Glen Evenbly, Pair-wise Tensor Optimization for Entanglement Renormalization скачать в хорошем качестве

Glen Evenbly, Pair-wise Tensor Optimization for Entanglement Renormalization

Although introduced almost 3 decades ago the DMRG algorithm has changed little since its inception: the original strategy for energy minimization proposed by White, where pairs of neighboring MPS tensors are updated simultaneously, remains one of the most efficient optimization algorithms available. One of the difficulties of working with more sophisticated tensor network ansatz, such as MERA or PEPS, is that the known optimization strategies, often based on single-tensor updates, are less reliable than traditional DMRG. In this talk I will describe how the traditional DMRG-style strategy, i.e. based upon simultaneous updates over pairs of tensors that share a common link within the network, can be applied to optimize MERA for the ground state of a lattice Hamiltonian. This pair-wise optimization strategy is demonstrated to have numerous advantages over previous algorithms based on single tensor updates, including (i) allowing for faster and more reliable convergence, (ii) allowing the bond dimension to be dynamically adjusted during an optimization, and (iii) allowing the optimal quantum numbers to be automatically determined in the case of networks that preserve a global symmetry.