arXiv subjects

Michael Cheng

Publications and source records attributed to Michael Cheng.

16 recordsLinked to original sources

arXiv2018

Lattice $\phi^4$ Field Theory on Riemann Manifolds: Numerical Tests for the 2-d Ising CFT on $\mathbb{S}^2$

We present a method for defining a lattice realization of the $\phi^4$ quantum field theory on a simplicial complex in order to enable numerical computation on a general Riemann manifold. The procedure begins with adopting methods from traditional Regge Calculus (RC) and finite element methods (FEM) plus the addition of ultraviolet counter terms required to reach the renormalized field theory in the continuum limit. The construction is tested numerically for the two-dimensional $\phi^4$ scalar field theory on the Riemann two-sphere, $\mathbb{S}^2$, in comparison with the exact solutions to the two-dimensional Ising conformal field theory (CFT). Numerical results for the Binder cumulants (up to 12th order) and the two- and four-point correlation functions are in agreement with the exact $c = 1/2$ CFT solutions.

hep-lat↗

arXiv2016

Accelerating Lattice QCD Multigrid on GPUs Using Fine-Grained Parallelization

The past decade has witnessed a dramatic acceleration of lattice quantum chromodynamics calculations in nuclear and particle physics. This has been due to both significant progress in accelerating the iterative linear solvers using multi-grid algorithms, and due to the throughput improvements brought by GPUs. Deploying hierarchical algorithms optimally on GPUs is non-trivial owing to the lack of parallelism on the coarse grids, and as such, these advances have not proved multiplicative. Using the QUDA library, we demonstrate that by exposing all sources of parallelism that the underlying stencil problem possesses, and through appropriate mapping of this parallelism to the GPU architecture, we can achieve high efficiency even for the coarsest of grids. Results are presented for the Wilson-Clover discretization, where we demonstrate up to 10x speedup over present state-of-the-art GPU-accelerated methods on Titan. Finally, we look to the future, and consider the software implications of our findings.

hep-lat↗

arXiv2014

Improved Lattice Radial Quantization

Lattice radial quantization was proposed in a recent paper by Brower, Fleming and Neuberger[1] as a nonperturbative method especially suited to numerically solve Euclidean conformal field theories. The lessons learned from the lattice radial quantization of the 3D Ising model on a longitudinal cylinder with 2D Icosahedral cross-section suggested the need for an improved discretization. We consider here the use of the Finite Element Methods(FEM) to descretize the universally-equivalent $\phi^4$ Lagrangian on $\mathbb R \times \mathbb S^2$. It is argued that this lattice regularization will approach the exact conformal theory at the Wilson-Fisher fixed point in the continuum. Numerical tests are underway to support this conjecture.

hep-lat↗

arXiv2013

The QCD chiral transition, $\ua$ symmetry and the Dirac spectrum using domain wall fermions

We report on a study of the finite-temperature QCD transition region for temperatures between 139 and 196 MeV, with a pion mass of 200 MeV and two space-time volumes: $24^3\times8$ and $32^3\times8$, where the larger volume varies in linear size between 5.6 fm (at T=139 MeV) and 4.0 fm (at T=195 MeV). These results are compared with the results of an earlier calculation using the same action and quark masses but a smaller, $16^3\times8$ volume. The chiral domain wall fermion formulation with a combined Iwasaki and dislocation suppressing determinant ratio gauge action are used. This lattice action accurately reproduces the $\sua$ and $\ua$ symmetries of the continuum. Results are reported for the chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum. We find a pseudo-critical temperature, $T_c$, of approximately 165 MeV consistent with previous results and strong finite volume dependence below $T_c$. Clear evidence is seen for $\ua$ symmetry breaking above $T_c$ which is quantitatively explained by the measured density of near-zero modes in accordance with the dilute instanton gas approximation.

hep-lat↗

arXiv2012

The chiral transition and U(1)_A symmetry restoration from lattice QCD using Domain Wall Fermions

