# How to konw what the state should be used to initialize MPS

**URL:** <https://itensor.discourse.group/t/how-to-konw-what-the-state-should-be-used-to-initialize-mps/1229>\
**Category:** DMRG and Numerical Methods\
**Tags:** julia, dmrg\
**Created:** [October 18, 2023, 1:44pm UTC](https://itensor.discourse.group/t/how-to-konw-what-the-state-should-be-used-to-initialize-mps/1229 "2023-10-18T13:44:08Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![gjduan](https://avatars.discourse-cdn.com/v4/letter/g/b38774/32.png) [@gjduan](https://itensor.discourse.group/u/gjduan)\
**Post date:** [October 18, 2023, 1:44pm UTC](https://itensor.discourse.group/t/how-to-konw-what-the-state-should-be-used-to-initialize-mps/1229/1 "2023-10-18T13:44:08Z")

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Hi, If I want to find the ground state for a spin system with U(1) symmetry, how to konw what the state should be used to initialize the MPS？

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**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:** [October 19, 2023, 2:17am UTC](https://itensor.discourse.group/t/how-to-konw-what-the-state-should-be-used-to-initialize-mps/1229/2 "2023-10-19T02:17:10Z")

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It depends on the physical system you are studying. In general, there isn’t an automatic way to know. But for most antiferromagnetic systems, the ground state has a total Sz of zero. So most likely that is the value you should take. You can always check nearby values of +1 and -1 to see if the ground state energy in those sectors is lower or higher.

At least exception to this is if the system is a ferromagnet with N spin 1/2’s, for which the (degenerate) ground states have total Sz ranging from N/2 to -N/2 in steps of 1.

Another exception is if the system has a field applied to it in the z direction. As the field is made stronger, the total Sz of the ground state will change.

If you are studying a system whose ground state you suspect might not have a total Sz of zero, one thing you can do is to study small systems without quantum number conservation turned on, which will explore all possible quantum numbers, and measure the total Sz after converging DMRG.

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**Author:** ![gjduan](https://avatars.discourse-cdn.com/v4/letter/g/b38774/32.png) [@gjduan](https://itensor.discourse.group/u/gjduan)\
**Post date:** [October 19, 2023, 3:40pm UTC](https://itensor.discourse.group/t/how-to-konw-what-the-state-should-be-used-to-initialize-mps/1229/3 "2023-10-19T15:40:02Z")

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Thank you for your response. I have conducted research on small quantum systems and measured the total Sz. Unfortunately, it appears that the total Sz is not a reliable quantum number(Sz is a strange number), despite the Hamiltonian having U(1) symmetry. I am considering the possibility of calculating all subspaces that conserve quantum numbers to determine the ground state.

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<div class="post-metadata">

**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:** [October 19, 2023, 5:10pm UTC](https://itensor.discourse.group/t/how-to-konw-what-the-state-should-be-used-to-initialize-mps/1229/4 "2023-10-19T17:10:56Z")

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Yes, if you did full exact diagonalization of a small system in a way that works in a basis that has well defined total Sz , it might be enough already to tell you what total Sz the ground state has.