Add C4v CTMRG #321
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| """ | ||
| $(TYPEDEF) | ||
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| CTMRG algorithm assuming a C₄ᵥ-symmetric PEPS, i.e. invariance under 90° spatial rotation and | ||
| Hermitian reflection. This requires a single-site unit cell. The projector is obtained from | ||
| `eigh` decomposing the Hermitian enlarged corner. | ||
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| ## Fields | ||
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| $(TYPEDFIELDS) | ||
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| ## Constructors | ||
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| C4vCTMRG(; kwargs...) | ||
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| Construct a C₄ᵥ CTMRG algorithm struct based on keyword arguments. | ||
| For a full description, see [`leading_boundary`](@ref). The supported keywords are: | ||
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| * `tol::Real=$(Defaults.ctmrg_tol)` | ||
| * `maxiter::Int=$(Defaults.ctmrg_maxiter)` | ||
| * `miniter::Int=$(Defaults.ctmrg_miniter)` | ||
| * `verbosity::Int=$(Defaults.ctmrg_verbosity)` | ||
| * `trunc::Union{TruncationStrategy,NamedTuple}=(; alg::Symbol=:$(Defaults.trunc))` | ||
| * `decomposition_alg::Union{<:EighAdjoint,NamedTuple}` | ||
| * `projector_alg::Symbol=:$(Defaults.projector_alg_c4v)` | ||
| """ | ||
| struct C4vCTMRG{P <: ProjectorAlgorithm} <: CTMRGAlgorithm | ||
| tol::Float64 | ||
| maxiter::Int | ||
| miniter::Int | ||
| verbosity::Int | ||
| projector_alg::P | ||
| end | ||
| function C4vCTMRG(; kwargs...) | ||
| return CTMRGAlgorithm(; alg = :c4v, kwargs...) | ||
| end | ||
| CTMRG_SYMBOLS[:c4v] = C4vCTMRG | ||
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| """ | ||
| $(TYPEDEF) | ||
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| Projector algorithm implementing the `eigh` decomposition of a Hermitian enlarged corner. | ||
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| ## Fields | ||
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| $(TYPEDFIELDS) | ||
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| ## Constructors | ||
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| C4vEighProjector(; kwargs...) | ||
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| Construct the C₄ᵥ `eigh`-based projector algorithm based on the following keyword arguments: | ||
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| * `decomposition_alg::Union{<:EighAdjoint,NamedTuple}=EighAdjoint()` : `eigh` algorithm including the reverse rule. See [`EighAdjoint`](@ref). | ||
| * `trunc::Union{TruncationStrategy,NamedTuple}=(; alg::Symbol=:$(Defaults.trunc))` : Truncation strategy for the projector computation, which controls the resulting virtual spaces. Here, `alg` can be one of the following: | ||
| - `:fixedspace` : Keep virtual spaces fixed during projection | ||
| - `:notrunc` : No singular values are truncated and the performed SVDs are exact | ||
| - `:truncerror` : Additionally supply error threshold `η`; truncate to the maximal virtual dimension of `η` | ||
| - `:truncrank` : Additionally supply truncation dimension `η`; truncate such that the 2-norm of the truncated values is smaller than `η` | ||
| - `:truncspace` : Additionally supply truncation space `η`; truncate according to the supplied vector space | ||
| - `:trunctol` : Additionally supply singular value cutoff `η`; truncate such that every retained singular value is larger than `η` | ||
| * `verbosity::Int=$(Defaults.projector_verbosity)` : Projector output verbosity which can be: | ||
| 0. Suppress output information | ||
| 1. Print singular value degeneracy warnings | ||
| """ | ||
| struct C4vEighProjector{S <: EighAdjoint, T} <: ProjectorAlgorithm | ||
| decomposition_alg::S | ||
| trunc::T | ||
| verbosity::Int | ||
