arXiv subjects

Thomas Luu

Publications and source records attributed to Thomas Luu.

At least 55 records · Page 3Linked to original sources

arXiv2021

Nonperturbative Renormalization of the Quark Chromoelectric Dipole Moment with the Gradient Flow:Power Divergences

The CP-violating quark chromoelectric dipole moment (qCEDM) operator, contributing to the electric dipole moment (EDM), mixes under renormalization and particularly on the lattice with the pseudoscalar density. The mixing coefficient is power-divergent with the inverse lattice spacing squared, $1/a^2$, regardless of the lattice action used. We use the gradient flow to define a multiplicatively renormalized qCEDM operator and study its behavior at small flow time. We determine nonperturbatively the linearly divergent coefficient with the flow time, $1/t$, up to subleading logarithmic corrections, and compare it with the 1-loop perturbative expansion in the bare and renormalized strong coupling. We also discuss the O($a$) improvement of the qCEDM defined at positive flow time.

hep-lat↗

arXiv2021

Gell-Mann-Low criticality in neural networks

Criticality is deeply related to optimal computational capacity. The lack of a renormalized theory of critical brain dynamics, however, so far limits insights into this form of biological information processing to mean-field results. These methods neglect a key feature of critical systems: the interaction between degrees of freedom across all length scales, which allows for complex nonlinear computation. We present a renormalized theory of a prototypical neural field theory, the stochastic Wilson-Cowan equation. We compute the flow of couplings, which parameterize interactions on increasing length scales. Despite similarities with the Kardar-Parisi-Zhang model, the theory is of a Gell-Mann-Low type, the archetypal form of a renormalizable quantum field theory. Here, nonlinear couplings vanish, flowing towards the Gaussian fixed point, but logarithmically slowly, thus remaining effective on most scales. We show this critical structure of interactions to implement a desirable trade-off between linearity, optimal for information storage, and nonlinearity, required for computation.

cond-mat.dis-nn↗

arXiv2021

The Ising Model with Hybrid Monte Carlo

The Ising model is a simple statistical model for ferromagnetism. There are analytic solutions for low dimensions and very efficient Monte Carlo methods, such as cluster algorithms, for simulating this model in special cases. However most approaches do not generalise to arbitrary lattices and couplings. We present a formalism that allows one to apply Hybrid Monte Carlo (HMC) simulations to the Ising model, demonstrating how a system with discrete degrees of freedom can be simulated with continuous variables. Because of the flexibility of HMC, our formalism is easily generalizable to arbitrary modifications of the model, creating a route to leverage advanced algorithms such as shift preconditioners and multi-level methods, developed in conjunction with HMC.

physics.comp-ph↗

arXiv2021

Simulating both parity sectors of the Hubbard Model with Tensor Networks

Tensor networks are a powerful tool to simulate a variety of different physical models, including those that suffer from the sign problem in Monte Carlo simulations. The Hubbard model on the honeycomb lattice with non-zero chemical potential is one such problem. Our method is based on projected entangled pair states (PEPS) using imaginary time evolution. We demonstrate that it provides accurate estimators for the ground state of the model, including cases where Monte Carlo simulations fail miserably. In particular it shows near to optimal, that is linear, scaling in lattice size. We also present a novel approach to directly simulate the subspace with an odd number of fermions. It allows to independently determine the ground state in both sectors. Without a chemical potential this corresponds to half filling and the lowest energy state with one additional electron or hole. We identify several stability issues, such as degenerate ground states and large single particle gaps, and provide possible fixes.

physics.comp-ph↗

arXiv2020

The Semimetal-Mott Insulator Quantum Phase Transition of the Hubbard Model on the Honeycomb Lattice

We take advantage of recent improvements in the grand canonical Hybrid Monte Carlo algorithm, to perform a precision study of the single-particle gap in the hexagonal Hubbard model, with on-site electron-electron interactions. After carefully controlled analyses of the Trotter error, the thermodynamic limit, and finite-size scaling with inverse temperature, we find a critical coupling of $U_c/κ=3.834(14)$ and the critical exponent $zν=1.185(43)$. Under the assumption that this corresponds to the expected anti-ferromagnetic Mott transition, we are also able to provide a preliminary estimate $β=1.095(37)$ for the critical exponent of the order parameter. We consider our findings in view of the $SU(2)$ Gross-Neveu, or chiral Heisenberg, universality class. We also discuss the computational scaling of the Hybrid Monte Carlo algorithm, and possible extensions of our work to carbon nanotubes, fullerenes, and topological insulators.

