Convergent series for polynomial lattice models with complex actions

Abstract

Lattice models with complex actions are important for the understanding of matter at finite densities, but not accessible by the standard Monte Carlo techniques due to the sign problem. Here we derive a new approach for avoiding the complex action/sign problem, by extending the method of convergent series with a non-Gaussian initial approximation. The main features of the new series are demonstrated on the example of the two dimensional oscillating integral.

Self-similar extrapolation in quantum field theory

“…More complicated forms for the initial approximation can also be chosen. For example, one can start perturbation theory with a non-Gaussian approximation [23][24][25][26] or one can use for the initial approximation nontrivial Hamiltonians, as in the method of Hamiltonian envelopes [27].…”

Infinite lattice models by an expansion with a non-Gaussian initial approximation

“…Second, Monte Carlo simulations are based on the probabilistic interpretations of the Boltzmann weight and, therefore, are not applicable to systems, described by complex actions. In the current work, we continue studying the convergent series (CS) method [1,2,3], which provides new possible ways for bypassing the sign problem [4] and for accessing the direct computations in the infinite volume limit, focusing on the latter issue.…”

“…In recent works [18,3,4] the convergent series for the real and certain complex action models defined on finite lattices was constructed in a rigorous way. It was shown there that the application of the dimensional regularization can be interpreted as an additional re-summation procedure accelerating the series convergence.…”