Analytic continuation from imaginary to real chemical potential in two-color QCD

Abstract

The method of analytic continuation from imaginary to real chemical potential is one of the most powerful tools to circumvent the sign problem in lattice QCD. Here we test this method in a theory, two-color QCD, which is free from the sign problem. We find that the method gives reliable results, within appropriate ranges of the chemical potential, and that a considerable improvement can be achieved if suitable functions are used to interpolate data with imaginary chemical potential.

Analytic continuation of the critical line in 2-color QCD at nonzero temperature and density

“…In Ref. [11], in particular, a high-precision numerical analysis in SU(2) (or 2-color QCD) with n f £ 8 degenerate staggered fermions has shown that, for temperatures above the pseudo-critical one at zero chemical potential, the extrapolation to real µ improves considerably if ratio of polynomials are used instead of simple polynomials in interpolating the behavior with imaginary µ of some test observables, this validating a proposal formulated in Ref. [12].…”

“…A control on the systematics of the method of analytic continuation and possible insights for its improvement can be achieved by testing it in theories which do not suffer the sign problem, by direct comparison of the analytic continuation with Monte Carlo results obtained directly at real µ [4,9,10,11]. In Ref.…”

“…[11] to the study of the analytic continuation of the pseudo-critical line. The strategy is the following: § for several fixed values of the chemical potential, both real and imaginary, we determine the (pseudo-)critical β 's by looking for peaks in the susceptibilities of a given observable; § we interpolate the determinations of the critical β 's at imaginary chemical potential with an analytic function of µ, to be then extrapolated to real chemical potential; § we compare the extrapolation with the determinations of the critical β 's at real chemical potential.…”

Phase diagram of QCD with two degenerate staggered quarks

“…As a matter of fact, importance sampling requires positive weights in the partition function In the last few years we approached the sign problem by the method of analytic continuation [2][3][4]. To this purpose we started our investigations [5][6][7] from some special cases where Monte Carlo simulations are both feasible at real and at imaginary chemical potential. The reason was to have the possibility to test the results of the analytical continuation by means of direct simulations at real chemical potential.…”

Imaginary chemical potentials and the phase of the fermionic determinant

“…Various possibilities have been explored to circumvent the problem, like reweighting techniques [1,2,3], the use of an imaginary chemical potential either for analytic continuation [4,5,6,7,8,9,10] or for reconstructing the canonical partition function [11,12,13], Taylor expansion techniques [14,15] and non-relativistic expansions [16,17,18]. The same is not true in the case of a finite isospin density, i.e.…”