アイテム詳細

要旨

The multi-scale entanglement renormalization ansatz (MERA) is a tensor
network that can efficiently parameterize critical ground states on a 1D
lattice, and also suggestively implement some aspects of the holographic
correspondence of string theory on a lattice. Extending our recent work [S.
Singh, Physical Review D 97, 026012 (2018); S. Singh, N. A. McMahon, and G. K.
Brennen, Phys. Rev. D 97, 026013 (2018)], we show how the MERA representation
of a 1D critical ground state---which has long range entanglement---can be
viewed as a strange correlator: the overlap of a 2D state with short range
entanglement and a 2D product state. Strange correlators were recently
introduced to map 2D symmetry protected or topologically ordered quantum states
to critical systems in one lower dimension. The 2D quantum state dual to the
input 1D critical state is obtained by lifting the MERA, a procedure which
introduces bulk quantum degrees of freedom by inserting intertwiner tensors on
each bond of the MERA tensor network. We show how this dual 2D bulk state
exhibits several features of holography, for example, appearance of
horizon-like holographic screens and bulk gauging of global on-site symmetries
at the boundary. We also derive a quantum corrected Ryu-Takayanagi formula
relating boundary entanglement entropy to bulk geodesic lengths---as measured
by bulk entropy---and numerically test it for ground states of a set of unitary
minimal model CFTs, as realized by 1D anyonic Heisenberg models.