# Excited states using dmrg calculations

**URL:** <https://itensor.discourse.group/t/excited-states-using-dmrg-calculations/2202>\
**Category:** DMRG and Numerical Methods\
**Tags:** excited\_states\
**Created:** [January 16, 2025, 1:48pm UTC](https://itensor.discourse.group/t/excited-states-using-dmrg-calculations/2202 "2025-01-16T13:48:09Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![shuklavaibhav](https://avatars.discourse-cdn.com/v4/letter/s/ce73a5/32.png) [@shuklavaibhav](https://itensor.discourse.group/u/shuklavaibhav)\
**Post date:** [January 16, 2025, 1:48pm UTC](https://itensor.discourse.group/t/excited-states-using-dmrg-calculations/2202/1 "2025-01-16T13:48:09Z")

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Hello there to the community, hope all are doing good.  
I was performing the DMRG to find ground energy and energy gap between first excited state and ground state.  
I got the energy gap of the order 10^ -11 which is very small  
my question is, is this the excited state or the degenerate ground state.  
so the function energy,psi1 , energy,psi2 are actually excited states or they can be degenerate ground and degenerate first excited states?  
With thanks and regards.

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**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [January 16, 2025, 2:10pm UTC](https://itensor.discourse.group/t/excited-states-using-dmrg-calculations/2202/2 "2025-01-16T14:10:31Z")

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To distinguish whether it is truly gapped or gapless, you would need to extrapolate the gap as a function of system size and bond dimension. Both finite system sizes and finite MPS bond dimensions will induce a nonzero gap, even if the exact state in the thermodynamic limit is gapless.