Tensor network approach to 2d Lorentzian quantum Regge calculus

Understand

We demonstrate a tensor renormalization group (TRG) calculation for a two-dimensional Lorentzian model of quantum Regge calculus (QRC).

• This model is expressed in terms of a tensor network by discretizing the continuous edge lengths of simplicial manifolds and identifying them as tensor indices.
• The expectation value of space-time area, which is obtained through the higher-order TRG method, nicely reproduces the exact value.
• The Lorentzian model does not have the spike configuration that was an obstacle in the Euclidean QRC, but it still has a length-divergent configuration called a pinched geometry.