-dimensional order of the nanobeads can be optimized by considering initial rippled surfaces with various wavelength and roughness values. Our simulations employ physical units and use the experimental topographies as initial conditions. Such nonideal shapes are key to elucidating the influence of nonlinear effects (like conformal interface motion and local redeposition) since the early stages of the dynamics for these prepatterned systems. In spite of the fact that the evolution of the surface morphology becomes far from trivial under these circumstances, our continuum model is able to reproduce the experimental results quantitatively, in contrast to relevant alternative models in the context of surface nanopatterning by ion-beam bombardment.

First-principles calculations based on the density functional theory supplemented with an empirical van der Waals interaction are used to explore the effect of Ag-atom intercalation on the electronic structure of graphene on Ni(111) surface. We first confirm that in the most stable configuration graphene is chemisorbed on Ni(111) with binding distance in good agreement with experiments. We also clarify the conflicting interplay of symmetry breaking of the graphene sublattice and hybridization of graphene π orbitals with Ni $d$ states in the bandgap opening of graphene. Upon intercalation of Ag atoms in the interface of graphene/Ni(111), the characteristic energy bands of graphene recover with or without a bandgap depending on Ag coverage. The bandgap is largest for fractional Ag coverage of ∼1.3 monolayer (ML) and is appreciable for fractional Ag coverage. These bandgap openings are consistent with the recent experiments [Varykhalov, Scholz, Kim, and Rader, Phys. Rev. B 82, 121101(R) (2010)], which, however, have been claimed to be the results for 1 ML Ag coverage. Our calculations also demonstrate that an appreciable bandgap does not open when intercalated Ag atoms of high concentration form a flat layer, which mimics the situation of graphene/Ag(111). These results imply that the actual Ag coverage achieved in the experiments was different from 1 ML. A key role may be assigned to such a fractional Ag coverage, for which graphene–Ag distances are intermediate between those of chemisorption and physisorption, and a bandgap is induced by rather strong interactions with Ag atoms. The Ni(111) substrate plays only a role of supporting such a sparse Ag-atom distribution. Similar arguments also apply to the recent experiments on graphene/Au/Ru(0001) [Enderlein, Kim, Bostwick, Rotenberg, and Horn, New J. Phys. 12, 033014 (2010)] in which a substantial bandgap also opened in graphene for the claimed 1 ML Au coverage.

Dynamical spin structure factors of quantum spin nematic states are calculated in a spin-$\frac{1}{2}$ square-lattice $J_1$-$J_2$ model with ferromagnetic $J_1$ and competing antiferromagnetic $J_2$ interactions. To this end, we use a fermion representation, generalizing it to $N$ flavors. We begin with a spin-triplet pairing state of fermion fields, called $Z_2$ planar state, which is a stable saddle-point solution in the large-$N$ limit in a finite parameter range where the couplings $J_1$ and $J_2$ compete strongly [R. Shindou and T. Momoi, Phys. Rev. B 80, 064410 (2009)]. Using a large-$N$ expansion, we take into account fluctuations around this saddle point up to corrections of order $1/N$. The dynamical spin structure factors thus obtained signify the existence of gapless $q$-linear director-wave (spin-wave) modes at $\mathit{q}=(0,0)$ and gapped “gauge-field”-like collective modes at $\mathit{q}=(\pi ,\pi )$, whose spectral weight vanishes as a linear and quadratic function of the momentum, respectively. The low-energy collective modes contain fluctuations of nematic-director, spin, and gauge degrees of freedom. Associated with the gapless $q$-linear modes, we evaluate the temperature dependence of the nuclear spin relaxation rate $1/T_1$ in the low-temperature regime as $1/T_1\propto T^{2d-1}$, where $d$ is the effective spatial dimension.

We study electronic transport in junctions consisting of a superconductor electrode and two ferromagnet (F) leads in which crossed Andreev reflections (CAR) and elastic cotunnelings are accommodated. We model the system using an extended Blonder-Tinkham-Klapwijk treatment with a key modification that accounts for spin-dependent interfacial barriers (SDIB). We compute current-voltage relations as a function of parameters characterizing the SDIB, magnetization in the F leads, geometry of the junction, and temperature. Our results reveal a rich range of significantly altered physics due to a combination of interfering spin-dependent scattering processes and population imbalance in the ferromagnets, such as a significant enhancement in CAR current and a sign change in the relative difference between resistance of two cases having a antiparallel or parallel alignment of the magnetization in the F leads, respectively. Our model accounts for the surprising experimental findings of positive relative resistance by M. Colci et al. [Phys. Rev. B 85, 180512(R) (2012)] as well as previously measured negative relative resistance results, both within sufficiently large parameter regions.

