Course Title

Large-scale Simulations for Lattice Quantum Chromodynamics

Course Code

COS 524

Course Type

Elective

Level

PhD

Instructor’s Name

Assoc. Prof. Giannis Koutsou (Lead Instructor), Dr. Simone Bacchio

ECTS

5

Lectures / week

1 (90 min. each)

Laboratories / week

1 (90 min. each)

Course Purpose and Objectives

The purpose of the course is to equip students with the necessary skills for carrying out large-scale simulations of physical systems, with focus on lattice gauge theories such as lattice Quantum Chromodynamics (QCD). The course will train PhD students to use state-of-the-art computational facilities and parallel software to study challenging physical systems such as those described by quantum fields and gauge theories. With focus on preparing PhD students for a research carrier in lattice Quantum Chromodynamics and related subjects, the course will include lectures and practical hands-on training with Hybrid Monte Carlo techniques, sparse linear solvers including Krylov methods, and noise reduction techniques.

Learning Outcomes

 By completing the course, students will have learned and applied techniques as used currently in state-of-the-art research in lattice QCD. These include:

-  Training on the use of High Performance Computing for lattice QCD, including implementation of own codes and training on the use of community software packages used on Peta- and Exa-scale computers.
-  Krylov methods and extensions to them (Conjugate Gradient, Generalized Minimal Residual, Multi-grid) used for inverting large sparse matrices such as the fermion matrix in lattice QCD
-  Simulation techniques, including Hybrid Monte Carlo (HMC) and variants used in lattice QCD (Polynomial HMC, Rational HMC)
-  Techniques used in calculating observables in lattice QCD, such as stochastic methods used for disconnected diagrams and hadron structure observables.

Prerequisites

 COS 522

Background Requirements

-  Knowledge of C/C++ and MPI for simulation codes
-  Knowledge of Python for data analysis
-  Background in quantum mechanics

Course Content

Week 1: Lattice formalism for gauge field theories: the Schwinger model

Week 2: Krylov methods for inverting sparse linear systems, such as conjugate gradient and multigrid algorithms

Week 3: Hybrid Monte Carlo (HMC) and extensions

Week 4: Fermions on the lattice, generalization of HMC and simulation of the Schwinger model

Week 5: Hadron masses using state-of-the-art lattice QCD codes; Practical exercises with introductory examples; Community codes with implementations for various architectures (CPUs, GPUs)

Week 6-7: Disconnected diagrams and noise reduction techniques. Application to hadronic structure observables.

Teaching Methodology

-  One 3-hour session per week including a lecture (c.a. 1.5 hours) and handson practical exercises applying the taught content (c.a. 1.5 hours)
-  After each session, students are expected to complete their practical exercise with remote assistance by lecturer
-  Students will be required to deliver two homework assignments, that will be requested after the third and fifth weeks.
-  A final project, report, and presentation by each student

Bibliography

-  Lattice Methods for Quantum Chromodynamics Thomas DeGrand, Carleton DeTar, https://doi.org/10.1142/6065
-  Quantum Fields on a Lattice, Istvan Montvay, Gernot Münster, Cambridge monographs on Mathematical Physics. Cambridge University Press, Cambridge (1994)

Assessment

-  Homework assignments
-  Final project   

Language

English