How do I set an MPS bond dimension that is higher than needed?

I am working on an implementation of the 1-site TDVP algorithm. In this variant of the algorithm I need to choose bond dimensions for my initial state MPS beforehand, as the bond dimension can not be changed during runtime. If I start with a product state, this means that I need to start with an MPS with a bond dimension that is higher than needed to exactly store the state.
I already tried merging and decomposing adjacent site tensors of the initial MPS via an svd and passing a mindim parameter, but this only resulted in bonds of dimension 1. I presume this is the case because no higher bond dimension is needed to represent a product state.

Is there some way to force an MPS to have an unnecessarily high bond dimension?

using ITensors: inner, linkdims, randomMPS, siteinds
using LinearAlgebra: norm
s = siteinds("S=1/2", 4)
a = randomMPS(s; linkdims=3)
b = 0 * randomMPS(s; linkdims=3)
c = +(a, b; alg="directsum")
@show linkdims(a), norm(a)
@show linkdims(b), norm(b)
@show linkdims(c), norm(c)
@show inner(a, b)
@show inner(a, c)
(linkdims(a), norm(a)) = ([3, 3, 2], 1.0)
(linkdims(b), norm(b)) = ([3, 3, 2], 0.0)
(linkdims(c), norm(c)) = ([6, 6, 4], 0.9999999999999998)
inner(a, b) = 0.0
inner(a, c) = 0.9999999999999993
1 Like

Hi Benjamin,
Please use Matt’s solution above, which should give you exactly what you need. From the inner part at the end of the example code above, you can see that the expanded MPS is exactly the same state as your input state, just with a large bond dimension now.

In the future, we are planning to offer a “global subspace expansion” feature to make this more “push button” for users like yourself.


1 Like