Ground state Energy and quantum_number conservation in iDMRG using VUMPS algorithm

ITensor Julia Questions
2

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  1. Note that when you make a unit cell, you need to include all connections to the next unit cell. This means that because you have U in 1-4, you’ll need whatever hops that are in 5,6,7,8

An example of the Hubbard model for 2 sites in this way:

function ITensorInfiniteMPS.unit_cell_terms(::Model"hubbard1d_2"; t,U)
  op = OpSum()

  op += -t, "Cdagup", 1, "Cup", 2
  op += -t, "Cdagup", 2, "Cup", 1
  op += -t, "Cdagdn", 1, "Cdn", 2
  op += -t, "Cdagdn", 2, "Cdn", 1

  # these connect to the next unit cell
  op += -t, "Cdagup", 2, "Cup", 3
  op += -t, "Cdagup", 3, "Cup", 2
  op += -t, "Cdagdn", 2, "Cdn", 3
  op += -t, "Cdagdn", 3, "Cdn", 2

  op += U, "Nupdn", 1
  op += U, "Nupdn", 2
  return op
end
  1. The “energy” is the energy per site for each site in your unit cell. You can average these together to create an overall “energy per site” of your model. To calculate the energy (which is also displayed during optimization), you can use
expect(ψ,H)

which will produce a vector of N elements (4 for your case). I would suggest playing around with the examples that have exact energy references to see how the final wave functions and their energy compare to the exact answers

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