cond-mat.str-el↗

arXiv2020

Misconceptions on Effective Field Theories and spontaneous symmetry breaking: Response to Ellis' article

In an earlier paper~\cite{Luu:2019jmb} we discussed emergence from the context of effective field theories, particularly as related to the fields of particle and nuclear physics. We argued on the side of reductionism and weak emergence. George Ellis has critiqued our exposition in~\cite{Ellis:2020vij}, and here we provide our response to his critiques. Many of his critiques are based on incorrect assumptions related to the formalism of effective field theories and we attempt to correct these issues here. We also comment on other statements made in his paper. Important to note is that our response is to his critiques made in archive versions arXiv:2004.13591v1-5 [physics.hist-ph]. That is, versions 1-5 of this archive post. Version 6 has similar content as versions 1-5, but versions 7-9 are seemingly a different paper altogether (even with a different title).

physics.hist-ph↗

arXiv2020

Leveraging Machine Learning to Alleviate Hubbard Model Sign Problems

Lattice Monte Carlo calculations of interacting systems on non-bipartite lattices exhibit an oscillatory imaginary phase known as the phase or sign problem, even at zero chemical potential. One method to alleviate the sign problem is to analytically continue the integration region of the state variables into the complex plane via holomorphic flow equations. For asymptotically large flow times the state variables approach manifolds of constant imaginary phase known as Lefschetz thimbles. However, flowing such variables and calculating the ensuing Jacobian is a computationally demanding procedure. In this paper we demonstrate that neural networks can be trained to parameterize suitable manifolds for this class of sign problem and drastically reduce the computational cost. We apply our method to the Hubbard model on the triangle and tetrahedron, both of which are non-bipartite. At strong interaction strengths and modest temperatures the tetrahedron suffers from a severe sign problem that cannot be overcome with standard reweighting techniques, while it quickly yields to our method. We benchmark our results with exact calculations and comment on future directions of this work.

cond-mat.str-el↗

arXiv2020

Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral

In the Kohn-Sham orbital basis imaginary-time path integral for electrons in a semiconductor nanoparticle has a mild Fermion sign problem and is amenable to evaluation by the standard stochastic methods. This is evidenced by the simulations of silicon hydrogen-passivated nanocrystals, such as $Si_{35}H_{36},~Si_{87}H_{76},~Si_{147}H_{100}$ and $Si_{293}H_{172},$ which contain $176$ to $1344$ valence electrons and range in size $1.0 - 2.4~nm$, utilizing the output of density functional theory simulations. We find that approximating Fermion action with just the leading order polarization term results in a positive-definite integrand in the functional integral, and that it is a good approximation of the full action. We compute imaginary-time electron propagators in these nanocrystals and extract the energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of high-precision calculations using $G_0W_0$ technique. This formalism can be extended to calculations of more complex excited states, such as excitons and trions.

cond-mat.str-el↗

arXiv2020

Avoiding Ergodicity Problems in Lattice Discretizations of the Hubbard Model

The Hubbard model arises naturally when electron-electron interactions are added to the tight-binding descriptions of many condensed matter systems. For instance, the two-dimensional Hubbard model on the honeycomb lattice is central to the ab initio description of the electronic structure of carbon nanomaterials, such as graphene. Such low-dimensional Hubbard models are advantageously studied with Markov chain Monte Carlo methods, such as Hybrid Monte Carlo (HMC). HMC is the standard algorithm of the lattice gauge theory community, as it is well suited to theories of dynamical fermions. As HMC performs continuous, global updates of the lattice degrees of freedom, it provides superior scaling with system size relative to local updating methods. A potential drawback of HMC is its susceptibility to ergodicity problems due to so-called exceptional configurations, for which the fermion operator cannot be inverted. Recently, ergodicity problems were found in some formulations of HMC simulations of the Hubbard model. Here, we address this issue directly and clarify under what conditions ergodicity is maintained or violated in HMC simulations of the Hubbard model. We study different lattice formulations of the fermion operator and provide explicit, representative calculations for small systems, often comparing to exact results. We show that a fermion operator can be found which is both computationally convenient and free of ergodicity problems.

