I have a code for an Ising model defined by a Hamiltonian. I want to obtain the first 10 eigenvalues of that hamiltonian. I tried 2 different approaches: a) First convert it into a sparse matrix and then use arpack’s eigensolver. b) Run DMRG sweep.

I have a running code for (a) but the result I am getting from there doesn’t seem to be right.

```
using ITensors
using LinearAlgebra
using SparseArrays
using Arpack
N = 4
NA = 2
chi = 5
chisigma = 2
n = 5 # number of batches, number of moments this generates is n-1
crit = 2
ITensors.set_warn_order(20)
# Ensure these operations are within the same scope
global ops1 = OpSum()
global ops2 = OpSum()
println("ops1 initialized: ", ops1)
println("ops2 initialized: ", ops2)
# Test loop to check for initialization issues
for j in 1:(N - 1)
global ops1
ops1 += -1, "Z", j, "Z", j + 1
end
println("ops1 after loop: ", ops1)
for j in 1:N
global ops2
ops2 += "X", j
end
println("ops2 after loop: ", ops2)
# Add crit*ops2 to ops1
global ops1 += crit * ops2
println("ops1 after adding crit*ops2: ", ops1)
sites = siteinds("S=1/2", N)
println("sites: ", sites)
H = MPO(ops1, sites)
println("Hamiltonian H created")
```

The above is the snippet of the code where I define my Hamiltonian. The reason I want to obtain the first 10 eigenvalues is because I want to know if the way I am adding ops1 + 2* ops 2 is working the way I intend it to or not. Method (a) tells me that it doesn’t (cause I get that the first 10 eigenvalues are all 0, which shouldn’t be for crit != 1). But I can’t get a working code for doing a DMRG sweep and obtaining the first 10 eigenvalues.

Here’s the code that I wrote to find the ground state wave function and energy, but I don’t really know how to obtain the next 9 eigenenergies:

H = MPO(ops1+crit*ops2, sites)

psi0 = randomMPS(sites; linkdims=chi)

```
# define parameters for DMRG sweeps
nsweeps = 10
maxdim = [10, 20, chi]
cutoff = [1E-10]
# We obtain the ground state via DMRG
energy, psi = dmrg(H, psi0; nsweeps, maxdim, cutoff, outputlevel = 0)
```

So, basically I have 2 questions:

- Is the code that I wrote to add ops1 with 2*ops2 doing what I want it to do (is the syntax right basically?)
- How to check that by obtaining the first 10 eigenenergies via DMRG sweep?