Optimizing large parameter sets in variational quantum Monte Carlo

We present a technique for optimizing hundreds of thousands of variational parameters in variational quantum Monte Carlo. By introducing iterative Krylov subspace solvers and by multiplying by the Hamiltonian and overlap matrices as they are sampled, we remove the need to construct and store these matrices and thus bypass the most expensive steps of the stochastic reconfiguration and linear method optimization techniques. We demonstrate the effectiveness of this approach by using stochastic reconfiguration to optimize a correlator product state wavefunction with a pfaffian reference for four example systems. In two examples on the two dimensional Hubbard model, we study 16 and 64 site lattices, recovering energies accurate to 1% in the smaller lattice and predicting particle-hole phase separation in the larger. In two examples involving an ab initio Hamiltonian, we investigate the potential energy curve of a symmetrically dissociated 4x4 hydrogen lattice as well as the singlet-triplet gap in free base porphin. In the hydrogen system we recover 98% or more of the correlation energy at all geometries, while for porphin we compute the gap in a 24 orbital active space to within 0.02eV of the exact result. The numbers of variational parameters in these examples range from 4x10^3 to 5x10^5, demonstrating an ability to go far beyond the reach of previous formulations of stochastic reconfiguration.Comment: 5 pages, 4 figures, suggested PACS numbers 02.70.Ss, 71.10.Fd, 31.15.-

Approximating strongly correlated spin and fermion wavefunctions with correlator product states

We explore correlator product states for the approximation of correlated wavefunctions in arbitrary dimensions. We show that they encompass many interesting states including Laughlin's quantum Hall wavefunction, Huse and Elser's frustrated spin states, and Kitaev's toric code. We further establish their relation to common families of variational wavefunctions, such as matrix and tensor product states and resonating valence bond states. Calculations on the Heisenberg and spinless Hubbard models show that correlator product states capture both two-dimensional correlations (independent of system width) as well as non-trivial fermionic correlations (without sign problems). In one-dimensional simulations, correlator product states appear competitive with matrix product states with a comparable number of variational parameters, suggesting they may eventually provide a route to practically generalise the density matrix renormalisation group to higher dimensions.Comment: Table 1 expanded, Table 2 updated, optimization method discussed, discussions expanded in some sections, earlier work on similar wavefunctions included in text and references, see also (arXiv:0905.3898). 5 pages, 1 figure, 2 tables, submitted to Phys. Rev.

Striped spin liquid crystal ground state instability of kagome antiferromagnets

The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities[1-4]. This has been suggested as the reason why it is not strongly supported in large-scale numerical calculations[5]. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks both spatial symmetry in an unusual way that may leave spinons deconfined along one direction. Second, it breaks the U(1) gauge symmetry down to $Z_2$. Third, it has the spatial symmetry of a previously proposed "monopole" suggesting that it is an instability of the Dirac spin liquid. The state described herein also shares a remarkable similarity to the distortion of the kagome lattice observed at low Zn concentrations in Zn-Paratacamite suggesting it may already be realized in these materials.Comment: 4+ pages, 3 figure

Cell-type phylogenetics and the origin of endometrial stromal cells

SummaryA challenge of genome annotation is the identification of genes performing specific biological functions. Here, we propose a phylogenetic approach that utilizes RNA-seq data to infer the historical relationships among cell types and to trace the pattern of gene-expression changes on the tree. The hypothesis is that gene-expression changes coincidental with the origin of a cell type will be important for the function of the derived cell type. We apply this approach to the endometrial stromal cells (ESCs), which are critical for the initiation and maintenance of pregnancy. Our approach identified well-known regulators of ESCs, PGR and FOXO1, as well as genes not yet implicated in female fertility, including GATA2 and TFAP2C. Knockdown analysis confirmed that they are essential for ESC differentiation. We conclude that phylogenetic analysis of cell transcriptomes is a powerful tool for discovery of genes performing cell-type-specific functions

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

New Zealand contributions to the global earthquake model’s earthquake consequences database (GEMECD)

The Global Earthquake Model’s (GEM) Earthquake Consequences Database (GEMECD) aims to develop, for the first time, a standardised framework for collecting and collating geocoded consequence data induced by primary and secondary seismic hazards to different types of buildings, critical facilities, infrastructure and population, and relate this data to estimated ground motion intensity via the USGS ShakeMap Atlas. New Zealand is a partner of the GEMECD consortium and to-date has contributed with 7 events to the database, of which 4 are localised in the South Pacific area (Newcastle 1989; Luzon 1990; South of Java 2006 and Samoa Islands 2009) and 3 are NZ-specific events (Edgecumbe 1987; Darfield 2010 and Christchurch 2011). This contribution to GEMECD represented a unique opportunity for collating, comparing and reviewing existing damage datasets and harmonising them into a common, openly accessible and standardised database, from where the seismic performance of New Zealand buildings can be comparatively assessed. This paper firstly provides an overview of the GEMECD database structure, including taxonomies and guidelines to collect and report on earthquake-induced consequence data. Secondly, the paper presents a summary of the studies implemented for the 7 events, with particular focus on the Darfield (2010) and Christchurch (2011) earthquakes. Finally, examples of specific outcomes and potentials for NZ from using and processing GEMECD are presented, including: 1) the rationale for adopting the GEM taxonomy in NZ and any need for introducing NZ-specific attributes; 2) a complete overview of the building typological distribution in the Christchurch CBD prior to the Canterbury earthquakes and 3) some initial correlations between the level and extent of earthquake-induced physical damage to buildings, building safety/accessibility issues and the induced human casualtie

A Proposal to Detect Dark Matter Using Axionic Topological Antiferromagnets

Antiferromagnetically doped topological insulators (A-TI) are among the candidates to host dynamical axion fields and axion-polaritons; weakly interacting quasiparticles that are analogous to the dark axion, a long sought after candidate dark matter particle. Here we demonstrate that using the axion quasiparticle antiferromagnetic resonance in A-TI's in conjunction with low-noise methods of detecting THz photons presents a viable route to detect axion dark matter with mass 0.7 to 3.5 meV, a range currently inaccessible to other dark matter detection experiments and proposals. The benefits of this method at high frequency are the tunability of the resonance with applied magnetic field, and the use of A-TI samples with volumes much larger than 1 mm$^3$.Comment: 6 pages, 4 figures. v2 accepted for publication in Physical Review Letters. Many points clarified, some parameter estimates revise

The Evolution of Cas A at Low Radio Frequencies

We have used archival 74 MHz VLA data spanning the last 15 years in combination with new data from the Long Wavelength Demonstrator Array (LWDA) and data from the literature covering the last 50 years to explore the evolution of Cas A at low radio frequencies. We find that the secular decrease of the flux density of Cas A at ~80 MHz is rather stable over five decades of time, decreasing at a rate of 0.7-0.8% yr^-1. This is entirely consistent with previous estimates at frequencies as low as 38 MHz, indicating that the secular decrease is roughly the same at low frequencies, at least between 38 and 80 MHz. We also find strong evidence for as many as four modes of flux density oscillation about the slower secular decrease with periods of 3.10+/-0.02$ yr, 5.1+/-0.3 yr, 9.0+/-0.2 yr, and 24+/-2 yr. These are also consistent with fluctuations seen previously to occur on scales of a few years. These results provide compelling motivation for a thorough low frequency monitoring campaign of Cas A to constrain the nature and physical origins of these fluctuations, and to be able to better predict the flux density of Cas A at any given epoch so that it may be used as a reliable low frequency calibrator.Comment: accepted for publication in A