PIRSA:17040033

Emergence of conformal symmetry in critical spin chains

Milsted, A. (2017). Emergence of conformal symmetry in critical spin chains. Perimeter Institute. https://pirsa.org/17040033

Milsted, Ashley. Emergence of conformal symmetry in critical spin chains. Perimeter Institute, Apr. 18, 2017, https://pirsa.org/17040033 

          @misc{ pirsa_PIRSA:17040033,
            doi = {10.48660/17040033},
            url = {https://pirsa.org/17040033},
            author = {Milsted, Ashley},
            keywords = {Condensed Matter, Quantum Fields and Strings, Quantum Gravity, Quantum Information},
            language = {en},
            title = {Emergence of conformal symmetry in critical spin chains},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {apr},
            note = {PIRSA:17040033 see, \url{https://pirsa.org}}
          }

Ashley Milsted

California Institute of Technology

Talk number
PIRSA:17040033
Collection
Talk Type
Subject
Abstract
We demonstrate that 1+1D conformal symmetry emerges in critical spin chains by constructing a lattice ansatz Hn for (certain combinations of) the Virasoro generators Ln. The generators Hn offer a new way of extracting conformal data from the low energy eigenstates of the lattice Hamiltonian on a finite circle. In particular, for each energy eigenstate, we can now identify which Virasoro tower it belongs to, as well as determine whether it is a Virasoro primary or a descendant (and similarly for global conformal towers and global conformal primaries/descendants). The central charge is obtained from a simple ground-state expectation value. Non-universal, finite-size corrections are the main source of error. We propose and demonstrate the use of periodic Matrix Product States, together with an improved ground state solver, to reach larger system sizes. We uncover that, importantly, the MPS single-particle excitation ansatz accurately describes all low energy excited states.