# The structure of fixed-point tensor network states characterizes the patterns of long-range entanglement

The structure of fixed-point tensor network states characterizes the patterns of long-range... The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, and conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holography. Furthermore, the entanglement of the fixed-point states leads to an emergence of pregeometry in the 3D TQFT bulk. We further extend these ideas to the case where an additional global on-site unitary symmetry is imposed on the tensor network states. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

# The structure of fixed-point tensor network states characterizes the patterns of long-range entanglement

, Volume 96 (3) – Jul 5, 2017

## The structure of fixed-point tensor network states characterizes the patterns of long-range entanglement

Abstract

The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, and conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holography. Furthermore, the entanglement of the fixed-point states leads to an emergence of pregeometry in the 3D TQFT bulk. We further extend these ideas to the case where an additional global on-site unitary symmetry is imposed on the tensor network states.

/lp/aps_physical/the-structure-of-fixed-point-tensor-network-states-characterizes-the-lAkxsNJ2GF
Publisher
The American Physical Society
ISSN
1098-0121
eISSN
1550-235X
D.O.I.
10.1103/PhysRevB.96.035101
Publisher site
See Article on Publisher Site

### Abstract

The algebraic structure of representation theory naturally arises from 2D fixed-point tensor network states, and conceptually formulates the pattern of long-range entanglement realized in such states. In 3D, the same underlying structure is also shared by Turaev-Viro state-sum topological quantum field theory (TQFT). We show that a 2D fixed-point tensor network state arises naturally on the boundary of the 3D manifold on which the TQFT is defined, and the fact that exactly the same information is needed to construct either the tensor network or the TQFT is made explicit in a form of holography. Furthermore, the entanglement of the fixed-point states leads to an emergence of pregeometry in the 3D TQFT bulk. We further extend these ideas to the case where an additional global on-site unitary symmetry is imposed on the tensor network states.

### Journal

Physical Review BAmerican Physical Society (APS)

Published: Jul 5, 2017

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