Spectral functions of strongly correlated extended systems via an exact quantum embedding

Density matrix embedding theory (DMET) [Phys. Rev. Lett., 109, 186404 (2012)], introduced a new approach to quantum cluster embedding methods, whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost, but was inherently limited by the construction of a bath designed to reproduce ground state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the 1D and 2D Hubbard model, where we obtain zero temperature, thermodynamic limit spectral functions, and show the trivial extension to two-particle Green functions. This advance therefore extends the scope and applicability of DMET in condensed matter problems as a computationally tractable route to correlated spectral functions of extended systems, and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.Comment: 6 pages, 6 figure

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The intermediate and spin-liquid phase of the half-filled honeycomb Hubbard model

We obtain the phase-diagram of the half-filled honeycomb Hubbard model with density matrix embedding theory, to address recent controversy at intermediate couplings. We use clusters from 2-12 sites and lattices at the thermodynamic limit. We identify a paramagnetic insulating state, with possible hexagonal cluster order, competitive with the antiferromagnetic phase at intermediate coupling. However, its stability is strongly cluster and lattice size dependent, explaining controver- sies in earlier work. Our results support the paramagnetic insulator as being a metastable, rather than a true, intermediate phase, in the thermodynamic limit

Spectroscopic accuracy directly from quantum chemistry: application to ground and excited states of beryllium dimer

We combine explicit correlation via the canonical transcorrelation approach with the density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods to compute a near-exact beryllium dimer curve, {\it without} the use of composite methods. In particular, our direct density matrix renormalization group calculations produce a well-depth of $D_e$=931.2 cm$^{-1}$ which agrees very well with recent experimentally derived estimates $D_e$=929.7$\pm 2$~cm$^{-1}$ [Science, 324, 1548 (2009)] and $D_e$=934.6~cm$^{-1}$ [Science, 326, 1382 (2009)]], as well the best composite theoretical estimates, $D_e$=938$\pm 15$~cm$^{-1}$ [J. Phys. Chem. A, 111, 12822 (2007)] and $D_e$=935.1$\pm 10$~cm$^{-1}$ [Phys. Chem. Chem. Phys., 13, 20311 (2011)]. Our results suggest possible inaccuracies in the functional form of the potential used at shorter bond lengths to fit the experimental data [Science, 324, 1548 (2009)]. With the density matrix renormalization group we also compute near-exact vertical excitation energies at the equilibrium geometry. These provide non-trivial benchmarks for quantum chemical methods for excited states, and illustrate the surprisingly large error that remains for 1$^1\Sigma^-_g$ state with approximate multi-reference configuration interaction and equation-of-motion coupled cluster methods. Overall, we demonstrate that explicitly correlated density matrix renormalization group and initiator full configuration interaction quantum Monte Carlo methods allow us to fully converge to the basis set and correlation limit of the non-relativistic Schr\"odinger equation in small molecules

Modeling the Formation of Secondary Organic Aerosol. 1. Application of Theoretical Principles to Measurements Obtained in the α-Pinene/, β-Pinene/, Sabinene/, Δ^3-Carene/, and Cyclohexene/Ozone Systems

Secondary organic aerosol (SOA) forms in the atmosphere when volatile parent compounds are oxidized to form low-volatility products that condense to yield organic particulate matter (PM). Under conditions of intense photochemical smog, from 40 to 80% of the particulate organic carbon can be secondary in origin. Because describing multicomponent condensation requires a compound-by-compound identification and quantification of the condensable compounds, the complexity of ambient SOA has made it difficult to test the ability of existing gas/particle (G/P) partitioning theory to predict SOA formation in urban air. This paper examines that ability using G/P data from past laboratory chamber experiments carried out with five parent hydrocarbons (HCs) (four monoterpenes at 308 K and cyclohexene at 298 K) in which significant fractions (61−100%) of the total mass of SOA formed from those HCs were identified and quantified by compound. The model calculations were based on a matrix representation of the multicomponent, SOA G/P distribution process. The governing equations were solved by an iterative method. Input data for the model included (i) ΔHC (μg m^(-3)), the amount of reacted parent hydrocarbon; (ii) the α values that give the total concentration T (gas + particle phase, ng m^(-3)) values for each product i according to Ti = 10^3 αiΔHC; (iii) estimates of the pure compound liquid vapor pressure P^o_L values (at the reaction temperature) for the products; and (iv) UNIFAC parameters for estimating activity coefficients in the SOA phase for the products as a function of SOA composition. The model predicts the total amount M_o (μg m^(-3)) of organic aerosol that will form from the reaction of ΔHC, the total aerosol yield Y (= M_o/ΔHC), and the compound-by-compound yield values Y_i. An impediment in applying the model is the lack of literature data on P^o_L values for the compounds of interest or even on P^o_L values for other, similarly low-volatility compounds. This was overcome in part by using the G/P data from the α-pinene and cyclohexene experiments to determine P^o_L values for use (along with a set of 14 other independent polar compounds) in calculating UNIFAC vapor pressure parameters that were, in turn, used to estimate all of the needed P^o_L values. The significant degree of resultant circularity in the calculations for α-pinene and cyclohexene helped lead to the good agreement that was found between the Y_i values predicted by the model, and those measured experimentally for those two compounds. However, the model was also able to predict the aerosol yield values from β-pinene, sabinene, and Δ^3-carene, for which there was significatly less circularity in the calculations, thereby providing evidence supporting the idea that given the correct input information, SOA formation can in fact be accurately modeled as a multicomponent condensation process

