[Paper Review] Charged Hadron Properties from Lattice QCD in Magnetic Fields

Brian C. Tiburzi, S. O. Vayl|arXiv (Cornell University)|Oct 16, 2012

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper introduces a coordinate-space projection technique to isolate the lowest Landau level in lattice QCD simulations of charged spinless hadrons under weak magnetic fields, enabling accurate computation of magnetic moments and polarizabilities. By leveraging continuum wave functions and accounting for discretization and finite-volume effects via perturbative and magnetic translational invariance methods, it demonstrates that quantized magnetic flux can induce severe volume artifacts independent of lattice size.

ABSTRACT

By analyzing the external field dependence of correlation functions, the magnetic properties of hadrons can be determined using lattice QCD in magnetic fields. To compute the magnetic moments and polarizabilities of charged hadrons, for example, one requires sufficiently weak magnetic fields. Such field strengths, however, lead to closely spaced Landau levels that are not straightforwardly resolved using standard lattice spectroscopy. Focusing on charged spinless hadrons, we introduce a simple projection technique that can be used to isolate the lowest Landau level. As the technique requires the explicit coordinate-space wave-function, we investigate the extent to which the continuum, infinite volume wave-function can be employed. We find that, in practice, the effects of discretization can be handled using a perturbative expansion about the continuum. Finite volume corrections are taken into account by using the discrete magnetic translational invariance of the torus. We show that quantized magnetic fields can lead to pernicious volume effects which depend on the magnetic flux quantum, rather than on the lattice volume.

Motivation & Objective

• To compute magnetic moments and polarizabilities of charged hadrons in lattice QCD under weak external magnetic fields.
• To overcome the challenge of closely spaced Landau levels in weak fields that hinder standard lattice spectroscopy.
• To develop a projection technique that isolates the lowest Landau level using explicit coordinate-space wave functions.
• To assess the validity of using continuum wave functions in place of discretized ones for such projections.
• To quantify finite-volume corrections arising from discrete magnetic translational invariance on the torus.

Proposed method

• Introduces a coordinate-space projection operator that isolates the lowest Landau level in the hadronic correlation function.
• Employs continuum wave functions as a proxy for discretized lattice wave functions, with corrections applied via perturbative expansion.
• Accounts for discretization effects by expanding in the lattice spacing around the continuum limit.
• Incorporates finite-volume corrections using the discrete magnetic translational invariance of the torus geometry.
• Identifies and analyzes volume effects induced by quantized magnetic flux, distinct from geometric lattice volume.

Experimental results

Research questions

• RQ1 Can a coordinate-space projection technique effectively isolate the lowest Landau level in weak magnetic fields for charged spinless hadrons?
• RQ2 How accurate is the use of continuum wave functions in place of lattice wave functions for such projections?
• RQ3 To what extent do discretization effects distort the extraction of magnetic properties in lattice QCD?
• RQ4 How do finite-volume effects from magnetic translational invariance influence the computed hadronic properties?
• RQ5 Do volume effects from quantized magnetic flux dominate over standard finite-size effects in lattice simulations?

Key findings

• The proposed projection technique successfully isolates the lowest Landau level in weak magnetic fields, enabling reliable extraction of hadronic magnetic properties.
• Discretization effects can be systematically handled using a perturbative expansion about the continuum limit, validating the use of continuum wave functions.
• Finite-volume corrections are effectively captured by enforcing discrete magnetic translational invariance on the torus.
• Quantized magnetic fields induce volume effects that depend on the magnetic flux quantum, not on the spatial lattice volume, indicating a novel and potentially problematic finite-size artifact.
• The method provides a viable pathway to compute magnetic moments and polarizabilities of charged hadrons in lattice QCD at physically relevant field strengths.