Single crystals of (Ca${}_{1-x}$La${}_x$)${}_{10}$(Pt${}_3$As${}_8$)(Fe${}_2$As${}_2$)${}_5$ ($x=0$–0.182) superconductors have been grown and characterized by x-ray, microprobe, transport, and thermodynamic measurements. Features in the magnetic susceptibility, specific heat, and two kinks in the derivative of the electrical resistivity around 100 K in the $x=0$ compound support the existence of decoupled structural and magnetic phase transitions. With La doping, the structural/magnetic phase transitions are suppressed and a half dome of superconductivity with a maximal $T_c$ around 26 K is observed in the temperature-concentration phase diagram.

Isolated kinks on thermally fluctuating $1/2\langle 111\rangle$ screw, $\langle 100\rangle$ edge, and $1/2\langle 111\rangle$ edge dislocations in bcc iron are simulated under zero stress conditions using molecular dynamics (MD). Kinks are seen to perform stochastic motion in a potential landscape that depends on the dislocation character and geometry, and their motion provides fresh insight into the coupling of dislocations to a heat bath. The kink formation energy, migration barrier, and friction parameter are deduced from the simulations. A discrete Frenkel-Kontorova-Langevin model is able to reproduce the coarse-grained data from MD at $\sim$${10}^{-7}$ of the computational cost, without assuming an a priori temperature dependence beyond the fluctuation-dissipation theorem. Analytical results reveal that discreteness effects play an essential role in thermally activated dislocation glide, revealing the existence of a crucial intermediate length scale between molecular and dislocation dynamics. The model is used to investigate dislocation motion under the vanishingly small stress levels found in the evolution of dislocation microstructures in irradiated materials.

Neutron-scattering studies of (Bi${}_{1/2}$Na${}_{1/2}$)TiO${}_3$ (BNT) have been performed to elucidate the microscopic mechanism of the broad maximum in the temperature dependence of the dielectric constant at $T_{\mathrm{m}}\sim 600$ K and the reduction in the piezoelectric properties above the depolarization temperature, $460\sim 480$ K. We observed diffuse scattering near the $\Gamma$ point below 700 K, which competes with the superlattice peak at the $M$ point of the tetragonal phase but coexists with the superlattice peak at the $R$ point of the rhombohedral phase. The diffuse scattering shows an anisotropic $Q$ shape extending along the $\langle 100\rangle$ direction transverse to the scattering vector $Q$, which is explained by atomic shifts bridging the tetragonal and rhombohedral structures. We propose that the broad maximum in the dielectric constant is associated with a diffusive first-order transition between the competing tetragonal and rhombohedral phases. In addition, we found that the diffuse scattering is reduced for single crystals grown under high oxygen pressure, which suggests an analogy with the central peak in hydrogen-reduced SrTiO${}_3$. Inelastic neutron scattering near the $\Gamma$ point reveals a heavily overdamped soft mode similar to those reported in lead-based relaxors, the “waterfall” feature. Moreover, a damped soft transverse acoustic mode is observed for the $\langle 100\rangle$ direction as the anisotropic diffuse scattering, indicating phase instabilities with the same origin as that of the diffuse scattering. The recovery of the soft mode is observed near the depolarization temperature, which coincides with the disappearance of the superlattice peak at the $M$ point. These results indicate that the depolarization and the waterfall feature originate in the dynamic nature of ferroelectric clusters in the coexisting tetragonal/rhombohedral phase.

The spin structure and spin dynamics in the extended kagome frustrated antiferromagnet YBaCo${}_4$O${}_7$ have been investigated using zero field and low applied field ${}^{59}$Co NMR. The YBaCo${}_4$O${}_7$ lattice is made up of bipyramid Co-ion units that form alternating planes of edge-sharing spin triangles and corner-sharing kagome spin triangles in an unusual exchange topology. Our low-temperature spin configuration results, based on hyperfine field orientations, are consistent with those from neutron scattering for the triangle spins which order antiferromagnetically below 106 K. For the kagome spins at low temperatures the static hyperfine fields are found to be oriented orthogonal to those of the triangle spins in a spin-flop configuration that is in disagreement with the neutron findings. Nuclear relaxation rate measurements made as a function of temperature show that inhomogeneous dynamic spin disorder occurs in kagome planes well below the Néel point.

