# Calculate dynamic correlation function for fermonic operators in ITensor

**URL:** <https://itensor.discourse.group/t/calculate-dynamic-correlation-function-for-fermonic-operators-in-itensor/2476>\
**Category:** DMRG and Numerical Methods\
**Created:** [August 24, 2025, 8:02am UTC](https://itensor.discourse.group/t/calculate-dynamic-correlation-function-for-fermonic-operators-in-itensor/2476 "2025-08-24T08:02:34Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![ZhouGD2000](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zhougd2000/32/669_2.png) [@ZhouGD2000](https://itensor.discourse.group/u/ZhouGD2000)\
**Post date:** [August 24, 2025, 8:02am UTC](https://itensor.discourse.group/t/calculate-dynamic-correlation-function-for-fermonic-operators-in-itensor/2476/1 "2025-08-24T08:02:34Z")

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Hi,  
I would like to calculate the dynamic correlation function, e.g., \langle c(t)c^{\dagger}(0)\rangle for fermionic operators by ITensor. Standard way to this using time evolution is

1. calculate the groundstate |\psi\_g\rangle
2. act c^\dagger on |\psi\_g\rangle
3. time evolution on c^\dagger|\psi\_g\rangle and obtain e^{-iHt} c^\dagger|\psi\_g\rangle
4. overlap with c^\dagger|\psi\_g\rangle and multiply the phase factor e^{iE\_g t}.

I first try define an MPO by `AutoMPO` for c^\dagger but it raises an error

```julia
Parity-odd fermionic terms not yet supported by OpSum to MPO conversion

```

So what is the correct way to do this? A possible way is to naively use `op("Cdag",sites[i])` (`sites[i]` is an `Index`) and then using `apply` to act it on |\psi\_g\rangle but creation/annihilation operators should be attached with an Jordan-Wigner string and I do not know if `apply` correctly treat this.  
Thanks!

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<div class="post-metadata">

**Author:** ![ZhouGD2000](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zhougd2000/32/669_2.png) [@ZhouGD2000](https://itensor.discourse.group/u/ZhouGD2000)\
**Post date:** [August 24, 2025, 8:48am UTC](https://itensor.discourse.group/t/calculate-dynamic-correlation-function-for-fermonic-operators-in-itensor/2476/2 "2025-08-24T08:48:43Z")

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I find that in [Proper way to construct fermion gates](https://itensor.discourse.group/t/proper-way-to-construct-fermion-gates/172) Mile’s reply mentioned that the `apply` function will automatically deal with the fermion string so maybe this should be the correct way.

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**Author:** ![system](https://global.discourse-cdn.com/free1/uploads/itensor/original/1X/d3072b13e047cd06df7f3981547c0917d940dfa4.png) [@system](https://itensor.discourse.group/u/system)\
**Post date:** [September 3, 2025, 8:49am UTC](https://itensor.discourse.group/t/calculate-dynamic-correlation-function-for-fermonic-operators-in-itensor/2476/3 "2025-09-03T08:49:17Z")

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