MERA tensor networks produce continuously varying effective scaling dimensions along the Z3 chiral clock critical line, starting from 3-state Potts values as the chiral parameter increases.
Quantum Criticality with the Multi-scale Entanglement Renormalization Ansatz
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abstract
The goal of this manuscript is to provide an introduction to the multi-scale entanglement renormalization ansatz (MERA) and its application to the study of quantum critical systems. Only systems in one spatial dimension are considered. The MERA, in its scale-invariant form, is seen to offer direct numerical access to the scale-invariant operators of a critical theory. As a result, given a critical Hamiltonian on the lattice, the scale-invariant MERA can be used to characterize the underlying conformal field theory. The performance of the MERA is benchmarked for several critical quantum spin chains, namely Ising, Potts, XX and (modified) Heisenberg models, and an insightful comparison with results obtained using a matrix product state is made. The extraction of accurate conformal data, such as scaling dimensions and operator product expansion coefficients of both local and non-local primary fields, is also illustrated.
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TensorFlow-backed TensorNetwork implementation of MERA for critical 1D Ising model with conformal data extraction and 200x GPU acceleration reported.
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Scaling at Chiral Clock Criticality via Entanglement Renormalization
MERA tensor networks produce continuously varying effective scaling dimensions along the Z3 chiral clock critical line, starting from 3-state Potts values as the chiral parameter increases.
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TensorNetwork on TensorFlow: Entanglement Renormalization for quantum critical lattice models
TensorFlow-backed TensorNetwork implementation of MERA for critical 1D Ising model with conformal data extraction and 200x GPU acceleration reported.