Tensor network studies of exotic phases in SU(N) Heisenberg models

Philippe Corboz (ETH Zurich)

30.11.2012 at 14:30 

Tensor networks are a class of variational wave functions enabling an efficient representation of quantum many-body states, where the accuracy can be systematically controlled by the so-called bond dimension. A well known example are matrix product states (MPS), the underlying tensor network of the density matrix renormalization group (DMRG) method, which has become the state-of-the-art tool to study (quasi-) one dimensional systems. Progress in quantum information theory, in particular a better understanding of entanglement in quantum many-body systems, has led to the development of tensor networks for two-dimensional systems, including e.g. projected entangled-pair states (PEPS) or the 2D multi-scale entanglement renormalization ansatz (MERA). These methods have recently been generalized to fermionic systems, and provide a promising route for the simulation of strongly correlated systems in two dimensions, in particular models where Quantum Monte Carlo fails due to the negative sign problem.

In this seminar I report on recent progress with infinite PEPS (iPEPS), which is an ansatz for a 2D wave function in the thermodynamic limit. I present simulation results for SU(N) Heisenberg models, which exhibit a rich variety of exotic phases on various lattices and values of N. These models have recently attracted increasing interest thanks to the proposals to realize SU(N) symmetric Hubbard models in experiments on ultracold alkaline-earth atoms in optical lattices. The N=4 case is also relevant for spin-orbital systems, since it is equivalent to the symmetric Kugel-Khomskii model, which describes the interaction between spin- and orbital degrees of freedom on a lattice. We show that this model exhibits an ordered ground state on the square and checkerboard lattice, however, on the honeycomb lattice we find that quantum fluctuations destroy any order, giving rise to a spin-orbital liquid.
Finally, I discuss prospects and future directions in the field of 2D tensor networks.