Algorithms

abstract type AbstractRenormalizationAlgorithm

Abstract supertype of all algorithms available in this package.

abstract type AbstractBoundaryAlgorithm <: AbstractRenormalizationAlgorithm

Abstract supertype of all boundary algorithms

abstract type AbstractGrainingAlgorithm <: AbstractRenormalizationAlgorithm

Abstract supertype of all coarse-graining algorithms.

abstract type AbstractRenormalizationRuntime

Abstract supertype of all algorithm-specific runtime state objects.

abstract type AbstractBoundaryRuntime <: AbstractRenormalizationRuntime

Abstract supertype of all boundary runtime objects.

abstract type AbstractGrainingRuntime <: AbstractRenormalizationRuntime

Abstract supertype of all coarse-graining runtime state objects.

struct VUMPS <: AbstractBoundaryAlgorithm

Stores the parameters for the variational uniform matrix product state (VUMPS) boundary algorithm.

Fields

• bonddim::Int64: The bond dimension of the boundary.

• maxiter::Int64: Maximum number of iterations.

• tol::Float64: Convergence tolerance.

• verbose::Bool: When true, will print algorithm convergence progress.

Constructor

VUMPS(; bonddim, maxiter=100, tol=1e-12, verbose=true)

struct VUMPSRuntime{G, AType, CType, FType<:AbstractUnitCell, SType<:AbstractUnitCell} <: AbstractBoundaryRuntime

Fields

• mps::MPS{G, AType, CType} where {G, AType, CType}: The boundary matrix product state (MPS)

• fixedpoints::FixedPoints{FType} where FType<:AbstractUnitCell: Left and right fixed points of the transfer matrix

• svals::AbstractUnitCell: Singular values used to compute the convergence measure

struct MPS{G<:AbstractUnitCellGeometry, AType<:AbstractTensorMap{N, 2}, CType<:AbstractTensorMap{0, 2}}

Infinite boundary matrix product state (MPS) in mixed canonical form. MPS tensors have N "physical" indices. Has fields AL, C, AR and derived field AC such that

\[A_L(x,y) C(x,y) \approx C(x - 1, y) A_R(x, y) \approx AC(x, y) \quad \forall x,y \in \Lambda\]

where $\Lambda$ defines the unit cell of geometry G.

Examples

using TensorKit
physbonds = UnitCell(fill(ComplexSpace(2), 2, 1))
virtbonds = UnitCell(fill(ComplexSpace(3), 2, 1))
mps = MPS(rand, ComplexF64, physbonds, virtbonds);
AL, C, AR, AC = mps;
C

struct FixedPoints{A<:(AbstractUnitCell{G, var"#s290"} where {var"#s290"<:(TensorKit.AbstractTensorMap{T, S, N₁, 2} where {N₁, S, T}), G})} <: TensorRenormalizationGroups.AbstractFixedPoints

Left and right fixed points of the transfer matrix formed from each row-to-row transfer matrix sandwiched between the a boundary MPS and it's adjoint. This struct has two fields :left and :right which can be accessed directly.

abstract type AbstractCornerMethod <: AbstractBoundaryAlgorithm

Abstract supertype of all corner-based boundary methods.

struct CTMRG{SVD<:TensorKit.OrthogonalFactorizationAlgorithm} <: AbstractCornerMethod

Stores the parameters for the corner transfer matrix renormalization group (CTMRG) boundary algorithm.

Fields

• bonddim::Int64: The bond dimension of the boundary.

• maxiter::Int64: Maximum number of iterations.

• tol::Float64: Convergence tolerance.

• verbose::Bool: When true, will print algorithm convergence progress.

• ptol::Float64: Tolerance used in the pseudoinverse.

• svdalg::TensorKit.OrthogonalFactorizationAlgorithm: Algorithm used for the SVD. Either TensorKit.SVD() or TensorKit.SDD().

• randinit::Bool: If true, intialize with random tensors.

Constructor

CTMRG(; bonddim, maxiter=100, tol=1e-12, verbose=true, ptol=5e-8, svdalg=TensorKit.SVD(), randinit=false)

struct CornerMethodTensors{C<:Corners, E<:Edges, P<:TensorRenormalizationGroups.Projectors, N<:(AbstractUnitCell{G, ElType} where {G, ElType<:TensorKit.AbstractTensorMap})}

Concreate struct containing tensors required for a corner method. Fields are not public. Tensors can be accessed using the field getters corners and edges.

struct CornerMethodRuntime{T<:CornerMethodTensors, S<:TensorRenormalizationGroups.CornerSingularValues} <: AbstractRenormalizationRuntime

Runtime state of a corner method renormalization algorithm. Fields are not public. Tensors can be accessed using the field getters corners and edges.

struct Corners{C<:AbstractUnitCell}

Struct containing the corner tensors C1, C2, C3 and C4 stored in it's only field :data as a tuple in that order.

struct Edges{E<:AbstractUnitCell}

Struct containing the edge tensors T1, T2, T3 and T4 stored in it's only field :data as a tuple in that order.

corners(x::Union{CornerMethodTensors, CornerMethodRuntime}) -> Corners

Return the corner tensors associated with the object x.

edges(x::Union{CornerMethodTensors, CornerMethodRuntime}) -> Edges

Return the edge tensors associated with the object x.

struct TRG{T<:TensorKit.TruncationScheme} <: AbstractRenormalizationAlgorithm

Stores the parameters for the tensor renormalization group (TRG) coarse graining algorithm.

Fields

• trunc::TensorKit.TruncationScheme: The TruncationScheme used during the SVD step. See TensorKit.TruncationScheme and TensorKit.tsvd for more details.

• maxiter::Int64: Maximum number of iterations.

• tol::Float64: Convergence tolerance.

• verbose::Bool: When true, will print algorithm convergence progress.

Constructor

TRG(; trunc, maxiter=20, tol=1e-12, verbose=true)

struct TRGRuntime{AType, SType} <: AbstractGrainingRuntime

Runtime objects containing state of a TRG algorithm. The current cumulative value of the contraction can be obtained using the field :

Fields

• tensors::Any: Coarse-grained tensors at the current stage of the algorithms runtime.

• svals::Any: Singular values used for computing convergence tolerance.

• cumsum::Matrix{Float64}: The current cumulative value of the contraction with respect to each tensor in the unit cell.