Tensor Renormalization Group and its Application

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Concept of renormalization groupEnergyH 0H 1H 2••• ••• H effRG iteration• 1943 Ernst Stueckelberg initialized a renormalizationprogram to attack the problems of infinities in QEDbut his paper was rejected by Physical Review.• 1953 Ernst Stueckelberg <strong>and</strong> Andre Petermannopened the field of renormalization groupErnst Stueckelberg
Page 1: Tensor Renormalization Group and it
Page 5: Characteristic Energy ScalesNumeric
Page 9 and 10: Basic Idea of Numerical Renormaliza
Page 11: Reasons for the Failure of Wilson b
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
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Tensor Renormalization Group and its Application

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