Se p 20 04 Testing new strategies in finite density

A new approach for non zero chemical potential simulations is tested in the Gross-Neveu model for infinite flavor number, where the critical line is reconstructed in a large µ/T interval. A comparison with results from standard imaginary chemical potential approach as well as first results for N f = 4 QCD are presented. Recently we proposed a new method for simulate systems at non zero chemical potential [1]. The starting point is to note that the temporal part of the Dirac operator (the one that contains the µ dependence) can be written as the sum of two contributions: the first, proportional to cosh(µ), multiplies an antihermitian operator, the second, proportional to sinh(µ), multiplies an hermitian operator. Since the spacial part of the fermionic operator is antihermitian too, we see that for non zero µ the Dirac matrix looses its global antihermiticity and this is the origin of the complex action problem. Clearly the imaginary chemical potential solves the problem: sinh(µ) gets an extra factor i and converts the corresponding operator to an antier-mitian one. Introducing an imaginary chemical potential we look for a critical line in the (β, iµ) plane to analytically continue in the (β, µ) one: in doing that we are forced to consider larger values of the physical temperature T than the ones of physical relevance. In our proposal we promote cosh(µ) and sinh(µ) to independent variables x and y and explore the phase structure as a function of such variables to recover the physical critical point along the line that corresponds to x = cosh(µ), y = sinh(µ). To do that we perform standard (i.e. with real and positive action) simulations at pure imaginary y and extend the results to real * Talk presented by A. Galante. y. This can be achieved in two different ways [1]. The first is to fix the inverse gauge coupling and (i) find the critical line in the (x, iy) plane, (ii) fit this line with an even polynomial of y, (iii) analytically continue the critical line to the (x, y) plane, (iv) from the intersection of the analytically continued critical line with the x 2 − y 2 = 1 line (which corresponds to real and positive values of µ) it is possible to read the critical value of µ. Working at fixed lattice temporal extent (N t) this is equivalent to do simulations at fixed T i.e. the …