Color superconductivity on the lattice -- analytic predictions from QCD in a small box

Abstract

We investigate color superconductivity on the lattice using the gap equation for the Cooper pair condensate. The weak coupling analysis is justified by choosing the physical size of the lattice to be smaller than the QCD scale, while keeping the aspect ratio of the lattice small enough to suppress thermal excitations. In the vicinity of the critical coupling constant that separates the superconducting phase and the normal phase, the gap equation can be linearized, and by solving the corresponding eigenvalue problem, we obtain the critical point and the Cooper pair condensate without assuming its explicit form. The momentum components of the condensate suggest spatially isotropic s-wave superconductivity with Cooper pairs formed by quarks near the Fermi surface. The chiral symmetry in the massless limit is spontaneously broken by the Cooper pair condensate, which turns out to be dominated by the scalar and the pseudo-scalar components. Our results provide useful predictions, in particular, for future lattice simulations based on methods to overcome the sign problem such as the complex Langevin method.

arXiv comment30 pages, 15 figures, 1 table, v2: A.3 modified, Ref. [57] added

References in corpus (37)

• Color superconductivity in dense quark matter
• QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
• The phase diagram of dense QCD
• Tensor renormalization group approach to 2D classical lattice models
• High density QCD on a Lefschetz thimble?
• The Complex Langevin method: When can it be trusted?
• Complex Langevin: Etiology and Diagnostics of its Main Problem
• Simulating full QCD at nonzero density using the complex Langevin equation
• Patterns of Symmetry Breaking in QCD at High Baryon Density
• Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
• Hybrid Monte Carlo on Lefschetz Thimbles -- A study of the residual sign problem
• Quark Hadron Continuity in QCD with one Flavor
• Finite-density lattice QCD and sign problem: current status and open problems
• The argument for justification of the complex Langevin method and the condition for correct convergence
• Single color and single flavor color superconductivity
• When the Transition Temperature in Color Superconductors is Not Like in BCS Theory
• Toward solving the sign problem with path optimization method
• The Transition Temperature to the Superconducting Phase of QCD at High Baryon Density
• Finite-Density Monte Carlo Calculations on Sign-Optimized Manifolds
• Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion
• Complex Langevin dynamics for dynamical QCD at nonzero chemical potential: a comparison with multi-parameter reweighting
• Parallel tempering algorithm for integration over Lefschetz thimbles
• Phase transitions in neutron stars and their links to gravitational waves
• Anisotropic admixture in color-superconducting quark matter
• Colour superconductivity in finite systems
• Application of neural network to sign problem via path optimization method
• Justification of the complex Langevin method with the gauge cooling procedure
• Calculating the EoS of the dense quark-gluon plasma using the Complex Langevin equation
• Applying Complex Langevin Simulations to Lattice QCD at Finite Density
• QCD with Chemical Potential in a Small Hyperspherical Box
• Worldvolume approach to the tempered Lefschetz thimble method
• Complex Langevin calculations in finite density QCD at large $\mu /T$ with the deformation technique
• Deconfinement transition line with the Complex Langevin equation up to $\mu /T\sim 5$
• Evidence for BCS Diquark Condensation in the 3+1d Lattice NJL Model
• Backpropagating Hybrid Monte Carlo algorithm for fast Lefschetz thimble calculations
• Complex Langevin calculations in QCD at finite density
• Numerical Study of the Two Color Attoworld

Cited by in corpus (3)

• Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice
• On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density
• The dynamics of zero modes in lattice gauge theory -- difference between SU(2) and SU(3) in 4D