Extracting Physics from Topologically Frozen Markov Chains

Abstract

In Monte Carlo simulations with a local update algorithm, the auto-correlation with respect to the topological charge tends to become very long. In the extreme case one can only perform reliable measurements within fixed sectors. We investigate approaches to extract physical information from such topologically frozen simulations. Recent results in a set of σ -models and gauge theories are encouraging. In a suitable regime, the correct value of some observable can be evaluated to a good accuracy. In addition there are ways to estimate the value of the topological susceptibility.

Metadynamics surfing on topology barriers: the CP N−1 case

“…In the recent literature the problem of very long autocorrelation times and of the theoretical control over the systematic error in numerical simulations has been addressed in a series of papers [2,3,5,[7][8][9][10] and several solutions to the topological critical slowing down have been proposed [4,6,[19][20][21][22][23][24][25].…”

Combining ordinary and topological finite volume effects for fixed topology simulations

“…This method has been tested in Refs. [7][8][9][10][11][12][13][14][15][16][17][18] with success. The static potential Vq q,Q,V has been computed for different separations (r = 1 .…”

“…In σ -model studies, also χt could be evaluated well in this manner [13,16]. In 4d Yang-Mills theory, however, the determination of χt turned out to be plagued by large statistical errors.…”

“…The method we are interested in is based on a relation between the physical mass of a hadron and its fixed topology counterpart [5][6][7]. This method has already been tested with success in various models [8][9][10][11][12][13][14][15][16][17]. So far ordinary finite volume effects have been neglected.…”

Hadron masses from fixed topological simulations: discussion of parity partners and SU(2) Yang-Mills results.

“…The calculations from these papers have been extended in [5,6] by including fixed topology correction terms up to O(1/V 3 ). Tests and applications of these equations to quantum mechanics, 2d O (3) model and the Schwinger model can be found in [7,8,9,10,5,11,6,12]. Here we discuss parity mixing due to topology fixing and its consequences, when extracting hadron masses from fixed topology simulations.…”