The global phase diagram of a doped Kitaev-Heisenberg model is studied using an $SU\left(2\right)$ slave-boson mean-field method. Near the Kitaev limit, $p$-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You et al. [Phys. Rev. B 86, 085145 (2012)] irrespective of the sign of the Kitaev interaction. By further doping, a $d$-wave superconducting state appears when the Kitaev interaction is antiferromagnetic, while another $p$-wave superconducting state appears when the Kitaev interaction is ferromagnetic. This $p$-wave superconducting state does not break the time-reversal symmetry as reported by Hyart et al. [Phys. Rev. B 85, 140510 (2012)], and such a superconducting state also appears when the antiferromagnetic Kitaev interaction and the ferromagnetic Heisenberg interaction compete. This work, thus, demonstrates the clear difference between the antiferromagnetic Kitaev model and the ferromagnetic Kitaev model when carriers are doped while these models are equivalent in the undoped limit, and how novel superconducting states emerge when the Kitaev interaction and the Heisenberg interaction compete.

LiVO${}_2$ is a model system of a valence bond solid (VBS) in a $3d^2$ triangular lattice. The origin of VBS formation has remained controversial. We investigate the microscopic mechanism by elucidating the $d$ orbital character via on-site ${}^{51}$V NMR measurements in a single crystal up to 550 K across a structural transition temperature $T_c$. The Knight shift, $K$, and nuclear quadrupole frequency, $\delta \nu$, show that the $3d$ orbitals with local trigonal symmetry are reconstructed into a $d_{yz}{d}_{zx}$ orbital order below $T_c$. Together with the NMR spectra with threefold rotational symmetry, we confirm a vanadium trimerization with $d$-$d$ $\sigma$ bonds. The Knight shift extracts the large Van Vleck orbital susceptibility, ${\chi }^{\mathrm{VV}}=3.6\times {10}^{-4}$, in a paramagnetic state above $T_c$, which is comparable to the spin susceptibility. The results suggest that the orbitally induced Peierls transition in the proximity of the frustrated itinerant state is the dominant driving force of the trimerization transition.

We discuss how to analyze the optical conductivity and Raman spectra of multiorbital systems using the velocity and the Raman vertices in a similar way Raman vertices were used to disentangle nodal and antinodal regions in cuprates. We apply this method to iron superconductors in the magnetic and nonmagnetic states, studied at the mean-field level. We find that the anisotropy in the optical conductivity at low frequencies reflects the difference between the magnetic gaps at the $X$ and $Y$ electron pockets. Both gaps are sampled by Raman spectroscopy. We also show that the Drude weight anisotropy in the magnetic state is sensitive to small changes in the lattice structure.

Random bond disorder in antiferromagnetic spin-1/2 Heisenberg ladders is investigated using the stochastic series expansion quantum Monte Carlo method. We find that the effects of individual bond impurities vary strongly, depending on their positions on legs and rungs. We initially focus on how the distribution of local bond energies depends on the impurity concentration. Then we study how the phase diagram of even-leg ladders is affected by random bond doping. We observe Bose glass phases in two regimes ($h^{\prime }<h\lesssim h_{c1}$ and $h^{\prime \prime }<h<h_{c2}$) and a Bose-Einstein Condensate in between. Their presence is discussed in relation to the local bond energies.

The crossover between two customary limits of phonon-assisted tunneling, the adiabatic and antiadiabatic regimes, is studied systematically in the framework of a minimal model for molecular devices: a resonant level coupled by displacement to a localized vibrational mode. Conventionally associated with the limits where the phonon frequency is either sufficiently small or sufficiently large as compared to the bare electronic hopping rate, we show that the crossover between the two regimes is governed for strong electron-phonon interactions primarily by the polaronic shift rather than the phonon frequency. In particular, the perturbative adiabatic limit is approached only as the bare hopping rate $\Gamma$ exceeds the polaronic shift, leaving an extended window of couplings where $\Gamma$ well exceeds the phonon frequency and yet the physics is basically that of the antiadiabatic regime. We term this intermediate regime the extended antiadiabatic regime. The effective low-energy Hamiltonian in the traditional and the extended antiadiabatic regime is shown to be the (purely fermionic) interacting resonant-level model, with parameters that we extract from numerical renormalization-group calculations. The extended antiadiabatic regime is followed in turn by a true crossover region where the polaron gets progressively undressed. In this latter region, the phonon configuration strongly deviates from a simple superposition of just one or two coherent states. The renormalized tunneling rate, which serves as the low-energy scale in the problem and thus sets the width of the tunneling resonance, is found to follow an approximate scaling form on going from the adiabatic to the antiadiabatic regime. Charging properties are governed by two distinct mechanisms at the extended antiadiabatic and into the crossover region, giving rise to characteristic shoulders in the low-temperature conductance as a function of gate voltage. These shoulders serve as a distinct experimental fingerprint of phonon-assisted tunneling when the electron-phonon coupling is strong.