# Non-Hermitian DMRG in ITensor **URL:** \ **Category:** General Discussion\ **Tags:** julia\ **Created:** [November 24, 2025, 12:58pm UTC](https://itensor.discourse.group/t/non-hermitian-dmrg-in-itensor/2536 "2025-11-24T12:58:34Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![tipfom](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/tipfom/32/838_2.png) [@tipfom](https://itensor.discourse.group/u/tipfom)\ **Post date:** [November 24, 2025, 12:58pm UTC](https://itensor.discourse.group/t/non-hermitian-dmrg-in-itensor/2536/1 "2025-11-24T12:58:34Z")
Hello everyone, I implemented a non-Hermitian DMRG variant [1, 2] in ITensor, which is available at [https://github.com/tipfom/ITensorNHDMRG.jl](https://github.com/tipfom/ITensorNHDMRG.jl). Using the library is very straightforward and amounts to replacing the call to `dmrg` with a call to `nhdmrg`, see the example in the REAMDE or the examples at [https://github.com/tipfom/ITensorNHDMRG.jl/tree/main/examples](https://github.com/tipfom/ITensorNHDMRG.jl/tree/main/examples). All normal functionality such as QN conservation should be supported. If you have any use for the library, feel free to check it out and let me know if you find are any bugs. [1] doi: 10.1103/5vnl-w9p4 [2] doi: 10.1103/PhysRevB.105.205125 ---
**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:** [November 25, 2025, 10:24pm UTC](https://itensor.discourse.group/t/non-hermitian-dmrg-in-itensor/2536/2 "2025-11-25T22:24:28Z")
This is very interesting to see. Thanks for sharing about it, and some of us or our collaborators may give it a try soon and we can then give you feedback about how it’s working for our cases. ---
**Author:** ![Jren](https://avatars.discourse-cdn.com/v4/letter/j/ecccb3/32.png) [@Jren](https://itensor.discourse.group/u/Jren)\ **Post date:** [December 15, 2025, 12:45pm UTC](https://itensor.discourse.group/t/non-hermitian-dmrg-in-itensor/2536/3 "2025-12-15T12:45:34Z")
Interesting and nice work. In the example 2401.15000\_nhdmrg.jl, the codes can not obtain the correct result, if we change biorthoalg = “biorthoblock”. LoadError: Index arrows must be the same to add, subtract, map, or scale QN ITensors Stacktrace: [1] error(s::String) @ Base ./error.jl:35 [2] \_map!!(f::Function, R::NDTensors.BlockSparseTensor{ComplexF64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{ComplexF64, Vector{ComplexF64}, 2}}, T1::NDTensors.BlockSparseTensor{ComplexF64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{ComplexF64, Vector{ComplexF64}, 2}}, T2::NDTensors.BlockSparseTensor{ComplexF64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{ComplexF64, Vector{ComplexF64}, 2}}) @ ITensors ~/.julia/packages/ITensors/SOADD/src/itensor.jl:1912 [3] map!(f::Function, R::ITensor, T1::ITensor, T2::ITensor) @ ITensors ~/.julia/packages/ITensors/SOADD/src/itensor.jl:1921 [4] copyto! @ ~/.julia/packages/ITensors/SOADD/src/broadcast.jl:309 [inlined] [5] materialize! @ ./broadcast.jl:878 [inlined] [6] materialize! @ ./broadcast.jl:875 [inlined] [7] \_add(A::NDTensors.BlockSparseTensor{ComplexF64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{ComplexF64, Vector{ComplexF64}, 2}}, B::NDTensors.BlockSparseTensor{ComplexF64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{ComplexF64, Vector{ComplexF64}, 2}}) @ ITensors ~/.julia/packages/ITensors/SOADD/src/itensor.jl:1815 [8] +(A::ITensor, B::ITensor) @ ITensors ~/.julia/packages/ITensors/SOADD/src/itensor.jl:1823 [9] nhfactorize(::NDTensors.BackendSelection.Algorithm{:biorthoblock, @NamedTuple{}}, phil::ITensor, phir::ITensor, drho::ITensor, lindsl::Vector{Index{Vector{Pair{QN, Int64}}}}, lindsr::Vector{Index{Vector{Pair{QN, Int64}}}}, targettags::ITensors.TagSets.GenericTagSet{BitIntegers.UInt256, 4}, identities::Nothing; kwargs::@Kwargs{mindim::Int64, maxdim::Int64, cutoff::Float64}) @ ITensorNHDMRG ~/.julia/dev/ITensorNHDMRG/src/nhfactorize.jl:16 [10] nhreplacebond!