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Quantum Monte Carlo calculations of electromagnetic moments and transitions in A≤9 nuclei with meson-exchange currents derived from chiral effective field theory
Here, quantum Monte Carlo calculations of electromagnetic moments and transitions are reported for A ≤ 9 nuclei. The realistic Argonne v 18 two-nucleon and Illinois-7 three-nucleon potentials are used to generate the nuclear wave functions. Contributions of two-body meson-exchange current (MEC) operators are included for magnetic moments and M1 transitions. The MEC operators have been derived in both a standard nuclear physics approach and a chiral effective field theory formulation with pions and nucleons including up to one-loop corrections. The two-body MEC contributions provide significant corrections and lead to very good agreement with experiment. Their effect is particularly pronounced in the A=9, T=3/2 systems, in which they provide up to ~20% (~40%) of the total predicted value for the 9 Li( 9 C) magnetic moment.
Improved convergence of chiral effective field theory for 1 S 0 of NN scattering
Not Available
Deep learning: Extrapolation tool for ab initio nuclear theory
Ab initio approaches in nuclear theory, such as the no-core shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and many observables have no proven extrapolation method. Herein, we propose a feed-forward artificial neural network (ANN) method as an extrapolation tool to obtain the ground-state energy and the ground-state point-proton root-mean-square (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in 6 Li from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN findings with other extrapolation methods are also provided.
Effective field theory interactions for liquid argon target in DarkSide-50 experiment
We reanalize data collected with the DarkSide-50 experiment and recently used to set limits on the spin-independent interaction rate of weakly interacting massive particles (WIMPs) on argon nuclei with an effective field theory framework. The dataset corresponds to a total (16660 ± 270) kg d exposure using a target of low-radioactivity argon extracted from underground sources. We obtain upper limits on the effective couplings of the 12 leading operators in the nonrelativistic systematic expansion. For each effective coupling we set constraints on WIMP-nucleon cross sections, setting upper limits between 2.4×10-45 cm2 and 2.3×10-42 cm2 (8.9 ×10-45 cm2 and 6.0 ×10-42 cm2) for WIMPs of mass of 100 GeV/c2 (1000 GeV/c2) at 90% confidence level.
Perturbation theory for modeling galaxy bias: validation with simulations of the Dark Energy Survey
We describe perturbation theory (PT) models of galaxy bias for applications to photometric galaxy surveys. We model the galaxy-galaxy and galaxy-matter correlation functions in configuration space and validate against measurements from mock catalogs designed for the Dark Energy Survey (DES). We find that an effective PT model with five galaxy bias parameters provides a good description of the 3D correlation functions above scales of 4 Mpc/$h$ and $z < 1$. Our tests show that at the projected precision of the DES-Year 3 analysis, two of the non-linear bias parameters can be fixed to their co-evolution values, and a third (the $k^2$ term for higher derivative bias) set to zero. The agreement is typically at the 2 percent level over scales of interest, which is the statistical uncertainty of our simulation measurements. To achieve this level of agreement, our {\it fiducial} model requires using the full non-linear matter power spectrum (rather than the 1-loop PT one). We also measure the relationship between the non-linear and linear bias parameters and compare them to their expected co-evolution values. We use these tests to motivate the galaxy bias model and scale cuts for the cosmological analysis of the Dark Energy Survey; our conclusions are generally applicable to all photometric surveys.
BPS spectrum of supersymmetric CP(N-1) theory with Z{sub N} twisted masses
We revisit the Bogomol'nyi-Prasad-Sommerfeld (BPS) monopoles spectrum of the supersymmetric CP(N-1) two-dimensional model with Z{sub N}-symmetric twisted masses m{sub l} (l=0,1,...,N-1). A related issue we address is that of the curves of marginal stability (CMS) in this theory. Previous analyses were incomplete. We close the gap by exploiting a number of consistency conditions. In particular, we amend the Dorey formula for the BPS spectrum. Our analysis is based on the exact Veneziano--Yankielowicz-type superpotential and on the strong-coupling spectrum of the theory found from the mirror representation at small masses, |m{sub l}|<<{Lambda}. We show that at weak coupling the spectrum, with necessity, must include N-1 BPS towers of states, instead of just one, as was thought before. Only one of the towers is seen in the quasiclassical limit. We find the corresponding CMS for these towers, and argue that in the large-N limit they become circles, filling out a band on the plane of a single mass parameter of the model at hand. Inside the CMS, N-1 towers collapse into N stable states.
