# How to correctly do TEBD with ITensor? **URL:** \ **Category:** ITensor Julia Questions\ **Tags:** julia, mps\ **Created:** [March 13, 2023, 4:01pm UTC](https://itensor.discourse.group/t/how-to-correctly-do-tebd-with-itensor/695 "2023-03-13T16:01:50Z")\ **Posts on this page:** 2\ **Page:** 1
**Author:** ![matijacell](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/matijacell/32/225_2.png) [@matijacell](https://itensor.discourse.group/u/matijacell)\ **Post date:** [March 13, 2023, 4:01pm UTC](https://itensor.discourse.group/t/how-to-correctly-do-tebd-with-itensor/695/1 "2023-03-13T16:01:50Z")
Hello, I am new to Julia and I am trying learn how to use ITensor to do time evolution block decimation (TEBD) for a certain system. I already have working code written in Python that I use to see if the results of my Julia code is correct, which it is not. To do TEBD with ITensor I used [this](https://itensor.github.io/ITensors.jl/stable/tutorials/MPSTimeEvolution.html) example. To give some context, time evolution in my model is given by applying two propagators, first an even one, then an odd one p(t+1) = U\_o U\_e p(t) Each propagator is made of gates that act on three sites U\_e = U\_{123} U\_{345} U\_{567} ... U\_{n-1, n} that commute (and U\_o = U\_{1,2} U\_{234} U\_{456} ... U\_{n-2,n-1,n}). The boundary is special, but simply consists of adding a two site gate. These are like e^{-itH} for quantum systems, but they require no Trotterization. So I make a random initial MPS, evolve it for a long time, and the system should decay to a steady state. ```auto using ITensors let N = 4 cutoff = 1E-8 tsteps = 1000 # Maximum bond dimension M = 100 # No truncation # Bulk gate U = [1 0 0 0 0 0 0 0; 0 0 0 1 0 0 0 0; 0 0 1 0 0 0 0 0; 0 1 0 0 0 0 0 0; 0 0 0 0 0 0 1 0; 0 0 0 0 0 0 0 1; 0 0 0 0 1 0 0 0; 0 0 0 0 0 1 0 0] # Boundary gates d = [1/4, 2/3, 2/5, 3/7]; U_L = [d[1] 0 d[1] 0; 0 d[2] 0 d[2]; 1-d[1] 0 1-d[1] 0; 0 1-d[2] 0 1-d[2]] U_R = [d[3] d[3] 0 0; 1-d[3] 1-d[3] 0 0; 0 0 d[4] d[4]; 0 0 1-d[4] 1-d[4]] # Make an array of 'site' indices S=1/2 s = siteinds("S=1/2", N) println("Making gates") gates = ITensor[] # First generate even, then odd gates for i in 1:2 for j in i:2:(N - 2) s1 = s[j] s2 = s[j + 1] s3 = s[j + 2] G = op(U, s1, s2, s3) push!(gates, G) end # Boundary driving if i == 1 push!(gates, op(U_R, s[N-1], s[N])) # Right boundary push!(gates, op(U_L, s[1], s[2])) # Left Boundary end end # Initialize psi to be a random MPS println("Making random MPS with bond dimension " * string(M)) p = randomMPS(s, linkdims=M); println("Doing time evolution.") # Apply gates for t in 0:1:tsteps p = apply(gates, p; cutoff) end println("Done.") return end ``` After running this code I contract all my bond indices to get a vector of size 2^N and check if it’s the same vector I get from my Python code, and it isn’t. The code looks correct to me, but I’m since this is my first time using ITensor I cannot figure out what the error would be. Thank you ---
**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\ **Post date:** [March 14, 2023, 1:35am UTC](https://itensor.discourse.group/t/how-to-correctly-do-tebd-with-itensor/695/2 "2023-03-14T01:35:21Z")
Hi, glad you are trying out ITensor. Your code looks possibly correct, so it’s hard to say why you aren’t getting the result you expect. It could be a bug like perhaps it’s not doing the steps that you think? I would suggest altering the code to print out more information to confirm (e.g. print things like your `t` variable parameterizing your for loop at the end - things like that). The other things I would suggest are to: 1. print out some of the gates (ITensors) explicitly to see whether they are being defined properly and as you think and 2. trying both codes for a much smaller number of layers (much smaller tsteps) and compare the results after one step, two steps, etc. You may be able to think of some other debugging strategies too.