cond-mat.str-el↗

arXiv2020

Renormalization of a Contact Interaction on a Lattice

Contact interactions can be used to describe a system of particles at unitarity, contribute to the leading part of nuclear interactions and are numerically non-trivial because they require a proper regularization and renormalization scheme. We explain how to tune the coefficient of a contact interaction between non-relativistic particles on a discretized space in 1, 2, and 3 spatial dimensions such that we can remove all discretization artifacts. By taking advantage of a latticized Lüscher zeta function, we can achieve a momentum-independent scattering amplitude at any finite lattice spacing.

hep-lat↗

arXiv2019

On the Topic of Emergence from an Effective Field Theory Perspective

Effective Field Theories have been used successfully to provide a "bottom-up" description of phenomena whose intrinsic degrees of freedom behave at length scales far different from their effective degrees of freedom. An example is the emergent phenomenon of bound nuclei, whose constituents are neutrons and protons, which in turn are themselves composed of more fundamental particles called quarks and gluons. In going from a fundamental description that utilizes quarks and gluons to an effective field theory description of nuclei, the length scales traversed span at least two orders of magnitude. In this article we provide an Effective Field Theory viewpoint on the topic of emergence, arguing on the side of reductionism and weak emergence. We comment on Anderson's interpretation of constructionism and its connection to strong emergence.

physics.hist-ph↗

arXiv2019

Confirming the Existence of the strong CP Problem in Lattice QCD with the Gradient Flow

We calculate the electric dipole moment of the nucleon induced by the QCD theta term. We use the gradient flow to define the topological charge and use $N_f = 2+1$ flavors of dynamical quarks corresponding to pion masses of $700$, $570$, and $410$ MeV, and perform an extrapolation to the physical point based on chiral perturbation theory. We perform calculations at $3$ different lattice spacings in the range of $0.07~{\rm fm} < a < 0.11$ fm at a single value of the pion mass, to enable control on discretization effects. We also investigate finite size effects using $2$ different volumes. A novel technique is applied to improve the signal-to-noise ratio in the form factor calculations. The very mild discretization effects observed suggest a continuum-like behavior of the nucleon EDM towards the chiral limit. Under this assumption our results read $d_{n}=-0.00152(71)\ \barθ e~\text{fm}$ and $d_{p}=0.0011(10)\ \barθ e~\text{fm}$. Assuming the theta term is the only source of CP violation, the experimental bound on the neutron electric dipole moment limits $\left|\barθ\right| < 1.98\times 10^{-10}$ ($90\%$ CL). A first attempt at calculating the nucleon Schiff moment in the continuum resulted in $S_{p} = 0.50(59)\times 10^{-4}\ \barθ e~\text{fm}^3$ and $S_{n} = -0.10(43)\times 10^{-4}\ \barθ e~\text{fm}^3$.

hep-lat↗

arXiv2019

Accelerating Hybrid Monte Carlo simulations of the Hubbard model on the hexagonal lattice

We present different methods to increase the performance of Hybrid Monte Carlo simulations of the Hubbard model in two-dimensions. Our simulations concentrate on a hexagonal lattice, though can be easily generalized to other lattices. It is found that best results can be achieved using a flexible GMRES solver for matrix inversions and the second order Omelyan integrator with Hasenbusch acceleration on different time scales for molecular dynamics. We demonstrate how an arbitrary number of Hasenbusch mass terms can be included into this geometry and find that the optimal speed depends weakly on the choice of the number of Hasenbusch masses and their values. As such, the tuning of these masses is amenable to automization and we present an algorithm for this tuning that is based on the knowledge of the dependence of solver time and forces on the Hasenbusch masses. We benchmark our algorithms to systems where direct numerical diagonalization is feasible and find excellent agreement. We also simulate systems with hexagonal lattice dimensions up to $102\times 102$ and $N_t=64$. We find that the Hasenbusch algorithm leads to a speed up of more than an order of magnitude.

cond-mat.str-el↗

arXiv2018

Three neutrons from Lattice QCD

We present a study on ab-initio calculations of three-neutron correlators from Lattice QCD. We extend the method of baryon blocks to systems of three spacially displaced baryons. This allows the measurement of three-neutron $p$-wave correlators with total spin $S=1/2$ and $3/2$. In addition, we use automatic code generation that has high flexibility and allows for easy inclusion of additional channels in the future while optimizing the evaluation of contractions. Our measurements were performed on a newly generated $96\times 48^3$ Clover-Wilson gauge field ensemble with $m_π \approx 370\,\text{MeV}$. We present preliminary results of our calculations of one pion and nucleon as well as two nucleon ($2N$) and three neutron ($3n$) correlators.

