Sign problem

At low temperatures and for non-zero chemical potential /r, as relevant for dense stars, Monte-Carlo calculations are, however, hampered by the sign problem. Several approaches to cope with it have been proposed only recently. 

Keywords effective theory, dense QCD, color superconductivity, sign problem... 

With the help of previous two examples, we propose a new way of simulating dense QCD, which evades the sign problem. Integrating out quarks far from the Fermi surface, which are suppressed by 1 //j at high density, we can expand the determinant of Dirac operator at finite density,... 

For importance sampling in the lattice simulation, one can use the leading part of the determinant, [real, positive]. This proposal provides a nontrivial check on analytic results at asymptotic density and can be used to extrapolate to intermediate density. Furthermore, it can be applied to condensed matter systems like High-Tc superconductors, which in general suffers from a sign problem. 

In order to study the origin of the deviations observed, we first consider the statistical convergence of the QCL data. As a representative example. Fig. 14 shows the absolute error of the adiabatic population as a function of the number of iterations N—that is, the number of initially starting random walkers. The data clearly reveal the well-known 1/Vn convergence expected for Monte Carlo sampling. We also note the occurrence of the sign problem mentioned above. It manifests itself in the fact that the number of iterations increases almost exponentially with propagation time While at time t = 10 fs only 200 iterations are sufficient to obtain an accuracy of 2%, one needs N = 10 000 at t = 50 fs. 

The second integral is one of those shown in Table 2.2 and is equal to (1/2)(7r/p2)1/2. As noted above, (d2 idr)m is negative since the point of evaluation is a maximum therefore (p2) is positive, and there is no sign problem with the square root. The fact that the function in question drops off sharply with distance from the maximum implies that the first integral can be written as... 

A general solution of the fermion sign problem is still unavailable, although interesting algorithms have been proposed [11]. A class of methods try to... 

A. Alavi and A.J.W. Thom Path Resummations and the Fermion Sign Problem, Lect. Notes Phys. 703, 685-704 (2006)... 

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