Kavli Affiliate: Natalia Chepiga
| First 5 Authors: Manu Canals, Natalia Chepiga, Luca Tagliacozzo, ,
| Summary:
The Lattice Gauge Theory Hilbert space is divided into gauge-invariant
sectors selected by the background charges. Such a projector can be directly
embedded in a tensor network ansatz for gauge-invariant states as originally
discussed in [Phys. Rev. B 83, 115127 (2011)] and in [Phys. Rev. X 4, 041024
(2014)] in the context of PEPS. The original ansatz is based on sparse tensors,
though parts of them are not explicitly symmetric, and thus their actual
implementation in numerical simulations has been hindered by the complexity of
developing ad hoc libraries. Here we provide a new PEPS tensor network
formulation of gauge-invariant theories purely based on symmetric elementary
tensors. The new formulation can be implemented in numerical simulation using
available state-of-the-art tensor network libraries but also holds interest
from a purely theoretical perspective since it requires embedding the original
gauge theory with gauge symmetry G into an enlarged globally symmetric theory
with symmetry GxG. By revisiting the original ansatz in the modern landscape of
i) duality transformations between gauge and spin systems, ii) finite depth
quantum circuits followed by measurements that allow generating topologically
ordered states, and iii) Clifford enhanced tensor networks, we show that such a
new formulation provides a novel duality transformation between lattice gauge
theories and specific sectors of globally invariant systems.
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