PIRSA:13050041

Directed Influence in the RG Flow

Evenbly, G. (2013). Directed Influence in the RG Flow. Perimeter Institute. https://pirsa.org/13050041

Evenbly, Glen. Directed Influence in the RG Flow. Perimeter Institute, May. 09, 2013, https://pirsa.org/13050041 

          @misc{ pirsa_PIRSA:13050041,
            doi = {10.48660/13050041},
            url = {https://pirsa.org/13050041},
            author = {Evenbly, Glen},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Directed Influence in the RG Flow},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {may},
            note = {PIRSA:13050041 see, \url{https://pirsa.org}}
          }

Glen Evenbly Georgia Institute of Technology

DOI 10.48660/13050041
Collection
Talk Type Conference
Subject

Abstract

Given two lattice Hamiltonians H_1 and H_2 that are identical everywhere except on a local region R of the lattice, we propose a relationship between their ground states psi_1 and psi_2.  Specifically, assuming the states can be represented as multi-scale entanglement renormalization ansatz (MERA), we propose a principle of directed influence which asserts that the tensors in the MERA’s that represent the ground states can be chosen to be identical everywhere except within a specific, localized region of the tensor network.  The validity of this principle is justified by demonstrating it to follow from Wilson's renormalization ideas towards systems with manifestly separated energy scales. This result is shown, through numerical examples, to have practical applications towards the efficient simulation of systems with impurities, boundaries and interfaces, and also argued to provide useful insights towards holographic representations of quantum states.