Tensor Renormalization Group and its Application

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Density Matrix <strong>Renormalization</strong> <strong>Group</strong> (DMRG)System Environmentm 1m 2n 2m 3S. White, PRL (1992)Use Environment as apump to probe thebasis states in Systemn 3m 4|i〉 sys|j〉 envψ = ∑ f i ji,jij sys env
Page 1: Tensor Renormalization Group and it
Page 5 and 6: Characteristic Energy ScalesNumeric
Page 8 and 9: Numerical Renormalization Group Met
Page 10 and 11: Wilson block-spin NRGH 2keep the lo
Page 14 and 15: NRG versus DMRGWilson NRGSystemSysD
Page 16 and 17: DMRG Wavefunction: Matrix Product S
Page 18 and 19: Haldane ConjectureInteger Heisenber
Page 20 and 21: Accuracy of the DMRG in 1DDMRG: Can
Page 22 and 23: Ground state energy of the 2D Heise
Page 24 and 25: Area Law of Entanglement EntropyFor
Page 26 and 27: Two Problems Need To Be SolvedΨ= T
Page 28 and 29: How to determine the local tensor?
Page 30 and 31: Projection IterationeH−τHα=≈e
Page 32 and 33: How accurate is this projection app
Page 34 and 35: Coarse Grain Tensor Renormalization
Page 36 and 37: Step II: Decimation
Page 38 and 39: Second renormalization of tensor-ne
Page 40 and 41: Accuracy of Poor Man’s SRGD = 24I
Page 42 and 43: ( n 1)M −ijkl1. Forward iteration
Page 44 and 45: Error versus D
Page 46 and 47: Quantum Heisenberg Model on Honeyco
Page 48 and 49: Staggered MagnetizationSRG D = 15M
Page 50 and 51: Staggered Magnetization4 th order p
Page 52 and 53: Kagome Lattice
Page 54 and 55: Tensor-Network Representation of Cl
Page 56: Tensor-network representationZ= Tr

Tensor Renormalization Group and its Application

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