# VUMPS slow convergence for the 2d exactly solvable Kitaev honeycomb model

**URL:** <https://itensor.discourse.group/t/vumps-slow-convergence-for-the-2d-exactly-solvable-kitaev-honeycomb-model/1393>\
**Category:** ITensor Julia Questions\
**Created:** [January 5, 2024, 5:25pm UTC](https://itensor.discourse.group/t/vumps-slow-convergence-for-the-2d-exactly-solvable-kitaev-honeycomb-model/1393 "2024-01-05T17:25:58Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![yangxusolidstate](https://avatars.discourse-cdn.com/v4/letter/y/90db22/32.png) [@yangxusolidstate](https://itensor.discourse.group/u/yangxusolidstate)\
**Post date:** [January 5, 2024, 5:25pm UTC](https://itensor.discourse.group/t/vumps-slow-convergence-for-the-2d-exactly-solvable-kitaev-honeycomb-model/1393/1 "2024-01-05T17:25:58Z")

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Hello ITensor community, I just tried the VUMPS julia “ITensorInfiniteMPS.jl” to study the 2d exactly solvable Kitaev model on a honeycomb lattice with the parameter Jx=Jy=0.4, Jz=1. I used a cylindrical geometry with Lx infinite and Ly=4 unit-cell (Ly is along n\_1 in Kitaev’s notation). And it shows very slow convergence, possibly due to the extensive amount of flux conservation laws. I understand that each time the VUMPS does subspace expansion, it is introducing new basis states to the variational searching space, but it seems not enough to achieve a fast convergence.

Do you have any suggestions on the possible noise term that can be added to the system or other methods to speed up the convergence?

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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:** [January 7, 2024, 4:19pm UTC](https://itensor.discourse.group/t/vumps-slow-convergence-for-the-2d-exactly-solvable-kitaev-honeycomb-model/1393/2 "2024-01-07T16:19:54Z")

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One possible thing to try for cases of slow convergence is to do a large number of sweeps or iterations while keeping the maximum bond dimension (maxdim) low, like 10 or 20. This can help to find a good approximation to the state while each such sweep can go very fast (eg you could do 100 of them). Then you can raise maxdim and do a smaller number of more accurate sweeps.