Complex Langevin dynamics for chiral random matrix theory

TY - JOUR

T1 - Complex Langevin dynamics for chiral random matrix theory

AU - Møllgaard, Anders Edsberg

AU - Splittorff, Kim

PY - 2013/12/9

Y1 - 2013/12/9

N2 - We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.

AB - We apply complex Langevin dynamics to chiral random matrix theory at nonzero chemical potential. At large quark mass, the simulations agree with the analytical results while incorrect convergence is found for small quark masses. The region of quark masses for which the complex Langevin dynamics converges incorrectly is identified as the region where the fermion determinant frequently traces out a path surrounding the origin of the complex plane during the Langevin flow. This links the incorrect convergence to an ambiguity in the Langevin force due to the presence of the logarithm of the fermion determinant in the action.

M3 - Journal article

SN - 2470-0010

VL - 88

JO - Physical Review D

JF - Physical Review D

IS - 11

M1 - 116007

ER -