This repository contains code which calculates the number of physical states in small gauge lattices with discrete non-abelian groups.
The main program is numeric.exp.na.HSScaling. It sets up a maximal tree gauge fixed lattice and generates all possible configurations of group elements on the unfixed links. It then generates all possible global gauge transformations, and transforms the initial configuration. If at some point a configuration that has been seen before is reached, it moves to the next initial configuration. If none of the gauge transformed configurations has been seen before, it counts the initial configuration as a physical state.
The process is repeated for lattice sizes of the form 1 x n, with n being in the range {1...9}. This range is mostly limited by available memory, since seen physical configurations must be stored in memory and the number of configurations tends to dim(G)^n, where dim(G) is the dimension of the group.
The process is then repeated for a number of groups, including Q8 and the dihedrals D3-D5.
The results are printed in a table with the following columns:
-
The size of the lattice (n)
-
dim(HS_phys) - the dimension of the physical Hilbert space
-
dim(HS_unphys) - the dimenion of the unphysical Hilbert space
-
dim(HS_abel) - for comparison purposes, the dimension of the physical space of a theory with an abelian group of the same dimension as the dimension of dim(HS_phys) for a single plaquette lattice.
You need a recent version of Java and Apache Ant and a unix-like environment, although this could be made to work in Windows with some effort.
To compile the code, run ant jar in the main directory. This should
produce lib/phys-hs-scaling-na.jar (although a pre-compiled version of
the jar file should be present in the repository).
To run the main program:
cd bin
./hs-scaling