PIRSA:08010005

Entanglement Renormalization, Quantum Criticality and Topological Order

Vidal, G. (2008). Entanglement Renormalization, Quantum Criticality and Topological Order. Perimeter Institute. https://pirsa.org/08010005

Vidal, Guifre. Entanglement Renormalization, Quantum Criticality and Topological Order. Perimeter Institute, Jan. 23, 2008, https://pirsa.org/08010005 

          @misc{ pirsa_PIRSA:08010005,
            doi = {10.48660/08010005},
            url = {https://pirsa.org/08010005},
            author = {Vidal, Guifre},
            keywords = {Quantum Information},
            language = {en},
            title = {Entanglement Renormalization, Quantum Criticality and Topological Order},
            publisher = {Perimeter Institute},
            year = {2008},
            month = {jan},
            note = {PIRSA:08010005 see, \url{https://pirsa.org}}
          }

Guifre Vidal

Alphabet (United States)

Talk number
PIRSA:08010005
Collection
Talk Type
Subject
Abstract
The renormalization group (RG) is one of the conceptual pillars of statistical mechanics and quantum field theory, and a key theoretical element in the modern formulation of critical phenomena and phase transitions. RG transformations are also the basis of numerical approaches to the study of low energy properties and emergent phenomena in quantum many-body systems. In this colloquium I will introduce the notion of \\\"entanglement renormalization\\\" and use it to define a coarse-graining transformation for quantum systems on a lattice [G.Vidal, Phys. Rev. Lett. 99, 220405 (2007)]. The resulting real-space RG approach is able to numerically address 1D and 2D lattice systems with thousands of quantum spins using only very modest computational resources. From the theoretical point of view, entanglement renormalization sheds new light into the structure of correlations in the ground state of extended quantum systems. I will discuss how it leads to a novel, efficient representation for the ground state of a system at a quantum critical point or with topological order.