Communication: Excited states, dynamic correlation functions and spectral properties from full configuration interaction quantum Monte Carlo

In this communication, we propose a method for obtaining isolated excited states within the full configuration interaction quantum Monte Carlo framework. This method allows for stable sampling with respect to collapse to lower energy states and requires no uncontrolled approximations. In contrast with most previous methods to extract excited state information from quantum Monte Carlo methods, this results from a modification to the underlying propagator, and does not require explicit orthogonalization, analytic continuation, transient estimators, or restriction of the Hilbert space via a trial wavefunction. Furthermore, we show that the propagator can directly yield frequency-domain correlation functions and spectral functions such as the density of states which are difficult to obtain within a traditional quantum Monte Carlo framework. We demonstrate this approach with pilot applications to the neon atom and beryllium dimer

Single-walled carbon nanotubes as excitonic optical wires

Although metallic nanostructures are useful for nanoscale optics, all of their key optical properties are determined by their geometry. This makes it difficult to adjust these properties independently, and can restrict applications. Here we use the absolute intensity of Rayleigh scattering to show that single-walled carbon nanotubes can form ideal optical wires. The spatial distribution of the radiation scattered by the nanotubes is determined by their shape, but the intensity and spectrum of the scattered radiation are determined by exciton dynamics, quantum-dot-like optical resonances and other intrinsic properties. Moreover, the nanotubes display a uniform peak optical conductivity of ~8 e^2/h, which we derive using an exciton model, suggesting universal behaviour similar to that observed in nanotube conductance. We further demonstrate a radiative coupling between two distant nanotubes, with potential applications in metamaterials and optical antennas

From plane waves to local Gaussians for the simulation of correlated periodic systems

We present a simple, robust, and black-box approach to the implementation and use of local, periodic, atom-centered Gaussian basis functions within a plane wave code, in a computationally efficient manner. The procedure outlined is based on the representation of the Gaussians within a finite bandwidth by their underlying plane wave coefficients. The core region is handled within the projected augment wave framework, by pseudizing the Gaussian functions within a cutoff radius around each nucleus, smoothing the functions so that they are faithfully represented by a plane wave basis with only moderate kinetic energy cutoff. To mitigate the effects of the basis set superposition error and incompleteness at the mean-field level introduced by the Gaussian basis, we also propose a hybrid approach, whereby the complete occupied space is first converged within a large plane wave basis, and the Gaussian basis used to construct a complementary virtual space for the application of correlated methods. We demonstrate that these pseudized Gaussians yield compact and systematically improvable spaces with an accuracy comparable to their non-pseudized Gaussian counterparts. A key advantage of the described method is its ability to efficiently capture and describe electronic correlation effects of weakly bound and low-dimensional systems, where plane waves are not sufficiently compact or able to be truncated without unphysical artifacts. We investigate the accuracy of the pseudized Gaussians for the water dimer interaction, neon solid, and water adsorption on a LiH surface, at the level of second-order Møller–Plesset perturbation theory

On-Chip Rayleigh Imaging and Spectroscopy of Carbon Nanotubes

We report a novel on-chip Rayleigh imaging technique using wide-field laser illumination to measure optical scattering from individual single-walled carbon nanotubes (SWNTs) on a solid substrate with high spatial and spectral resolution. This method in conjunction with calibrated AFM measurements accurately measures the resonance energies and diameters for a large number of SWNTs in parallel. We apply this technique for fast mapping of key SWNT parameters, including the electronic-types and chiral indices for individual SWNTs, position and frequency of chirality-changing events, and intertube interactions in both bundled and distant SWNTs