(Ml::MPS, Mr::MPS, b::Int64, phil::ITensor, phir::ITensor, alg::String, identities::Nothing; ortho::String, eigen\_perturbation::ITensor, mindim::Int64, maxdim::Int64, cutoff::Float64, kwargs::@Kwargs{}) @ ITensorNHDMRG ~/.julia/dev/ITensorNHDMRG/src/nhfactorize.jl:100 [11] nhreplacebond! @ ~/.julia/dev/ITensorNHDMRG/src/nhfactorize.jl:65 [inlined] [12] macro expansion @ ~/.julia/dev/ITensorNHDMRG/src/nhdmrg.jl:243 [inlined] [13] macro expansion @ ./timing.jl:421 [inlined] [14] nhdmrg(PH::ITensorNHDMRG.ProjNHMPO, psil0::MPS, psir0::MPS, sweeps::Sweeps; alg::String, biorthoalg::String, isbiortho::Bool, observer::NoObserver, outputlevel::Int64, eigsolve\_tol::Float64, eigsolve\_krylovdim::Int64, eigsolve\_maxiter::Int64, eigsolve\_verbosity::Int64, eigsolve\_which\_eigenvalue::Symbol, biorthokwargs::@Kwargs{}) @ ITensorNHDMRG ~/.julia/dev/ITensorNHDMRG/src/nhdmrg.jl:186 [15] nhdmrg @ ~/.julia/dev/ITensorNHDMRG/src/nhdmrg.jl:125 [inlined] [16] #nhdmrg#8 @ ~/.julia/dev/ITensorNHDMRG/src/nhdmrg.jl:17 [inlined] [17] nhdmrg @ ~/.julia/dev/ITensorNHDMRG/src/nhdmrg.jl:8 [inlined] [18] gap(N::Int64; alg::String, biorthoalg::String, t1::Float64, γ::Float64, V::Float64, t2::Float64, u::Float64, nexcitedstates::Int64, weight::Float64, offset::Nothing, scale::Float64) @ Main ~/.julia/packages/ITensorNHDMRG/iZOiP/examples/2401.15000\_nhdmrg.jl:96 [19] gap @ ~/.julia/packages/ITensorNHDMRG/iZOiP/examples/2401.15000\_nhdmrg.jl:45 [inlined] [20] main() @ Main ~/.julia/packages/ITensorNHDMRG/iZOiP/examples/2401.15000\_nhdmrg.jl:163 [21] top-level scope @ ~/.julia/packages/ITensorNHDMRG/iZOiP/examples/2401.15000\_nhdmrg.jl:170 in expression starting at /Users/renjie/.julia/packages/ITensorNHDMRG/iZOiP/examples/2401.15000\_nhdmrg.jl:170 > [@tipfom](#): > > Hello everyone, > > I implemented a non-Hermitian DMRG variant [1, 2] in ITensor, which is available at [GitHub - tipfom/ITensorNHDMRG.jl: Collection of non-hermitian DMRG algorithms for ITensors.jl](https://github.com/tipfom/ITensorNHDMRG.jl). > Using the library is very straightforward and amounts to replacing the call to `dmrg` with a call to `nhdmrg`, see the example in the REAMDE or the examples at [ITensorNHDMRG.jl/examples at main · tipfom/ITensorNHDMRG.jl · GitHub](https://github.com/tipfom/ITensorNHDMRG.jl/tree/main/examples). > All normal functionality such as QN conservation should be supported. > > If you have any use for the library, feel free to check it out and let me know if you find are any bugs. > > [1] doi: 10.1103/5vnl-w9p4 > [2] doi: 10.1103/PhysRevB.105.205125 ---
**Author:** ![tipfom](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/tipfom/32/838_2.png) [@tipfom](https://itensor.discourse.group/u/tipfom)\ **Post date:** [December 17, 2025, 10:13am UTC](https://itensor.discourse.group/t/non-hermitian-dmrg-in-itensor/2536/4 "2025-12-17T10:13:34Z")
Dear @Jren, thanks for bringing this up! It is fixed now in the repository. Sorry for taking so long, I overlooked the notification. Let me know if there is anything else I can help with! Bests, tipfom ---
**Author:** ![Ashinxinl](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/ashinxinl/32/265_2.png) [@Ashinxinl](https://itensor.discourse.group/u/Ashinxinl)\ **Post date:** [December 19, 2025, 7:11am UTC](https://itensor.discourse.group/t/non-hermitian-dmrg-in-itensor/2536/5 "2025-12-19T07:11:42Z")
Hello tipfom， Thanks for sharing about it，I have a somewhat naive question: how do you calculate the expectation value under a biorthogonal basis？ Bests， jie