arXiv subjects

Andrei Alexandru

Publications and source records attributed to Andrei Alexandru.

At least 73 records · Page 4Linked to original sources

arXiv2017

Deep Learning Beyond Lefschetz Thimbles

The generalized thimble method to treat field theories with sign problems requires repeatedly solving the computationally-expensive holomorphic flow equations. We present a machine learning technique to bypass this problem. The central idea is to obtain a few field configurations via the flow equations to train a feed-forward neural network. The trained network defines a new manifold of integration which reduces the sign problem and can be rapidly sampled. We present results for the $1+1$ dimensional Thirring model with Wilson fermions on sizable lattices. In addition to the gain in speed, the parameterization of the integration manifold we use avoids the "trapping" of Monte Carlo chains which plagues large-flow calculations, a considerable shortcoming of the previous attempts.

hep-lat↗

arXiv2017

Schwinger-Keldysh on the lattice: a faster algorithm and its application to field theory

A new algorithm is developed allowing the Monte Carlo study of a 1 + 1 dimensional theory in real time. The main algorithmic development is to avoid the explicit calculation of the Jacobian matrix and its determinant in the update process. This improvement has a wide applicability and reduces the cost of the update in thimble-inspired calculations from O(N^3) to less than O(N^2). As an additional feature, the algorithm leads to improved Monte Carlo proposals. We exemplify the use of the algorithm to the real time dynamics of a scalar ϕ^4 theory with weak and strong couplings.

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arXiv2017

Strange and Charm Quark Spins from Anomalous Ward Identity

We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_π = 330$ MeV. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite $q^2$. For the charm quark, we find that the negative pseudoscalar term almost cancels the positive topological term. For the strange quark, the pseudoscalar term is less negative than that of the charm. By imposing the AWI, the strange $g_A(q^2)$ at $q^2 =0$ is obtained by a global fit of the pseudoscalar and the topological form factors, together with $g_A(q^2)$ and the induced pseudoscalar form factor $h_A(q^2)$ at finite $q^2$. The chiral extrapolation to the physical pion mass gives $Δs + Δ{\bar{s}} = -0.0403(44)(78)$.

hep-ph↗

arXiv2017

Tempered transitions between thimbles

Quantum field theories with complex actions cannot be investigated using importance sampling due to the sign problem. One possible solution is to use the holomorphic gradient flow, a method we introduced related to the Lefschetz thimbles idea. In many cases the probability distribution generated by this method is multi-modal and standard Monte-Carlo sampling fails. We propose an algorithm that incorporates tempered proposals to solve this problem. We apply this algorithm to the 0+1 dimensional Thirring model at finite density for a parameter set where standard sampling fails and show that tempered proposals cure this problem.

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arXiv2017

Locality and Efficient Evaluation of Lattice Composite Fields: Overlap-Based Gauge Operators

We propose a novel general approach to locality of lattice composite fields, which in case of QCD involves locality in both quark and gauge degrees of freedom. The method is applied to gauge operators based on the overlap Dirac matrix elements, showing for the first time their local nature on realistic path-integral backgrounds. The framework entails a method for efficient evaluation of such non-ultralocal operators, whose computational cost is volume-indepenent at fixed accuracy, and only grows logarithmically as this accuracy approaches zero. This makes computation of useful operators, such as overlap-based topological density, practical. The key notion underlying these features is that of exponential insensitivity to distant fields, made rigorous by introducing the procedure of statistical regularization. The scales associated with insensitivity property are useful characteristics of non-local continuum operators.

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arXiv2017

Strange Quark Magnetic Moment of the Nucleon at Physical Point

We report a lattice QCD calculation of the strange quark contribution to the nucleon's magnetic moment and charge radius. This analysis presents the first direct determination of strange electromagnetic form factors including at the physical pion mass. We perform a model-independent extraction of the strange magnetic moment and the strange charge radius from the electromagnetic form factors in the momentum transfer range of $0.051 \,\text{GeV}^2 \lesssim Q^2 \lesssim 1.31 \,\text{GeV}^2 $. The finite lattice spacing and finite volume corrections are included in a global fit with $24$ valence quark masses on four lattices with different lattice spacings, different volumes, and four sea quark masses including one at the physical pion mass. We obtain the strange magnetic moment $G^s_M(0) = - 0.064(14)(09)\, μ_N$. The four-sigma precision in statistics is achieved partly due to low-mode averaging of the quark loop and low-mode substitution to improve the statistics of the nucleon propagator. We also obtain the strange charge radius $\langle r_s^2\rangle_E = -0.0043 (16)(14)\,$ $\text{fm}^2$.

hep-ph↗

arXiv2017

Glue spin and helicity in proton from lattice QCD

We report the first lattice QCD calculation of the glue spin in the nucleon. The lattice calculation is carried out with valence overlap fermions on 2+1 flavor DWF gauge configurations on four lattice spacings and four volumes including an ensemble with physical values for the quark masses. The glue spin $S_{G}$ in the Coulomb gauge in the $\overline{\text{MS}}$ scheme is obtained with the 1-loop perturbative matching. We find the results fairly insensitive to lattice spacing and quark masses. We also find that the proton momentum dependence of $S_G$ in the range $0\leq |\vec{p}| < 1.5$ GeV is very mild, and we determine it in the large momentum limit to be $S_{G}=0.251(47)(16)$ at the physical pion mass in the $\overline{\text{MS}}$ scheme at $μ^2=10$ GeV$^2$. If the matching procedure in large momentum effective theory is neglected, $S_G$ is equal to the glue helicity measured in high-energy scattering experiments.