We present results on both the restoration of the spontaneously broken chiral symmetry and the effective restoration of the anomalously broken U(1)_A symmetry in finite temperature QCD at zero chemical potential using lattice QCD. We employ domain wall fermions on lattices with fixed temporal extent N_\tau = 8 and spatial extent N_\sigma = 16 in a temperature range of T = 139 - 195 MeV, corresponding to lattice spacings of a \approx 0.12 - 0.18 fm. In these calculations, we include two degenerate light quarks and a strange quark at fixed pion mass m_\pi = 200 MeV. The strange quark mass is set near its physical value. We also present results from a second set of finite temperature gauge configurations at the same volume and temporal extent with slightly heavier pion mass. To study chiral symmetry restoration, we calculate the chiral condensate, the disconnected chiral susceptibility, and susceptibilities in several meson channels of different quantum numbers. To study U(1)_A restoration, we calculate spatial correlators in the scalar and pseudo-scalar channels, as well as the corresponding susceptibilities. Furthermore, we also show results for the eigenvalue spectrum of the Dirac operator as a function of temperature, which can be connected to both U(1)_A and chiral symmetry restoration via Banks-Casher relations.

hep-lat↗

arXiv2012

The finite temperature phase transition from domain wall fermions

We present results on the finite temperature QCD transition with 2+1 flavors using Domain Wall Fermions (DWF) with the Dislocation Suppressing Determinant Ratio (DSDR). In particular, we discuss how the use of DSDR allows us to study the finite temperature transition at the coarse lattice spacings corresponding to the transition region (T = 139 - 195 MeV) with DWF at N_\tau = 8. The residual chiral symmetry breaking at these lattice spacings is sufficiently small so that a constant pion mass of m_\pi \approx 200 MeV is obtained in our calculations. The strange quark mass is set to near its physical value. We show results on the restoration of chiral symmetry and deconfinement at finite temperature.

hep-lat↗

arXiv2012

Approaching Conformality with Ten Flavors

We present first results for lattice simulations, on a single volume, of the low-lying spectrum of an SU(3) Yang-Mills gauge theory with ten light fermions in the fundamental representation. Fits to the fermion mass dependence of various observables are found to be globally consistent with the hypothesis that this theory is within or just outside the strongly-coupled edge of the conformal window, with mass anomalous dimension consistent with 1 over the range of scales simulated. We stress that we cannot rule out the possibility of spontaneous chiral-symmetry breaking at scales well below our infrared cutoff. We discuss important systematic effects, including finite-volume corrections, and consider directions for future improvement.

hep-ph↗

arXiv2012

WW Scattering Parameters via Pseudoscalar Phase Shifts

Using domain-wall lattice simulations, we study pseudoscalar-pseudoscalar scattering in the maximal isospin channel for an SU(3) gauge theory with two and six fermion flavors in the fundamental representation. This calculation of the S-wave scattering length is related to the next-to-leading order corrections to WW scattering through the low-energy coefficients of the chiral Lagrangian. While two and six flavor scattering lengths are similar for a fixed ratio of the pseudoscalar mass to its decay constant, six-flavor scattering shows a somewhat less repulsive next-to-leading order interaction than its two-flavor counterpart. Estimates are made for the WW scattering parameters and the plausibility of detection is discussed.

hep-lat↗

arXiv2010

Parity Doubling and the S Parameter Below the Conformal Window

We describe a lattice simulation of the masses and decay constants of the lowest-lying vector and axial resonances, and the electroweak S parameter, in an SU(3) gauge theory with $N_f = 2$ and 6 fermions in the fundamental representation. The spectrum becomes more parity doubled and the S parameter per electroweak doublet decreases when $N_f$ is increased from 2 to 6, motivating study of these trends as $N_f$ is increased further, toward the critical value for transition from confinement to infrared conformality.

hep-ph↗

arXiv2010

Lattice QCD and Hydro/Cascade Model of Heavy Ion Collisions

We report here on a recent lattice study of the QCD transition region at finite temperature and zero chemical potential using domain wall fermions (DWF). We also present a parameterization of the QCD equation of state obtained from lattice QCD that is suitable for use in hydrodynamics studies of heavy ion collisions. Finally, we show preliminary results from a multi-stage hydrodynamics/hadron cascade model of a heavy ion collision, in an attempt to understand how well the experimental data (e.g. particle spectra, elliptic flow, and HBT radii) can constrain the inputs (e.g. initial temperature, freezeout temperature, shear viscosity, equation of state) of the theoretical model.

