Anyonic braiding statistics from density matrix renormalization group (DMRG) simulations How does the ground state energy of the system change when we braid two anyons? Can the braiding of anyons be simulated with a computational method such as the density matrix renormalization group, and if so, could someone please give me some references? I've tried looking around, but I haven't been able to find anything.
EDIT:
I am specifically referring to the following slides, specifically around slide 56 or so, where he talks about DMRG and the quantum Hall Hamiltonian:
http://www.phys.virginia.edu/Announcements/Seminars/Slides/S2678.pdf
If, as Slaviks states below, that the ground state doesn't change, how can we learn about braiding statistics from DMRG?
 A: In these modern DMRG algorithms for topological phases, braiding statistics is rarely computed directly. The reason is that it is not clear how to trap a particular anyon in the bulk, and to get braiding statistics requires a careful calculation of adiabatic non-Abelian Berry phase which is often very computationally demanding. Instead, one calculates modular transformations on cylinders (to be more precise, the Dehn twist) by measuring the so-called momentum polarization of the Schmit states. It contains a lot of useful information about the topological order. The latter part of the slides explained these ideas.
A: Yes tensor network algorithms have been developed to describe braiding of anyons, Abelian and non-Abelian. The networks are constructed from tensors that explicitly conserve topological charge and the braiding, fusion, and recoupling data are taken as input to the algorithms.
This reference:
https://arxiv.org/abs/1311.0967
describes how to use the Time Evolved Block Decimation (TEBD) algorithm with anyonic Matrix Product States to compute ground states and dynamics of braiding anyons.
This reference:
https://arxiv.org/abs/1505.00100
shows how to compute ground states of braiding anyons using DMRG.