| end | ||
| function C4vEighProjector(; kwargs...) | ||
| return ProjectorAlgorithm(; alg = :c4v_eigh, kwargs...) | ||
| end | ||
| PROJECTOR_SYMBOLS[:c4v_eigh] = C4vEighProjector | ||
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| # struct C4vQRProjector{S, T} <: ProjectorAlgorithm | ||
| # decomposition_alg::S | ||
| # verbosity::Int | ||
| # end | ||
| # function C4vQRProjector(; kwargs...) | ||
| # return ProjectorAlgorithm(; alg = :c4v_qr, kwargs...) | ||
| # end | ||
| # PROJECTOR_SYMBOLS[:c4v_qr] = C4vQRProjector | ||
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| # | ||
| ## C4v-symmetric CTMRG iteration (called through `leading_boundary`) | ||
| # | ||
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| function ctmrg_iteration( | ||
| network, | ||
| env::CTMRGEnv, | ||
| alg::C4vCTMRG, | ||
| ) | ||
| enlarged_corner = c4v_enlarge(network, env, alg.projector_alg) | ||
| corner′, projector, info = c4v_projector(enlarged_corner, alg.projector_alg) | ||
| edge′ = c4v_renormalize(network, env, projector) | ||
| return CTMRGEnv(corner′, edge′), info | ||
| end | ||
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| """ | ||
| c4v_enlarge(network, env, ::C4vEighProjector) | ||
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| Compute the normalized and Hermitian-symmetrized C₄ᵥ enlarged corner. | ||
| """ | ||
| function c4v_enlarge(network, env, ::C4vEighProjector) | ||
| enlarged_corner = TensorMap(EnlargedCorner(network, env, (NORTHWEST, 1, 1))) | ||
| return 0.5 * (enlarged_corner + enlarged_corner') / norm(enlarged_corner) | ||
| end | ||
| # function c4v_enlarge(enlarged_corner, alg::C4vQRProjector) | ||
| # # TODO | ||
| # end | ||
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| """ | ||
| c4v_projector(enlarged_corner, alg::C4vEighProjector) | ||
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| Compute the C₄ᵥ projector from `eigh` decomposing the Hermitian `enlarged_corner`. | ||
| Also return the normalized eigenvalues as the new corner tensor. | ||
| """ | ||
| function c4v_projector(enlarged_corner, alg::C4vEighProjector) | ||
| trunc = truncation_strategy(alg, enlarged_corner) | ||
| D, U, info = eigh_trunc!(enlarged_corner, decomposition_algorithm(alg); trunc) | ||
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| # Check for degenerate eigenvalues | ||
| Zygote.isderiving() && ignore_derivatives() do | ||
| if alg.verbosity > 0 && is_degenerate_spectrum(D) | ||
| vals = TensorKit.SectorDict(c => diag(b) for (c, b) in blocks(D)) | ||
| @warn("degenerate eigenvalues detected: ", vals) | ||
| end | ||
| end | ||
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| return D / norm(D), U, (; D, U, info...) | ||
| end | ||
| # function c4v_projector(enlarged_corner, alg::C4vQRProjector) | ||
| # # TODO | ||
| # end | ||
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| """ | ||
| c4v_renormalize(network, env, projector) | ||
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| Renormalize the single edge tensor. | ||
| """ | ||
| function c4v_renormalize(network, env, projector) | ||
| new_edge = renormalize_north_edge(env.edges[1], projector, projector', network[1, 1]) | ||
| return new_edge / norm(new_edge) | ||
| end | ||
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| # TODO: this should eventually be the constructor for a new C4vCTMRGEnv type | ||
| function CTMRGEnv( | ||
| corner::AbstractTensorMap{T, S, 1, 1}, edge::AbstractTensorMap{T′, S, N, 1} | ||
| ) where {T, T′, S, N} | ||
| corners = fill(corner, 4, 1, 1) | ||
| edge_SW = physical_flip(edge) | ||
| edges = reshape([edge, edge, edge_SW, edge_SW], (4, 1, 1)) | ||
| return CTMRGEnv(corners, edges) | ||
| end | ||
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| # | ||
| ## utility | ||
| # | ||
