J. E. Gubernatis

Bayesian inference and the analytic continuation of imaginary-time quantum Monte Carlo data

Abstract We present a way to use Bayesian statistical inference and the principle of maximum entropy to analytically continue imaginary-time quantum Monte Carlo data. We supply the details that are lacking in the seminal literature but are important for the motivated reader to understand the assumptions and approximations embodied in these methods. First, we summarize the general relations between quantum correlation functions and spectral densities. We then review the basic principles, formalism, and philosophy of Bayesian inference and discuss the application of this approach in the context of the analytic continuation problem. Next, we present a detailed case study for the symmetric, infinite-dimension Anderson Hamiltonian. We chose this Hamiltonian because the qualitative features of its spectral density are well established and because a particularly convenient algorithm exists to produce the imaginary-time Greens function data. Shown are all the intermediate steps of data and solution qualification. The importance of careful data preparation and error propagation in the analytic continuation is discussed in the context of this example. Then, we review the different physical systems and physical quantities to which these, or related, procedures have been applied. Finally, we describe other features concerning the application of our methods, their possible improvement, and areas for additional study.

Simulating physical phenomena by quantum networks

Physical systems, characterized by an ensemble of interacting constituents, can be represented and studied by different algebras of operators (observables). For example, a fully polarized electronic system can be studied by means of the algebra generated by the usual fermionic creation and annihilation operators or by the algebra of Pauli (spin-½) operators. The Jordan-Wigner isomorphism gives the correspondence between the two algebras. As we previously noted, similar isomorphisms enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental observation to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g., the spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian H.

Quantum algorithms for fermionic simulations

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner transformation) that allows exact algebraic invertible mappings of operators with different statistical properties. We give an explicit implementation of a simple problem using a quantum computer based on standard qubits.

CONSTRAINED PATH MONTE CARLO METHOD FOR FERMION GROUND STATES

We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function {vert_bar}{psi}{sub T}{r_angle}, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if {vert_bar}{psi}{sub T}{r_angle} is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to 16{times}16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as {vert_bar}{psi}{sub T}{r_angle}, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm. {copyright} {ital 1997} {ital The American Physical Society}

Machine learning bandgaps of double perovskites.

The ability to make rapid and accurate predictions on bandgaps of double perovskites is of much practical interest for a range of applications. While quantum mechanical computations for high-fidelity bandgaps are enormously computation-time intensive and thus impractical in high throughput studies, informatics-based statistical learning approaches can be a promising alternative. Here we demonstrate a systematic feature-engineering approach and a robust learning framework for efficient and accurate predictions of electronic bandgaps of double perovskites. After evaluating a set of more than 1.2 million features, we identify lowest occupied Kohn-Sham levels and elemental electronegativities of the constituent atomic species as the most crucial and relevant predictors. The developed models are validated and tested using the best practices of data science and further analyzed to rationalize their prediction performance.

Band Structure of SnTe Studied by Photoemission Spectroscopy

We present an angle-resolved photoemission spectroscopy study of the electronic structure of SnTe and compare the experimental results to ab initio band structure calculations as well as a simplified tight-binding model of the p bands. Our study reveals the conjectured complex Fermi surface structure near the L points showing topological changes in the bands from disconnected pockets, to open tubes, and then to cuboids as the binding energy increases, resolving lingering issues about the electronic structure. The chemical potential at the crystal surface is found to be 0.5 eV below the gap, corresponding to a carrier density of p=1.14 × 10(21)  cm(-3) or 7.2 × 10(-2) holes per unit cell. At a temperature below the cubic-rhombohedral structural transition a small shift in spectral energy of the valance band is found, in agreement with model predictions.

Effects of microstructure on the speed and attenuation of elastic waves in porous materials

Abstract We investigated the effects of microstructure statistics on the speed and attenuation of an elastic wave propagating through a porous material. We derived a general set of equations from which the effective wavenumber (and hence the phase velocity, group velocity and attenuation) can be found, depending on the level of statistical information known. We solved this equation in the independent scatterer approximation and computed the effective wavenumber for several distribution of pore radii. We found the effective wavenumber to be most sensitive to the most probable pore radius and more sensitive to radii larger than this value than to those smaller.

Magnetic Impurities In Graphene

We used a quantum Monte Carlo method to study the magnetic impurity adatoms on graphene. We found that by tuning the chemical potential we could switch the values of the impurity local magnet moment between relatively large and small values. Our computations of the impurity spectral density found its behavior to differ significantly from that of an impurity in a normal metal and our computations of the charge-charge and spin-spin correlations between the impurity and the conduction-band electrons found them to be strongly suppressed. In general, our results are consistent with those from poor mans scaling and numerical renormalization group methods.

Thermoelectric transport with electron-phonon coupling and electron-electron interaction in molecular junctions

Department of Physics, Zhejiang University, Hangzhou 310027, P. R. China(Dated: June 28, 2011)Within the framework of nonequilibrium Green’s functions, we investigate the thermoelectrictransport in a single molecular junction non-perturbatively for arbitrary strengths of its electron-phonon and electron-electron interactions. At low temperatures, resonances of the thermoelectricfigure of merit ZT occur around the sides of resonances of electronic conductance but drops dramat-ically to zero at exactly these resonant points. ZT can be enhanced by increasing electron-phononcoupling and Coulomb repulsion, and optimal values are obtained at competition regimes of thesetwo interactions. Our results indicate a great potential for single-molecular-junctions as good ther-moelectric devices over a wide range of temperatures.

Tin telluride: a weakly co-elastic metal

We report resonant ultrasound spectroscopy (RUS), dilatometry/magnetostriction, magnetotransport, magnetization, specific-heat, and 119Sn Mossbauer spectroscopy measurements on SnTe and Sn0.995Cr0.005Te. Hall measurements at T=77 K indicate that our Bridgman-grown single crystals have a p-type carrier concentration of 3.4×1019 cm−3 and that our Cr-doped crystals have an n-type concentration of 5.8×1022 cm−3. Although our SnTe crystals are diamagnetic over the temperature range 2≤T≤1100 K, the Cr-doped crystals are room-temperature ferromagnets with a Curie temperature of 294 K. For each sample type, three-terminal capacitive dilatometry measurements detect a subtle 0.5 μm distortion at Tc≈85 K. Whereas our RUS measurements on SnTe show elastic hardening near the structural transition, pointing to co-elastic behavior, similar measurements on Sn0.995Cr0.005Te show a pronounced softening, pointing to ferroelastic behavior. Effective Debye temperature, θD, values of SnTe obtained from 119Sn Mossbauer studies show a hardening of phonons in the range 60–115 K (θD=162 K) as compared with the 100–300 K range (θD=150 K). In addition, a precursor softening extending over approximately 100 K anticipates this collapse at the critical temperature and quantitative analysis over three decades of its reduced modulus finds ΔC44/C44=A|(T−T0)/T0|−κ with κ=0.50±0.02, a value indicating a three-dimensional softening of phonon branches at a temperature T0∼75 K, considerably below Tc. We suggest that the differences in these two types of elastic behaviors lie in the absence of elastic domain-wall motion in the one case and their nucleation in the other.