Generalized slow roll in the unified effective field theory of inflation
In this paper, we provide a compact and unified treatment of power spectrum observables for the effective field theory (EFT) of inflation with the complete set of operators that lead to second-order equations of motion in metric perturbations in both space and time derivatives, including Horndeski and GLPV theories. We relate the EFT operators in ADM form to the four additional free functions of time in the scalar and tensor equations. Using the generalized slow roll formalism, we show that each power spectrum can be described by an integral over a single source that is a function of its respective sound horizon. With this correspondence, existing model independent constraints on the source function can be simply reinterpreted in the more general inflationary context. By expanding these sources around an optimized freeze-out epoch, we also provide characterizations of these spectra in terms of five slow-roll hierarchies whose leading order forms are compact and accurate as long as EFT coefficients vary only on timescales greater than an e-fold. Finally, we also clarify the relationship between the unitary gauge observables employed in the EFT and the comoving gauge observables of the post-inflationary universe.
Linear sigma model for multiflavor gauge theories
We consider a linear sigma model describing $2N_f^2$ bosons ($\sigma$, a 0 , $\eta$' and π) as an approximate effective theory for a $SU(3)$ local gauge theory with $N_f$ Dirac fermions in the fundamental representation. The model has a renormalizable U(N f ) L Ⓧ invariant part, which has an approximate $O(2N_f^2)$ symmetry, and two additional terms, one describing the effects of a $SU(N_f)_V$ invariant mass term and the other the effects of the axial anomaly. We calculate the spectrum for arbitrary $N_f$. Using preliminary and published lattice results from the LatKMI collaboration, we found combinations of the masses that vary slowly with the explicit chiral symmetry breaking and $N_f$. This suggests that the anomaly term plays a leading role in the mass spectrum and that simple formulas such as $M_\sigma^2\simeq (2/N_f-C_\sigma)M_{\eta'}^2$ should apply in the chiral limit. Lattice measurements of $M_{\eta'}^2$ and of approximate constants such as $C_\sigma$ could help locating the boundary of the conformal window. Here, we show that our calculation can be adapted for arbitrary representations of the gauge group and in particular to the minimal model with two sextets, where similar patterns are likely to apply.
Perturbation theory of solid-liquid interfacial free energies of bcc metals
Not Available
Thermal effects in dislocation theory. II. Shear banding
The thermodynamic dislocation theory presented in previous papers is used in this paper to describe shear-banding instabilities. Central ingredients of the theory are a thermodynamically defined effective configurational temperature and a formula for the plastic strain rate determined by thermally activated depinning of entangled dislocations. This plastic strain rate is extremely sensitive to variations of the stress and the ordinary temperature. As a result of this sensitivity, the system undergoes rapid shear banding instabilities when ordinary thermal relaxation is slow. Finally, it also undergoes rapid changes from elastic to plastic behaviors at yielding transitions.
Density response from kinetic theory and time-dependent density-functional theory for matter under extreme conditions
The density linear response function for an inhomogeneous system of electrons in equilibrium with an array of fixed ions is considered. Two routes to its evaluation for extreme conditions (e.g., warm dense matter) are considered. The first is from a recently developed short-time kinetic equation; the second is from time-dependent density functional theory. The result from the latter approach agrees with that from kinetic theory in the “adiabatic approximation,” providing support and contextual clarity for each. Both provide a connection to the phenomenological Kubo-Greenwood method for calculating transport properties.
Higher-Spin Theory of the Magnetorotons
Fractional quantum Hall liquids exhibit a rich set of excitations, the lowest-energy of which are the magnetorotons with dispersion minima at a finite momentum. We propose a theory of the magnetorotons on the quantum Hall plateaux near half filling, namely, at filling fractions ν = N/(2N+1) at large N. The theory involves an infinite number of bosonic fields arising from bosonizing the fluctuations of the shape of the composite Fermi surface. At zero momentum there are O(N) neutral excitations, each carrying a well-defined spin that runs integer values 2,3,…. The mixing of modes at nonzero momentum q leads to the characteristic bending down of the lowest excitation and the appearance of the magnetoroton minima. A purely algebraic argument shows that the magnetoroton minima are located at qℓB = z i /(2N+1), where ℓ B is the magnetic length and zi are the zeros of the Bessel function J 1 , independent of the microscopic details. We argue that these minima are universal features of any two-dimensional Fermi surface coupled to a gauge field in a small background magnetic field.
