Bridging Perturbative Expansions with Tensor Networks

          @misc{ pirsa_PIRSA:17040044,
            doi = {10.48660/17040044},
            url = {https://pirsa.org/17040044},
            author = {Haegeman, Jutho},
            keywords = {Condensed Matter, Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Bridging Perturbative Expansions with Tensor Networks},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040044 see, \url{https://pirsa.org}}
          }
          

Abstract

We demonstrate that perturbative expansions for quantum many-body systems can be rephrased in terms of tensor networks, thereby providing a natural framework for interpolating perturbative expansions across a quantum phase transition. This approach leads to classes of tensor-network states parameterized by few parameters with a clear physical meaning, while still providing excellent variational energies. We also demonstrate how to construct perturbative expansions of the entanglement Hamiltonian, whose eigenvalues form the entanglement spectrum, and how the tensor-network approach gives rise to order parameters for topological phase transitions.