Lee-Yang Zeros Analysis of Finite Density Lattice QCD

Crompton, P. R (2001) Lee-Yang Zeros Analysis of Finite Density Lattice QCD. PhD thesis, University of Glasgow.

Abstract

Recent results from four-fermion interaction models have suggested that new exotic phases form at finite baryon density which give rise to colour superconductivity. The main stumbling block in making a first principles lattice QCD measurement in this regime is that the introduction of the chemical potential makes the QCD lattice action complex, prohibiting naive probabilistic Monte Carlo methods for the evaluation of the functional integral. A re-weighting method developed in Glasgow makes use of ensembles generated at zero chemical potential but suffers from the pathologies common to re-weighting methods. This thesis describes two new methods developed for lattice measurements at finite baryon density, which we finally combine to give a resolution to the pathologies of the Glasgow re-weighting method in SU(3). Firstly we investigate SU(2) QCD at finite density, where we are free to vary the chemical potential we use to generate ensembles. In our measurements of the Lee-Yang zeros of the grand canonical partition function and related thermodynamic observables we find similar pathologies to SU(3). We attribute this to the normalisation in the reweighting method and ensemble-averaging of the polynomial expansion coefficients of the method. However, as we are able to vary the chemical potential in our SU(2) measurements we further establish that the ensemble-averaging of the polynomial coefficients are effected selectively in the expansion. By combining the expansion coefficients from different ensembles (through the ratio of the normalisations) we are thus able to alleviate the bias in our sampling. We then further develop this method for SU(3) with static quarks by generating a range of canonical ensembles which we combine with our new re-weighting approach. From our SU(2) measurements we establish the existence of a diquark superfluid at high densities and low temperatures. We also determine the position and order of the associated symmetry breaking transitions in the mass-chemical potential plane. From our measurements of static SU(3) we establish that the finite density transition at intermediate coupling is a first order percolation transition. Having addressed the pathologies of the re-weighting method in two nonabelian gauge field theories which are simpler to evaluate numerically, in future work SU(3) QCD can be evaluated at finite density.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Theoretical physics
• Date of Award: 2001
• Depositing User: Enlighten Team
• Unique ID: glathesis:2001-76091
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 19 Nov 2019 16:50
• Last Modified: 19 Nov 2019 16:50
• URI: https://theses.gla.ac.uk/id/eprint/76091