The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well studied in the regimes of few-body physics and noninteracting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve for it. In this paper I fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. I demonstrate my algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is nonintegrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, I show that the algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians. My algorithm scales similarly to conventional methods as a function of system size and energy gap, and therefore should prove a valuable tool in investigating the quantum geometry of many-body systems.

Density functional theory (DFT) calculations of the magnetic shielding for solid state nuclear magnetic resonance (NMR) provide an important contribution for the understanding of the experimentally observed chemical shifts. Therefore, methods allowing us to compute those parameters with high precision are very valuable. Recently, we have presented a formalism for computing the NMR parameters in solids based on the augmented plane wave (APW) method [Phys. Rev. B 85, 035132 (2012)]. In the present work we derive an improvement of the original schema, which greatly boosts its precision and efficiency. Although the APW method is virtually an exact method for the ground state wave functions in a solid, its optimized basis set is incomplete and we need to extend it by including basis functions containing the radial derivative of the standard APW basis functions in order to efficiently describe the perturbation due to a magnetic field. In addition we also include the core states in the first-order perturbation formula correcting an error resulting from separation of the core and valence states. These allow us to obtain the NMR parameters that are nearly numerically exact within a given DFT functional.

The dynamic properties of magnetic nanoparticles are known to be substantially influenced by the dipole-dipole interaction. In this paper we study how this affects the efficiency of magnetic hyperthermia experiments. In particular we ask whether it is possible to use the dipolar interaction as a mechanism to increase the heat released by the nanoparticles, thus improving the application. The investigation is carried out via numerical simulations based on a mean-field model developed to include the dipolar interaction in the Fokker-Planck equation describing the time evolution of the system. Both the linear and nonlinear regimes (related to the amplitude of the external magnetic field) are studied in detail. It is shown that even moderate changes in the particle concentration may have substantial effects on the magnetization dynamics of the system, being capable of increasing or decreasing the heat released by orders of magnitude, depending on the values of other system parameters. It is found that the dipolar interaction can be used to increase the dissipation of magnetically soft particles, but should be avoided in the case of hard particles.

We study critical behavior in the classical cubic dimer model (CDM) in the presence of a finite density of monomers. With attractive interactions between parallel dimers, the monomer-free CDM exhibits an unconventional transition from a Coulomb phase to a dimer crystal. Monomers act as charges (or monopoles) in the Coulomb phase and, at nonzero density, lead to a standard Landau-type transition. We use large-scale Monte Carlo simulations to study the system in the neighborhood of the critical point, and find results in agreement with detailed predictions of scaling theory. Going beyond previous studies of the transition in the absence of monomers, we explicitly confirm the distinction between conventional and unconventional criticality, and quantitatively demonstrate the crossover between the two. Our results also provide additional evidence for the theoretical claim that the transition in the CDM belongs in the same universality class as the deconfined quantum critical point in the $\mathrm{SU}\left(2\right)$ JQ model.

Recently the signs of both superconducting transition temperature ($T_c$) beyond 60 K and spin density wave (SDW) have been observed in FeSe thin film on SrTiO${}_3$ (STO) substrate, which suggests a strong interplay between superconductivity and magnetism. With the first-principles calculations, we find that the substrate-induced tensile strain tends to stabilize the collinear antiferromagnetic (CAF) state in FeSe thin film by enhancing of the next-nearest-neighbor superexchange antiferromagnetic interaction bridged through Se atoms. On the other hand, we find that when there are oxygen vacancies in the substrate, the significant charge transfer from the substrate to the first FeSe layer would suppress the magnetic order there, and thus the high-temperature superconductivity could occur. In addition, the stability of the CAF state is lowered when FeSe is on a defect-free STO substrate due to the redistribution of charges among the Fe $3d$ orbitals. Normally heavy electron doping would kill superconductivity as it suppresses the spin fluctuations as well, but the expanded lattice constants in this system enhance the magnetism and thus preserve the superconductivity. Our results provide a comprehensive microscopic explanation for the recent experimental findings, and build a foundation for the further exploration of the superconductivity and magnetism in this superconducting interface.

We report remarkably low residual resistivity, giant residual resistivity ratio, free-electron-like Hall resistivity, and high mobility ($\approx$10${}^4$ cm${}^2$ V${}^{-1}$ s${}^{-1}$) charge transport in epitaxial films of Co${}_2$MnSi and Co${}_2$FeSi grown on (001) SrTiO${}_3$. This unusual behavior is not observed in films deposited on other cubic oxide substrates of comparable lattice parameters. The scaling of the resistivity with thickness of the films allows the extraction of interface conductance, which can be attributed to a layer of oxygen vacancies confined within 1.9 nm of the interface as revealed by atomically resolved electron microscopy and spectroscopy. The high mobility transport observed here at the interface of a fully spin polarized metal is potentially important for spintronics applications.

