You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
The [hard hexagon model](https://en.wikipedia.org/wiki/Hard_hexagon_model) is a 2-dimensional lattice model of a gas, where particles are allowed to be on the vertices of a triangular lattice, but no two particles may be adjacent.
27
+
This can be encoded in a transfer matrix with a local MPO tensor using anyonic symmetries, and the resulting MPO has been implemented in MPSKitModels.
28
+
29
+
In order to use these anyonic symmetries, we need to generalise the notion of the bond dimension and define how it interacts with the symmetry. Thus, we implement away of converting integers to symmetric spaces of the given dimension, which provides a crude guess for how the final MPS would distribute its Schmidt spectrum.
30
+
"""
31
+
mpo =adapt(CuArray, hard_hexagon())
32
+
P =physicalspace(mpo, 1)
33
+
functionvirtual_space(D::Integer)
34
+
_D =round(Int, D /sum(dim, values(FibonacciAnyon)))
35
+
return Vect[FibonacciAnyon](sector => _D for sector in (:I, :τ))
One way to study statistical mechanics in infinite systems with tensor networks is by approximating the dominant eigenvector of the transfer matrix by an MPS.
44
+
This dominant eigenvector contains a lot of hidden information.
45
+
For example, the free energy can be extracted by computing the expectation value of the mpo.
46
+
Additionally, we can compute the entanglement entropy as well as the correlation length of the state:
The dominant eigenvector is of course only an approximation. The finite bond dimension enforces a finite correlation length, which effectively introduces a length scale in the system. This can be exploited to formulate a scaling hypothesis [pollmann2009](@cite), which in turn allows to extract the central charge.
65
+
66
+
First we need to know the entropy and correlation length at a bunch of different bond dimensions. Our approach will be to re-use the previous approximated dominant eigenvector, and then expanding its bond dimension and re-running VUMPS.
67
+
According to the scaling hypothesis we should have ``S \propto \frac{c}{6} log(ξ)``. Therefore we should find ``c`` using
0 commit comments