3 research outputs found
Beyond Complex Langevin Equations: a Progress Report
After a short review of one of proposals to avoid complex stochastic
processes in Complex Langevin studies, the recent progress in the former is
reported. In particular, the new developments allow now to construct positive
and normalizable representations for gaussian quantum mechanical, as well as
field theoretical, path integrals directly in the Minkowski time. A relation to
the idea of thimbles is also discussed.Comment: 7 pages, 2 figures, contribution to the Lattice2018 Symposiu
Constraints of kinematic bosonization in two and higher dimensions
Contrary to the common wisdom, local bosonizations of fermionic systems exist
in higher dimensions. Interestingly, resulting bosonic variables must satisfy
local constraints of a gauge type. They effectively replace long distance
exchange interactions. In this work we study in detail the properties of such a
system which was proposed a long time ago. In particular, dependence of the
constraints on lattice geometry and fermion multiplicity is further elaborated
and is now classified for all two dimensional, rectangular lattices with
arbitrary sizes. For few small systems the constraints are solved analytically
and the complete spectra of reduced spin hamiltonias are shown to agree with
the original fermionic ones. The equivalence is extended to fermions in an
external Wegner field. It is also illustrated by an explicit calculation
for a particular configuration of Wegner variables. Finally, a possible
connection with the recently proposed web of dualities is discussed.Comment: discussion of dualities and the outlook added, references updated, 18
pages, 1 figure, 5 table