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dmrg with nonlocal basis states

Cambridge University Press (1)

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9 - DMRG with Nonlocal Basis States
Tao Xiang, Chinese Academy of Sciences, Beijing
Book:

Density Matrix and Tensor Network Renormalization

Published online:

18 January 2024

Print publication:

31 August 2023, pp 137-153
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Summary

This chapter extends DMRG from real space to an arbitrary basis space in which each basis state, such as a momentum eigenstate or a molecular orbital, serves as an effective lattice site. Unlike in real space, the interaction potentials become nonlocal and off-diagonal in an arbitrary basis representation. To solve this nonlocal problem, one should optimize the order of basis states and introduce the so-called complementary operators to minimize the number of operators whose matrix elements must be computed and stored. We illustrate the momentum-space DMRG using the Hubbard model and discuss its application in other interacting fermion models. Finally, we introduce a DMRG scheme for optimizing the single-particle basis states and their order simultaneously in a more general basis space without momentum conservation.