In order to elucidate the magnetic ground state of Sr${}_2$VO${}_4$, we have measured muon spin rotation and relaxation (${\mu }^{+}$SR) spectra of a powder sample in the temperature range between 1.8 and 140 K. As a result, we have clarified that the transition at 105 K is not magnetic but structural and/or electric in origin and found the appearance of static antiferromagnetic (AF) order below 8 K. Moreover, the distribution of the internal AF field was found to be very broad, even at the lowest temperature measured. These results are consistent with the formation of an orbital-stripe order with collinear AF order for the magnetic ground state of Sr${}_2$VO${}_4$.

The ferroelectric phase transition at $T_C=340\mathrm{K}$ in (${{\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{CH}}_2{\mathrm{CH}}_2{\mathrm{NH}}_3{)}_2\mathrm{CuCl}}_4$ is studied by means of temperature-dependent low-frequency Raman scattering, focusing on the coupling of a low-energy librational mode to the order parameter of the transition. Analysis of the symmetry and characteristics of this mode links the dipolar order to the tilt angle of the organic cations. The thermal evolution of the Raman spectrum demonstrates the displacive component of the phase transition in combination with order-disorder phenomena and the importance of the organic-inorganic interplay to the physical properties of the compound. The ferroelectric properties investigated here can be generalized to the family of layered organic-inorganic hybrids.

We predict, using a free-energy calculation, that the quantum phase transition between the $U\left(1\right)$ quantum spin liquid (QSL) and antiferromagnet (AFM) phases in certain pyrochlore quantum spin ice is first order rather than second order. This change in order from second to first order is induced by gauge fluctuations, which are explicitly taken into account at gauge theory level in our effective low-energy theory. We therefore have identified a fluctuation-induced first-order quantum phase transition in pyrochlore quantum spin ice. We explicitly derive the quantum free-energy description of this QSL-to-AFM phase transition and predict that it is a weakly first-order phase transition. We also briefly discuss the experimental relevance of this result.

We show that the magnetism of double perovskite AFe${}_{1/2}$M${}_{1/2}$O${}_3$ systems may be described by the Heisenberg model on the simple cubic lattice, where only half of sites are occupied by localized magnetic moments. The nearest-neighbor interaction $J_1$ is more than 20 times the next-nearest-neighbor interaction $J_2$, the third-nearest interaction along the space diagonal of the cube being negligible. We argue that the variety of magnetic properties observed in different systems is connected with the variety of chemical ordering in them. We analyze six possible types of the chemical ordering in a 2 $\times$ 2 $\times$ 2 supercell, and argue that the probability to find them in a real compound does not correspond to a random occupation of lattice sites by magnetic ions. The exchange $J_2$ rather than $J_1$ define the magnetic energy scale of most double perovskite compounds that means the enhanced probability of 1:1 short-range ordering. Two multiferroic compounds PbFe${}_{1/2}$M${}_{1/2}$O${}_3$ (M = Nb, Ta) are exceptions. We show that the relatively high temperature of the antiferromagnetic transition is compatible with a layered short-range chemical order, which was recently shown to be most stable for these two compounds [I. P. Raevski et al., Phys. Rev. B 85, 224412 (2012)]. We show also that one of the types of ordering has a ferrimagnetic ground state. The clusters with a short-range order of this type may be responsible for a room-temperature superparamagnetism, and may form the cluster glass at low temperatures.

We use a combination of analytical and numerical techniques to study the phase diagram of the frustrated Heisenberg model on the bilayer honeycomb lattice. Using the Schwinger-boson description of the spin operators followed by a mean-field decoupling, the magnetic phase diagram is studied as a function of the frustration coupling $J_2$ and the interlayer coupling $J_{\perp }$. The presence of both magnetically ordered and disordered phases is investigated by means of the evaluation of ground-state energy, spin gap, local magnetization, and spin-spin correlations. We observe a phase with a spin gap and short-range Néel correlations that survives for nonzero next-nearest-neighbor interaction and interlayer coupling. Furthermore, we detect signatures of a reentrant behavior in the melting of the Néel phase and symmetry restoring when the system undergoes a transition from an on-layer nematic valence-bond crystal phase to an interlayer valence-bond crystal phase. We complement our work with exact diagonalization on small clusters and dimer-series expansion calculations, together with a linear spin-wave approach to study the phase diagram as a function of the spin $S$, the frustration, and the interlayer couplings.

We use exact diagonalization and cluster perturbation theory to address the role of strong interactions and quantum fluctuations for spinless fermions on the honeycomb lattice. We find quantum fluctuations to be very pronounced both at weak and strong interactions. A weak second-neighbor Coulomb repulsion $V_2$ induces a tendency toward an interaction-generated quantum anomalous Hall phase, as borne out in mean-field theory. However, quantum fluctuations prevent the formation of a stable quantum Hall phase before the onset of the charge-modulated phase predicted at large $V_2$ by mean-field theory. Consequently, the system undergoes a direct transition from the semimetal to the charge-modulated phase. For the latter, charge fluctuations also play a key role. While the phase, which is related to pinball liquids, is stabilized by the repulsion $V_2$, the energy of its low-lying charge excitations scales with the electronic hopping $t$, as in a band insulator.

