MERA++: An Implementation of the Multi-scale Entanglement Renormalization Ansatz

The multi-scale entanglement renormalization ansatz (MERA) efficiently represents the ground state of short-ranged correlated electron Hamiltonians in any dimension [Vidal, 2006]. I will introduce MERA++, a computer program that implements MERA in two parts: a symbolic code and a numeric code. The symbolic code generates the MERA equations given a lattice, a model, and an ary for the MERA. The numeric code uses these equations to optimize the tensors that make up the MERA, and produces the ground state of the Hamiltonian in question, in any dimension, with bounded errors, and with systematic improvement by increasing the number of states that are kept. I will briefly discuss the technical challenges that MERA faces, when used to simulate (for example) the two dimensional and even three dimensional quantum Heisenberg models, without bias and with controlled errors. The code repositories for MERA++ are available at https://code.ornl.gov/gonzalo_3/merapp and at https://github.com/g1257/merapp.