PIRSA:12090056

Multiplets in the Entanglement Spectrum

Turner, A. (2012). Multiplets in the Entanglement Spectrum. Perimeter Institute. https://pirsa.org/12090056

Turner, Ari. Multiplets in the Entanglement Spectrum. Perimeter Institute, Sep. 06, 2012, https://pirsa.org/12090056 

          @misc{ pirsa_PIRSA:12090056,
            doi = {10.48660/12090056},
            url = {https://pirsa.org/12090056},
            author = {Turner, Ari},
            keywords = {},
            language = {en},
            title = {Multiplets in the Entanglement Spectrum},
            publisher = {Perimeter Institute},
            year = {2012},
            month = {sep},
            note = {PIRSA:12090056 see, \url{https://pirsa.org}}
          }

Ari Turner Universiteit van Amsterdam

DOI 10.48660/12090056
Collection
Talk Type Scientific Series

Abstract

What information can be determined about a state given just the ground state wave function? Quantum ground states, speaking intuitively, contain fluctuations between many of the configurations one might want to understand. The information about them can be organized by introducing an imaginary system, dubbed the entanglement Hamiltonian. What light does the dynamics of this Hamiltonian (a precise version of the notion of "zero point motion") shed on the actual system? 

I will start my discussion near critical points, where Lorentz invariance often emerges and the entanglement Hamiltonian becomes tractable, revealing that it exists in one dimension less than the real system. One application is to the fluctuations of angular momentum in a spin chain. 

The entanglement Hamiltonian is especially successful at clarifying the properties of quantum phases without order, such as topological insulators. In particular, spin chains often have no long range order due to quantum fluctuations. Nevertheless there can be phase transitions between two of these disordered states, suggesting the existence of a hidden order.  

My main aim in the talk will be to demonstrate that the entanglement spectrum can serve as an order parameter for these unusual  transitions; this observation leads to a classification of one-dimensional phases. One can understand the phases of the actual system simply by looking at the spectrum of the entanglement Hamiltonian, just as one deduces the properties of atoms from their spectra.