Renormalization group flows of Hamiltonians using tensor networks

Matthias Bal; Michaël Mariën; Jutho Haegeman; Frank Verstraete

doi:10.1103/physrevlett.118.250602

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arXiv · 1703.00365

Renormalization group flows of Hamiltonians using tensor networks

Matthias Bal·Michaël Mariën·Jutho Haegeman·Frank Verstraete

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Abstract

A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks. Similar to tensor network renormalization ([G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015)], [S. Yang, Z.-C. Gu, and X.-G Wen, Phys. Rev. Lett. 118, 110504 (2017)]) we obtain approximate fixed point tensor networks at criticality. Our formalism however preserves positivity of the tensors at every step and hence yields an interpretation in terms of Hamiltonian flows. We emphasize that the key difference between tensor network approaches and Kadanoff's spin blocking method can be understood in terms of a change of local basis at every decimation step, a property which is crucial to overcome the area law of mutual information. We derive algebraic relations for fixed point tensors, calculate critical exponents, and benchmark our method on the Ising model and the six-vertex model.

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Matthias Bal, Michaël Mariën, Jutho Haegeman, Frank Verstraete. 2017-05-24. Renormalization group flows of Hamiltonians using tensor networks. https://doi.org/10.1103/physrevlett.118.250602

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