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| # Adjoint of an edge tensor, but permutes the physical spaces back into the codomain. | ||
| # Intuitively, this conjugates a tensor and then reinterprets its 'direction' as an edge tensor. | ||
| function _dag(A::AbstractTensorMap{T, S, N, 1}) where {T, S, N} | ||
| return permute(A', ((1, (3:(N + 1))...), (2,))) | ||
| end | ||
| function physical_flip(A::AbstractTensorMap{T, S, N, 1}) where {T, S, N} | ||
| return flip(A, 2:N) | ||
| end | ||
| function project_hermitian(E::AbstractTensorMap{T, S, N, 1}) where {T, S, N} | ||
| E´ = (E + physical_flip(_dag(E))) / 2 | ||
| return E´ | ||
| end | ||
| function project_hermitian(C::AbstractTensorMap{T, S, 1, 1}) where {T, S} | ||
| C´ = (C + C') / 2 | ||
| return C´ | ||
| end | ||
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| # should perform this check at the beginning of `leading_boundary` really... | ||
| function check_symmetry(state, ::RotateReflect; atol = 1.0e-10) | ||
| @assert length(state) == 1 "check_symmetry only works for single site unit cells" | ||
| @assert norm(state[1] - _fit_spaces(rotl90(state[1]), state[1])) / | ||
| norm(state[1]) < atol "not rotation invariant" | ||
| @assert norm(state[1] - _fit_spaces(herm_depth(state[1]), state[1])) / | ||
| norm(state[1]) < atol "not hermitian-reflection invariant" | ||
| return nothing | ||
| end | ||
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| # | ||
| ## environment initialization | ||
| # | ||
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| """ | ||
| initialize_random_c4v_env([f=randn, T=scalartype(state)], state, Venv::ElementarySpace) | ||
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| Initialize a C₄ᵥ-symmetric `CTMRGEnv` on virtual spaces `Venv` with random entries created | ||
| by `f` and scalartype `T`. | ||
| """ | ||
| function initialize_random_c4v_env(state, Venv::ElementarySpace) | ||
| return initialize_random_c4v_env(randn, scalartype(state), state, Venv) | ||
| end | ||
| function initialize_random_c4v_env(f, T, state::InfinitePEPS, Venv::ElementarySpace) | ||
| Vpeps = domain(state[1])[1] | ||
| return initialize_random_c4v_env(f, T, Vpeps ⊗ Vpeps', Venv) | ||
| end | ||
| function initialize_random_c4v_env(f, T, state::InfinitePartitionFunction, Venv::ElementarySpace) | ||
| Vpf = domain(state[1])[1] | ||
| return initialize_random_c4v_env(f, T, Vpf, Venv) | ||
| end | ||
| function initialize_random_c4v_env(f, T, Vstate::VectorSpace, Venv::ElementarySpace) | ||
| corner₀ = DiagonalTensorMap(randn(real(T), Venv ← Venv)) | ||
| edge₀ = f(T, Venv ⊗ Vstate ← Venv) | ||
| edge₀ = project_hermitian(edge₀) | ||
| return CTMRGEnv(corner₀, edge₀) | ||
| end | ||
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| """ | ||
| initialize_singlet_c4v_env([T=scalartype(state)], state::InfinitePEPS, Venv::ElementarySpace) | ||
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| Initialize a C₄ᵥ-symmetric `CTMRGEnv` with a singlet corner of dimension `dim(Venv)` and an | ||
| identity edge from `id(T, Venv ⊗ Vpeps)`. | ||
| """ | ||
| function initialize_singlet_c4v_env(state::InfinitePEPS, Venv::ElementarySpace) | ||
| return initialize_singlet_c4v_env(scalartype(state), state, Venv) | ||
| end | ||
| function initialize_singlet_c4v_env(T, state::InfinitePEPS, Venv::ElementarySpace) | ||
| Vpeps = domain(state[1])[1] | ||
| return initialize_singlet_c4v_env(T, Vpeps, Venv) | ||
| end | ||
| function initialize_singlet_c4v_env(T, Vpeps::ElementarySpace, Venv::ElementarySpace) | ||
| corner₀ = DiagonalTensorMap(zeros(real(T), Venv ← Venv)) | ||
| corner₀.data[1] = one(real(T)) | ||
| edge₀ = permute(id(T, Venv ⊗ Vpeps), ((1, 2, 4), (3,))) | ||
| return CTMRGEnv(corner₀, edge₀) | ||
| end | ||
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Can we use a different name for this? I think MatrixAlgebraKit already exports this as well.