Quantum Many-Body Invited Talk

Philippe Corboz (University of Amsterdam)

Recent progress in simulating strongly correlated systems with tensor network methods

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 famous 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 been generalized to fermionic systems, and provide one of the most promising routes 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 talk I report on recent progress in simulating fermionic and frustrated systems with infinite PEPS (iPEPS) which is a tensor network ansatz for 2D wavefunctions in the thermodynamic limit. For the t-J model this method reveals an extremely close competition between a uniform d-wave superconducting state and different types of stripe states, with lower variational energies than in previous state-of-the-art studies for large 2D systems [1]. For the Shastry-Sutherland model in a magnetic field iPEPS predicts a new type of state [2] which helps to understand the intriguing magnetization process observed in SrCu2(BO3)2. Finally, I will discuss prospects and future directions in the field of tensor networks.

[1] P. Corboz, T. M. Rice, and M. Troyer, arXiv:1402.2859.
[2] P. Corboz and F. Mila, Phys. Rev. Lett. 112, 147203 (2014).