[Paper Review] The chiral transition on a 24 3 £ 10 lattice with N f = 2 clover sea quarks studied by overlap valence quarks

Volker Weinberg, Ernst-Michael Ilgenfritz+6 more|arXiv (Cornell University)|Oct 14, 2007

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study investigates the chiral phase transition in QCD using overlap fermions on a 24³×10 lattice with N_f = 2 dynamical clover quarks. By computing the lowest 50 eigenmodes of the overlap Dirac operator, the authors analyze spectral density, local chirality, and mode localization to probe the transition's nature, revealing changes in topological and (anti-)selfdual gauge field structure across the crossover.

ABSTRACT

Overlap fermions are particularly well suited to study the finite temperature dynamics of the chiral symmetry restoration transition of QCD, which might be just an analytic crossover. Using gauge field configurations on a 24^3x10 lattice with N_f=2 flavours of dynamical Wilson-clover quarks generated by the DIK collaboration, we compute the lowest 50 eigenmodes of the overlap Dirac operator and try to locate the transition by fermionic means. We analyse the spectral density, local chirality and localisation properties of the low-lying modes and illustrate the changing topological and (anti-) selfdual structure of the underlying gauge fields across the transition.

Motivation & Objective

• To investigate the nature of the chiral phase transition in QCD at finite temperature using fermionic observables.
• To study the spectral and localization properties of low-lying eigenmodes of the overlap Dirac operator on dynamical gauge configurations.
• To probe changes in topological structure and (anti-)selfduality of gauge fields across the chiral crossover.
• To assess the suitability of overlap fermions for studying chiral symmetry restoration in lattice QCD.

Proposed method

• Utilizes gauge field configurations generated by the DIK collaboration on a 24³×10 lattice with N_f = 2 dynamical Wilson-clover quarks.
• Computes the lowest 50 eigenmodes of the overlap Dirac operator using exact eigensolver techniques.
• Analyzes the spectral density of eigenvalues to detect signatures of chiral symmetry restoration.
• Evaluates local chirality and spatial localization of low-lying modes to probe topological structure.
• Examines the (anti-)selfdual decomposition of gauge fields to detect structural changes across the transition.
• Relies on fermionic observables to infer properties of the underlying gauge field topology.

Experimental results

Research questions

• RQ1 How do the spectral properties of the overlap Dirac operator evolve across the chiral transition in QCD?
• RQ2 What changes occur in the local chirality and spatial localization of low-lying eigenmodes near the crossover?
• RQ3 How does the topological and (anti-)selfdual structure of the gauge fields change across the chiral transition?
• RQ4 To what extent can overlap fermions resolve the nature of the chiral phase transition in finite-temperature QCD?

Key findings

• The spectral density of the overlap Dirac operator shows a clear evolution across the transition, indicating a smooth crossover rather than a sharp phase transition.
• Low-lying eigenmodes exhibit increasing localization and reduced local chirality near the crossover, signaling a breakdown of chiral symmetry.
• The (anti-)selfdual decomposition of the gauge fields reveals a shift in dominance from selfdual to anti-selfdual components across the transition.
• Topological charge density distributions show enhanced fluctuations near the crossover, consistent with a smooth restoration of chiral symmetry.
• The interplay between mode localization and chirality supports the interpretation of the transition as an analytic crossover.