Update correlation length normalization (#212)

* Update correlation length normalization

* Fix typo

* Fix and update tests

* Format

* Add sectortype/spacetype

* Add missing space/sectortypes

Author: lkdvos

src/algorithms/toolbox.jl

@@ -275,26 +275,50 @@ in a specific symmetry sector).
 MPSKit.correlation_length(state, env::CTMRGEnv; num_vals=2, kwargs...) =
     _correlation_length(env; num_vals, kwargs...)
 
-function _correlation_length(env::CTMRGEnv; num_vals=2, kwargs...)
+function _correlation_length(
+    env::CTMRGEnv; num_vals=2, sector=one(sectortype(env)), kwargs...
+)
     _, n_rows, n_cols = size(env)
 
     # Horizontal
     λ_h = map(1:n_rows) do r
         above = InfiniteMPS(env.edges[NORTH, r, :])
         below = InfiniteMPS(_dag.(env.edges[SOUTH, _next(r, n_rows), :]))
-        vals = MPSKit.transfer_spectrum(above; below, num_vals, kwargs...)
-        return vals ./ abs(vals[1]) # normalize largest eigenvalue
+        vals = MPSKit.transfer_spectrum(above; below, num_vals, sector, kwargs...)
+
+        # normalize using largest eigenvalue in trivial sector
+        if isone(sector)
+            N = first(vals)
+        else
+            vals_triv = MPSKit.transfer_spectrum(above; below, num_vals=1, kwargs...)
+            N = first(vals_triv)
+        end
+        return vals ./ N # normalize largest eigenvalue
     end
-    ξ_h = map(λ -> -1 / log(abs(λ[2])), λ_h)
 
     # Vertical
     λ_v = map(1:n_cols) do c
         above = InfiniteMPS(env.edges[EAST, :, c])
         below = InfiniteMPS(_dag.(env.edges[WEST, :, _next(c, n_cols)]))
-        vals = MPSKit.transfer_spectrum(above; below, num_vals, kwargs...)
-        return vals ./ abs(vals[1]) # normalize largest eigenvalue
+        vals = MPSKit.transfer_spectrum(above; below, num_vals, sector, kwargs...)
+
+        # normalize using largest eigenvalue in trivial sector
+        if isone(sector)
+            N = first(vals)
+        else
+            vals_triv = MPSKit.transfer_spectrum(above; below, num_vals=1, kwargs...)
+            N = first(vals_triv)
+        end
+        return vals ./ N # normalize largest eigenvalue
+    end
+
+    if isone(sector)
+        ξ_h = map(λ -> -1 / log(abs(λ[2])), λ_h)
+        ξ_v = map(λ -> -1 / log(abs(λ[2])), λ_v)
+    else
+        ξ_h = map(λ -> -1 / log(abs(λ[1])), λ_h)
+        ξ_v = map(λ -> -1 / log(abs(λ[1])), λ_v)
     end
-    ξ_v = map(λ -> -1 / log(abs(λ[2])), λ_v)
 
     return ξ_h, ξ_v, λ_h, λ_v
 end

src/environments/ctmrg_environments.jl

@@ -379,6 +379,16 @@ end
 Base.real(env::CTMRGEnv) = CTMRGEnv(real.(env.corners), real.(env.edges))
 Base.complex(env::CTMRGEnv) = CTMRGEnv(complex.(env.corners), complex.(env.edges))
 
+cornertype(env::CTMRGEnv) = cornertype(typeof(env))
+cornertype(::Type{CTMRGEnv{C,E}}) where {C,E} = C
+edgetype(env::CTMRGEnv) = edgetype(typeof(env))
+edgetype(::Type{CTMRGEnv{C,E}}) where {C,E} = E
+
+TensorKit.spacetype(env::CTMRGEnv) = spacetype(typeof(env))
+TensorKit.spacetype(::Type{E}) where {E<:CTMRGEnv} = spacetype(cornertype(E))
+TensorKit.sectortype(env::CTMRGEnv) = sectortype(typeof(env))
+TensorKit.sectortype(::Type{E}) where {E<:CTMRGEnv} = sectortype(cornertype(E))
+
 # In-place update of environment
 function update!(env::CTMRGEnv{C,T}, env´::CTMRGEnv{C,T}) where {C,T}
     env.corners .= env´.corners

src/states/infinitepeps.jl

@@ -139,6 +139,10 @@ end
 
 ## Spaces
 
+TensorKit.sectortype(t::InfinitePEPS) = sectortype(typeof(t))
+TensorKit.sectortype(::Type{T}) where {T<:InfinitePEPS} = sectortype(eltype(T))
+TensorKit.spacetype(t::InfinitePEPS) = spacetype(typeof(t))
+TensorKit.spacetype(::Type{T}) where {T<:InfinitePEPS} = spacetype(eltype(T))
 virtualspace(n::InfinitePEPS, r::Int, c::Int, dir) = virtualspace(n[r, c], dir)
 physicalspace(n::InfinitePEPS, r::Int, c::Int) = physicalspace(n[r, c])
 

test/ctmrg/correlation_length.jl

@@ -1,4 +1,5 @@
 using Test: @test, @testset
+using TensorKit
 using TensorKit: ←, ⊗, SU2Irrep, Vect, permute, truncdim, truncbelow
 using MPSKit: correlation_length, leading_boundary
 using PEPSKit: CTMRGEnv, InfinitePEPS
@@ -8,15 +9,15 @@ using PEPSKit: CTMRGEnv, InfinitePEPS
     vD = Vect[SU2Irrep](1//2 => 1)
     vd = Vect[SU2Irrep](2 => 1)
     tAKLT_A = ones(vd ← vD ⊗ vD ⊗ vD ⊗ vD)
-    tAKLT_B = permute(adjoint(tAKLT_A), (5,), (1, 2, 3, 4))
+    tAKLT_B = permute(adjoint(tAKLT_A), ((5,), (1, 2, 3, 4)))
 
     ψ = InfinitePEPS([tAKLT_A tAKLT_B; tAKLT_B tAKLT_A])
-    trscheme = truncdim(20) & truncbelow(1e-12)
-    boundary_alg = (; tol=1e-10, trscheme=trscheme, maxiter=1, verbosity=0)
+    trscheme = truncbelow(1e-12) & truncdim(48)
+    boundary_alg = (; tol=1e-10, trscheme=trscheme, maxiter=400, verbosity=3)
     env0 = CTMRGEnv(randn, Float64, ψ, oneunit(vD))
     env, info_ctmrg = leading_boundary(env0, ψ; boundary_alg...)
 
-    ξ_h, ξ_v, λ_h, λ_v = correlation_length(ψ, env)
+    ξ_h, ξ_v, λ_h, λ_v = correlation_length(ψ, env; sector=SU2Irrep(1))
     @test ξ_h isa Vector{Float64}
     @test size(ξ_h) == (2,)
     @test all(isfinite.(ξ_h))
@@ -26,4 +27,9 @@ using PEPSKit: CTMRGEnv, InfinitePEPS
     @test size(ξ_v) == (2,)
     @test all(isfinite.(ξ_v))
     @test all(ξ_v .> 0)
+
+    # AKLT state should have correlation length ~ 2sites
+    # https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.121115
+    @test all(x -> isapprox(x * size(ψ, 2), 2; atol=0.1), ξ_h)
+    @test all(x -> isapprox(x * size(ψ, 1), 2; atol=0.1), ξ_v)
 end