nucl-th↗

arXiv2010

Lattice study of ChPT beyond QCD

We describe initial results by the Lattice Strong Dynamics (LSD) collaboration of a study into the variation of chiral properties of chiral properties of SU(3) Yang-Mills gauge theory as the number of massless flavors changes from $N_f = 2$ to $N_f = 6$, with a focus on the use of chiral perturbation theory.

hep-lat↗

arXiv2010

Toward TeV Conformality

We study the chiral condensate $<\barψ ψ>$ for an SU(3) gauge theory with $N_f$ massless Dirac fermions in the fundamental representation when $N_f$ is increased from 2 to 6. For $N_f=2$, our lattice simulations of $<\barψ ψ>/F^3$, where $F$ is the Nambu-Goldstone-boson decay constant, agree with the measured QCD value. For $N_f = 6$, this ratio shows significant enhancement, presaging an even larger enhancement anticipated as $N_f$ increases further, toward the critical value for transition from confinement to infrared conformality.

hep-ph↗

arXiv2008

QCD Thermodynamics with Domain Wall Fermions

We present our recent studies of the pseudo-critical temperature, $T_c$, of QCD using domain wall fermions. Domain wall fermions have the advantage that they preserve exact SU(2) chiral symmetry at finite lattice spacing in the limit that $L_s \to \infty$. The RBC Collaboration has performed a set of dynamical calculations at $L_s = 32$ and $N_t = 8$ using the Iwasaki gauge action with two light quarks ($m_l a = 0.003$) and one strange quark ($m_s a = 0.037$). A clear signal for the crossover transition can be seen in the light chiral susceptibility, as well as in the Wilson line. However, at $L_s = 32$, the residual chiral symmetry breaking is not yet fully under control. We also present preliminary results from the HotQCD Collaboration with $N_t = 8$ and $L_s = 96$, where the effects of the residual chiral symmetry breaking are reduced compared to $L_s = 32$.

hep-lat↗

arXiv2007

Charm Quarks and the QCD Equation of State

We present a study of the effect of charm quarks on the QCD equation of state using partially-quenched p4 charm quarks on a dynamically generated 2+1 flavor background, at zero chemical potential. We show preliminary results for the charm quark contribution to the energy density and pressure in the high temperature region ($T_c < T < 4 T_c$) and compare it to the free-field calculation. The charm quark mass is determined by measuring the charmonium spectrum.

hep-lat↗

arXiv2006

Analysis of the finite temperature transition for 3 flavor QCD using p4-improved staggered fermions

We present a calculation of the transition temperature for 3 flavor QCD using p4-improved staggered fermions with two different variants of fattened links. We examine various susceptibilities at two different values for the temporal extent - $N_t = 4$ and $N_t = 6$ - in the vicinity of the 3 flavor transition at vanishing chemical potential. For $N_t = 4$, we study bare quark masses in the range $m_qa = 0.005$ to $m_qa = 0.1$, and for $N_t = 6$, we use $m_qa = 0.02$ to $m_qa = 0.2$. We also calculate hadron masses and the static quark potential at zero temperature in order to set the scale for the transition temperature and to study quark mass and cut-off dependent scaling properties of the transition temperature. A comparison of the R Algorithm and the RHMC algorithm for finite-temperature simulations is also made

hep-lat↗

arXiv2005

Scaling test of the P4-improved staggered fermion action

We present a scaling study of the QCD spectrum using a smeared P4 staggered fermion formulation, in which three, five, and seven-link staples are added to reduce the effects of flavor symmetry breaking. These studies are performed on quenched lattices generated using the one-loop improved Symanzik gauge action, with Beta=10/g^2=7.40,7.75,8.00. The corresponding lattice spacings are a = .31 fm, .21 fm, and .14 fm. Particularly, we study the O(a^2) flavor symmetry violations in the pion spectrum as well as the scaling dependence of m_rho, measured in physical units, on lattice spacing. These results are compared against previous results for the Asqtad action.

hep-lat↗