hep-ph↗

arXiv2016

Monte Carlo calculations of the finite density Thirring model

We present results of the numerical simulation of the two-dimensional Thirring model at finite density and temperature. The severe sign problem is dealt with by deforming the domain of integration into complex field space. This is the first example where a fermionic sign problem is solved in a quantum field theory by using the holomorphic gradient flow approach, a generalization of the Lefschetz thimble method.

hep-lat↗

arXiv2016

$π$N and strangeness sigma terms at the physical point with chiral fermions

Lattice QCD calculations with chiral fermions of the $π$N sigma term $σ_{πN}$ and strangeness sigma term $σ_{sN}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $σ_{πN}=45.9(7.4)(2.8)$ MeV, with the disconnected insertion part contributing 20(12)(4)\%, and $σ_{sN}=40.2(11.7)(3.5)$ MeV, which is somewhat smaller than $σ_{πN}$. The ratio of the strange/light scalar matrix elements is $y$ = 0.09(3)(1).

hep-lat↗

arXiv2016

Rho resonance parameters from lattice QCD

We perform a high-precision calculation of the phase shifts for $π$-$π$ scattering in the I = 1, J = 1 channel in the elastic region using elongated lattices with two mass-degenerate quark favors ($N_f = 2$). We extract the $ρ$ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to $m_π = 226$MeV and $m_π = 315$MeV, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase-shifts around the resonance for both quark masses. We find that the extrapolated value, $m_ρ = 720(1)(15)$MeV, is significantly lower that the physical rho mass and we argue that this shift could be due to the absence of the strange quark in our calculation.

hep-lat↗

arXiv2016

Monte Carlo study of real time dynamics

Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from highly oscillatory phase of the path integral. In this letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced "contraction algorithm" to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and in principle applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.

hep-lat↗

arXiv2016

A study of symmetry breaking in a relativistic Bose gas using the contraction algorithm

A relativistic Bose gas at finite density suffers from a sign problem that makes direct numerical simulations not feasible. One possible solution to the sign problem is to re-express the path integral in terms of Lefschetz thimbles. Using this approach we study the relativistic Bose gas both in the symmetric phase (low-density) and the spontaneously broken phase (high-density). In the high-density phase we break explicitly the symmetry and determine the dependence of the order parameter on the breaking. We study the relative contributions of the dominant and sub-dominant thimbles in this phase. We find that the sub-dominant thimble only contributes substantially when the explicit symmetry breaking is small, a regime that is dominated by finite volume effects. In the regime relevant for the thermodynamic limit, this contribution is negligible.

hep-lat↗

arXiv2016

Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles

A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.

hep-lat↗

arXiv2016

Glue Spin of the Proton

We report the progress on the lattice QCD calculation of the glue spin contribution to proton spin. This calculation is carried out with valence overlap fermion on 2+1 flavor DWF gauge configurations at two lattice spacings with the momentum of the frame in the kinematic range $0\leq p^2 \leq 2$ GeV$^2$. A mild frame dependence is observed. The matching and mixing with large-momentum effective field theory are in progress. The unrenormalized result at $p^2=4$ GeV$^2$ with $O(a^2)$ correction gives $S_G$ = 0.13(3).

hep-ph↗

arXiv2016

Sign problem and Monte Carlo calculations beyond Lefschetz thimbles

We point out that Monte Carlo simulations of theories with severe sign problems can be profitably performed over manifolds in complex space different from the one with fixed imaginary part of the action. We describe a family of such manifolds that interpolate between the tangent space at one critical point, where the sign problem is milder compared to the real plane but in some cases still severe, and the union of relevant thimbles, where the sign problem is mild but a multimodal distribution function complicates the Monte Carlo sampling. We exemplify this approach using a simple 0 + 1 dimensional fermion model previously used on sign problem studies and show that it can solve the model for some parameter values where a solution using Lefshetz thimbles was elusive.

hep-lat↗

arXiv2016

Stochastic method with low mode substitution for nucleon isovector matrix elements

We introduce a stochastic sandwich method with low-mode substitution to evaluate the connected three-point functions. The isovector matrix elements of the nucleon for the axial-vector coupling $g_A^3$, scalar couplings $g_S^3$ and the quark momentum fraction $\langle x\rangle_{u -d}$ are calculated with overlap fermion on 2+1 flavor domain-wall configurations on a $24^3 \times 64$ lattice at $m_π = 330$ MeV with lattice spacing $a = 0.114$ fm.

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arXiv2015

Classifying the Phases of Gauge Theories by Spectral Density of Probing Chiral Quarks

We describe our recent proposal that distinct phases of gauge theories with fundamental quarks translate into specific types of low-energy behavior in Dirac spectral density. The resulting scenario is built around new evidence substantiating the existence of a phase characterized by bimodal (anomalous) density, and corresponding to deconfined dynamics with broken valence chiral symmetry. We argue that such anomalous phase occurs quite generically in these theories, including in "real world" QCD above the crossover temperature, and in zero-temperature systems with many light flavors.

hep-lat↗

arXiv2015

Resonance Parameters for the rho-meson from Lattice QCD

We present a calculation of the phase-shift for $π$-$π$ scattering in isospin-1, spin-1 channel in the elastic region. The mass and width of the rho resonance is extracted by fitting these phaseshifts. To vary the scattering momentum we employ asymmetric boxes. We use $N_f = 2$ nHYP-smeared clover fermions and generate two sets of ensembles with pion masses about 315MeV and 227MeV. To determine the phase shifts we compute the energy spectrum both for states at rest and boosted. We employ a variational analysis with interpolating fields including several $q$-$\bar{q}$ and $π$-$π$ interpolating fields with different scattering momenta.

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