We report on the importance of $GW$ self-energy corrections for the electronic structure of light actinides in the weak-to-intermediate coupling regime. Our study is based on calculations of the band structure and total density of states of Np, U, and Pu using a one-shot $GW$ approximation that includes spin-orbit coupling within a full potential LAPW framework. We also present RPA screened effective Coulomb interactions for the $f$-electron orbitals for different lattice constants, and show that there is an increased contribution from electron-electron correlation in these systems for expanded lattices. We find a significant amount of electronic correlation in these highly localized electronic systems.

Bipartite entanglement entropies, calculated from the reduced density matrix of a subsystem, provide a description of the resources available within a system for performing quantum information processing. However, these quantities are not uniquely defined on a system of non-Abelian anyons. This paper describes how reduced density matrices and bipartite entanglement entropies (such as the von Neumann and Renyi entropies) may be constructed for non-Abelian anyonic systems, in ways which reduce to the conventional definitions for systems with only local degrees of freedom.

We address conservation laws associated with current, momentum, and energy and show how they can be satisfied within many body theories which focus on pair correlations. Of interest are two well known $T$-matrix theories which represent many body theories which incorporate pairing in the normal state. The first of these is associated with the Nozieres Schmitt-Rink theory, while the second involves the $T$ matrix of a BCS-Leggett-like state as identified by Kadanoff and Martin. $T$-matrix theories begin with an ansatz for the single particle self energy and are to be distinguished from $\Phi$-derivable theories which introduce an ansatz for a particular contribution to the thermodynamical potential. Conservation laws are equivalent to Ward identities which we address in some detail here. Although $\Phi$-derivable theories are often referred to as “conserving theories,” a consequence of this work is the demonstration that these two $T$-matrix approaches similarly can be made to obey all conservation laws. When simplifying approximations are made in $\Phi$-derivable or other theories, one has to take care that the end results are not incompatible with conservation.

We present in this work measurements of the Raman excitation profile of the high-energy phonons ($G$ band) in single-chirality ($n,m$) semiconducting single-wall carbon nanotubes using more than 70 laser excitation energies, and a theoretical description based on the third-order quantum model for Raman scattering. We show that the observed asymmetry in the $G$ band Raman excitation profile is rigorously explained by considering all physical elements associated with Raman scattering in ($n,m$) carbon nanotubes, such as the existence of van Hove singularities in the electronic density of states and wave-vector dependence of the matrix elements of the Raman process. We conclude that the proposed violation of the Condon approximation is not a fundamental principle underlying the nanotube photophysics.

Silicene is systematically investigated as an epitaxial overlayer on an Ag(111) substrate based on the ab initio density functional theory. The geometry and stability of five silicene-silver adsorbate systems with four coincidence lattices, $\sqrt{7}\times \sqrt{7}$ on $\sqrt{13}\times \sqrt{13}$, $3\times 3$ on $4\times 4$, $2\times 2$ on $\sqrt{7}\times \sqrt{7}$, and $\sqrt{7}\times \sqrt{7}$ on $2\sqrt{3}\times 2\sqrt{3}$, are related to the Si coverage, biaxial strain, and preparation conditions. Their phase diagram is calculated for varying chemical potential of the Si reservoir. The scanning tunneling microscopy images calculated for the optimized atomic geometries agree with those observed experimentally. The destruction of the original honeycomb symmetry and the strong adsorbate-substrate interaction significantly influence the electronic structure. Four peeled-off silicene sheets show conical linear bands, with small gaps. However, the band edges of the $3\times 3$ on $4\times 4$ geometry cannot be explained in terms of gap opening between Dirac cones for symmetry reasons. We confirm the conclusion that the linear bands observed by ARPES are due to folded Ag bands.

In this theoretical work, we show that substrates play key roles in the properties of layered systems such as graphene by focusing on magnetic properties associated with adsorbates. Local magnetic moments formed in fluorinated and hydrogenated graphene layers are quenched when they are deposited on a copper substrate due to several interconnected effects: doping by the substrate, increased structural distortion, and broadening of the defect states. We find that these effects contribute in different degrees to the changes in the structural, electronic and magnetic properties of the system and that they vary between adsorbates. The most important factor in the disappearance of magnetism in the functionalized graphene is shown to be the formation of metal-carbide bonds and the subsequent broadening of the impurity states that erases their spin splitting. We show that interactions with the substrate and the formation of local magnetic moments can be modified using multiple layers of graphene.

We derive an ab initio $\pi$-band tight-binding model for $AB$ stacked bilayer graphene based on maximally localized Wannier wave functions centered on the carbon sites, finding that both intralayer and interlayer hopping is longer in range than assumed in commonly used phenomenological tight-binding models. Starting from this full tight-binding model, we derive two effective models that are intended to provide a convenient starting point for theories of $\pi$-band electronic properties by achieving accuracy over the full width of the $\pi$ bands, and especially at the Dirac points, in models with a relatively small number of hopping parameters. The simplified models are then compared with phenomenological Slonczewski-Weiss-McClure–type tight-binding models in an effort to clarify confusion that exists in the literature concerning tight-binding model parameter signs.