hep-lat↗

arXiv2018

Towards a determination of the nucleon EDM from the quark chromo-EDM operator with the gradient flow

In this proceedings, we lay the foundation for computing the contribution of quark chromo-electric dipole moment (qCEDM) operator to the nucleon electric dipole moment. By applying the gradient flow technique, we can parameterize the renormalization and operator mixing issues associated with the qCEDM operator on the lattice. As the nucleon mixing angle $α_N$ is a key component for determining the neutron and proton electric dipole moments induced by the qCEDM operator, we present the formalism and preliminary results for $α_N$ with respect to the gradient flow time $t_f$. The results are computed on $N_f=2+1$ Wilson-clover lattices provided by PACS-CS. The 3 ensembles have lattice spacing values of $a=\lbrace 0.1095,\,0.0936,\,0.0684\rbrace $fm, whilst keeping a similar $m_π\approx701$MeV, and a fixed box size of $L\approx1.9$fm.

hep-lat↗

arXiv2018

Improvements to Nucleon Matrix Elements within a $θ$ Vacuum from Lattice QCD

Using the gradient flow, we calculated the nucleon mixing angle $α_{N}$ and the nucleon electric dipole moment (EDM) induced by the QCD $θ$-term. To do so, we computed the topological charge, and the nucleon two-point and three-point correlation functions. The purpose of these proceedings is to explore how the topological charge density interacts with the nucleon interpolation operators. By understanding this relation, we can try to suppress noise contributions to the $α_{N}$ and EDM signals by selecting specific regions where the signal dominates. Using gauge fields provided by PACS-CS at $N_{f}=2+1$, a first collection of ensembles were selected at a fixed lattice spacing $a=0.0907$ fm ($β=1.90$), fixed dimensions $32^{3}\times 64$ and varying $m_π\approx\lbrace 411,\,570,\,701\rbrace$ MeV. A second collection was selected at fixed $m_π\approx701$ MeV, fixed box size of $L\approx1.9$ fm and varying $a=\lbrace 0.1215,\,0.0980,\,0.0685\rbrace $ fm.

hep-lat↗

arXiv2018

Quasi-Parton Distribution Function in Lattice Perturbation Theory

Large momentum effective field theory provides a new direction for lattice QCD calculations of hadronic structure functions, such as parton distribution functions (PDFs), meson distribution amplitudes, and so on, directly with $x$-dependence. In the framework of Lattice Perturbation Theory (LPT), we compute the one-loop quark-in-quark quasi-PDF with the naïve fermion action ($\tilde{q}^{\mathrm{nv}}$) and quasi-PDF with Wilson-Clover action ($\tilde{q}^{\mathrm{WC}}$) and show that $\tilde{q}^{\mathrm{nv}}$ reduces to the continuum quasi-PDF in the continuum limit. We point out, however, that the continuum limit and massless quark limit do not commute. We find that the condition to recover the same collinear divergence that the quasi-PDF has in continuum QCD is $aP_3^2\approx m$ and $m\ll P_3$, while the condition to fully recover the continuum quasi-PDF is $aP_{3}^{2}\ll m\ll P_{3}$, where $P_3$ is the momentum in the direction of the quark's motion (longitudinal direction). These two conditions are based on perturbation calculations and should not be applied to non-perturbative calculations because the non-perturbative effects cure the collinear divergence. The correction to the quasi-PDF using the naïve fermion action is due to the Wilson term and can be viewed as an $\mathcal{O}\left(a^{1}\right)$ correction. For nonzero $r$, the $\mathcal{O}\left(a^{1}\right)$ corrections are subsequently mixed with the quasi-PDF using the naïve fermion action.

hep-ph↗

arXiv2017

Electric Dipole Moment Results from lattice QCD

We utilize the gradient flow to define and calculate electric dipole moments induced by the strong QCD $θ$-term and the dimension-6 Weinberg operator. The gradient flow is a promising tool to simplify the renormalization pattern of local operators. The results of the nucleon electric dipole moments are calculated on PACS-CS gauge fields (available from the ILDG) using $N_{f}=2+1$, of discrete size $32^{3}\times 64$ and spacing $a \simeq 0.09$ fm. These gauge fields use a renormalization-group improved gauge action and a non-perturbatively $O(a)$ improved clover quark action at $β= 1.90$, with $c_{SW} = 1.715$. The calculation is performed at pion masses of $m_π \simeq 411,701$ MeV.

hep-lat↗