Comparing time-dependent density functional theory with many-body perturbation theory for semiconductors: Screened range-separated hybrids and the GW plus Bethe-Salpeter approach
We present band structure and optical absorption spectra obtained from density functional theory (DFT) and linear response time-dependent DFT (TDDFT) calculations using a screened range-separated hybrid (SRSH) functional, including spin-orbit coupling, for seven prototypical semiconductors. The results are compared to those obtained from highly converged many-body perturbation theory calculations using the GW approximation and the GW plus Bethe-Salpeter equation (GW-BSE) approaches. We use a single empirical parameter for our SRSH calculations, fit such that the SRSH band gap reproduces the GW band gap at the Γ point. We then find that ground-state generalized Kohn-Sham SRSH eigenvalues accurately reproduce the band structure obtained from GW calculations, typically to within 0.1–0.2 eV, and optical absorption spectra obtained using TDDFT with the SRSH functional agree well with those of GW-BSE, with a mean deviation of 0.03 and 0.11 eV for the location of the first and second absorption peaks, respectively, at a fraction of the computational cost.
Theory of Trotter Error with Commutator Scaling
The Lie-Trotter formula, together with its higher-order generalizations, provides a simple approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly understood. We develop a theory of Trotter error that overcomes the limitations of truncating the Baker-Campbell-Hausdorff expansion. Our analysis directly exploits the commutativity of operator summands, producing tighter error bounds for both real- and imaginary-time evolutions. Whereas previous work achieves similar goals for systems with geometric locality or Lie-algebraic structure, our approach holds in general. We give a host of improved algorithms for digital quantum simulation and quantum Monte Carlo methods, nearly matching or even outperforming the best previous results. Our applications include: (i) a simulation of second-quantized plane-wave electronic structure, nearly matching the interaction-picture algorithm of Low and Wiebe; (ii) a simulation of $k$-local Hamiltonians almost with induced one-norm scaling, faster than the qubitization algorithm of Low and Chuang; (iii) a simulation of rapidly decaying power-law interactions, outperforming the Lieb-Robinson-based approach of Tran et al.; (iv) a hybrid simulation of clustered Hamiltonians, dramatically improving the result of Peng, Harrow, Ozols, and Wu; and (v) quantum Monte Carlo simulations of the transverse field Ising model and quantum ferromagnets, tightening previous analyses of Bravyi and Gosset. We obtain further speedups using the fact that product formulas can preserve the locality of the simulated system. Specifically, we show that local observables can be simulated with complexity independent of the system size for power-law interacting systems, which implies a Lieb-Robinson bound nearly matching a recent result of Tran et al. Our analysis reproduces known tight bounds for first- and second-order formulas. We further investigate the tightness of our bounds for higher-order formulas. For quantum simulation of a one-dimensional Heisenberg model with an even-odd ordering of terms, our result overestimates the complexity by only a factor of $5$. Our bound is also close to tight for power-law interactions and other orderings of terms. This suggests that our theory can accurately characterize Trotter error in terms of both the asymptotic scaling and the constant prefactor.
The Gauge Theory of the Glass Transition in the Three-Dimensional XY Model with Quenched Disorder
The gauge theory of phase transitions in a three-dimensional XY-model with a hardened disorder is considered. It is shown that the topological phase transition occurring in the vortex subsystem of this model is a transition in the state of spin glass.
Bulk Diffusion of Cl through O Vacancies in α-Cr 2 O 3 : A Density Functional Theory Study
Many metals form passive oxides which are broken or weakened by anionic-induced degradation leading to material failure and anionic diffusion is an important step of this degradation process. The diffusion of anionic species through oxides involves a combination of diffusion along grain boundaries, cracks, and channels, as well as bulk diffusion via point defects which is the focus of this study. Using density functional theory, we study bulk diffusion of Cl through O vacancies in α -Cr 2 O 3 as a model system for passive metal oxides. Little is known about Cl diffusion and bonding characteristics, so we benchmark our work through comparison to numerous studies on O diffusion in α -Cr 2 O 3 to analyze similarities and differences between the O and Cl diffusion in the passivation and degradation process of α -Cr 2 O 3 respectively. Unlike O diffusion, the lowest diffusion barrier for Cl is cross-plane diffusion between two (0001) planes through a vacant cation site but the much shorter in-plane diffusion path within the same coordination polyhedron has 35% higher barrier. This work provides the basis for considering the contributions of Cl bulk-diffusion in the overall diffusion kinetics of Cl through α -Cr 2 O 3 .
Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory
Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation, we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N = 2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstances be regarded as more complex than the physics of a spin-orbital chain.