11565770445

Committed 29 Oct 2024 01:46AM UTC coverage: 94.31% (-0.5%) from 94.852%

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Feature/ExtendedHubbardMom1D (#286)

* Create ExtendedHubbardMom1D.jl

- New model (i.e. ``ExtendedHubbardMom1D`` is added to Rimu

* Update excitations.jl

- ``extended_momentum_transfer_diagonal`` is added for the nearest neighbour term in ``ExtendedHubbardMom1D``

* Update Hamiltonians.jl

- ``ExtendedHubbardMom1D`` is added to all the necessary test sets.

* Update Hamiltonians.jl

* Update hamiltonians.md

* Update Hamiltonians.jl

* Update src/Hamiltonians/ExtendedHubbardMom1D.jl

Co-authored-by: Joachim Brand <joachim.brand@gmail.com>

* Update src/Hamiltonians/ExtendedHubbardMom1D.jl

Co-authored-by: Joachim Brand <joachim.brand@gmail.com>

* Update src/Hamiltonians/excitations.jl

Co-authored-by: Joachim Brand <joachim.brand@gmail.com>

* Update src/Hamiltonians/ExtendedHubbardMom1D.jl

Co-authored-by: Joachim Brand <joachim.brand@gmail.com>

* Update HubbardMom1D.jl

* Update HubbardMom1D.jl

* Update HubbardMom1D.jl

* Update HubbardMom1D.jl

* Update HubbardMom1D.jl

* Update excitations.jl

* Update ExtendedHubbardMom1D.jl

* Update HubbardMom1D.jl

* Update Hamiltonians.jl

* Update Hamiltonians.jl

* Update HubbardMom1D.jl

* Update Hamiltonians.jl

* Update excitations.jl

* Update ExtendedHubbardMom1D.jl

* Update ExtendedHubbardMom1D.jl

* docstring fix for HubbardMom1DEP

* Update HubbardMom1DEP.jl

* Update excitations.jl

* Update ExtendedHubbardMom1D.jl

* Update ExtendedHubbardMom1D.jl

* Update HubbardMom1D.jl

* Update ExtendedHubbardMom1D.jl

* Update Hamiltonians.jl

- Added test for comparison between energies of ``ExtendedHubbardMom1D`` and ``ExtendedHubbardReal1D``

* Update src/Hamiltonians/ExtendedHubbardMom1D.jl

Co-authored-by: mtsch <matijacufar@gmail.com>

* Update src/Hamiltonians/ExtendedHubbardMom1D.jl

Co-authored-by: mtsch <matijacufar@gmail.com>

* Update Hamiltonians.jl

* Update Hamiltonians.jl

* Update Hamiltonian... (continued)

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/src/Hamiltonians/GuidingVectorSampling.jl

"""
    GuidingVectorSampling

Wrapper over any [`AbstractHamiltonian`](@ref) that implements guided vector a.k.a. guided
wave function sampling. In this importance sampling scheme the Hamiltonian is modified as
follows.

```math
\\tilde{H}_{ij} = v_i H_{ij} v_j^{-1}
```

and where `v` is the guiding vector. `v_i` and `v_j` are also thresholded to avoid dividing
by zero (see below).

# Constructors

* `GuidingVectorSampling(::AbstractHamiltonian, vector, eps)`
* `GuidingVectorSampling(::AbstractHamiltonian; vector, eps)`

`eps` is a thresholding parameter used to avoid dividing by zero; all values below `eps` are
set to `eps`. It is recommended that `eps` is in the same value range as the guiding
vector. The default value is set to `eps=norm(v, Inf) * 1e-2`

After construction, we can access the underlying hamiltonian with `G.hamiltonian`, the
`eps` parameter with `G.eps`, and the guiding vector with `G.vector`.

# Example

```jldoctest
julia> H = HubbardReal1D(BoseFS(1,1,1); u=6.0, t=1.0);

julia> v = DVec(starting_address(H) => 10; capacity=1);

julia> G = GuidingVectorSampling(H, v, 0.1);

julia> get_offdiagonal(H, starting_address(H), 4)
(BoseFS{3,3}(2, 0, 1), -1.4142135623730951)

julia> get_offdiagonal(G, starting_address(G), 4)
(BoseFS{3,3}(2, 0, 1), -0.014142135623730952)
```

# Observables

To calculate observables, pass the transformed Hamiltonian `G` to
[`AllOverlaps`](@ref) with keyword argument `transform=G`.
"""
struct GuidingVectorSampling{A,T,H<:AbstractHamiltonian{T},D,E} <: AbstractHamiltonian{T}
    # The A parameter sets whether this is an adjoint or not.
    # The E parameter is the epsilon value.
    hamiltonian::H
    vector::D
end

function GuidingVectorSampling(h, v::AbstractDVec, eps=1e-2 * norm(v, Inf))
    return GuidingVectorSampling{false,eltype(h),typeof(h),typeof(v),eps}(h, v)
end
function GuidingVectorSampling(h; vector, eps=1e-2 * norm(vector, Inf))
    return GuidingVectorSampling(h, vector, eps)
end

starting_address(h::GuidingVectorSampling) = starting_address(h.hamiltonian)
LOStructure(::Type{<:GuidingVectorSampling{<:Any,<:Any,H}}) where {H} = _lo_str(LOStructure(H))

function LinearAlgebra.adjoint(h::GuidingVectorSampling{A,T,<:Any,D,E}) where {A,T,D,E}
    h_adj = h.hamiltonian'
    return GuidingVectorSampling{!A,T,typeof(h_adj),D,E}(h_adj, h.vector)
end

dimension(h::GuidingVectorSampling, addr) = dimension(h.hamiltonian, addr)

Base.getproperty(h::GuidingVectorSampling, s::Symbol) = getproperty(h, Val(s))
Base.getproperty(h::GuidingVectorSampling{<:Any,<:Any,<:Any,<:Any,E}, ::Val{:eps}) where E = E
Base.getproperty(h::GuidingVectorSampling, ::Val{:hamiltonian}) = getfield(h, :hamiltonian)
Base.getproperty(h::GuidingVectorSampling, ::Val{:vector}) = getfield(h, :vector)

# Forward some interface functions.
num_offdiagonals(h::GuidingVectorSampling, add) = num_offdiagonals(h.hamiltonian, add)
diagonal_element(h::GuidingVectorSampling, add) = diagonal_element(h.hamiltonian, add)

_apply_eps(x, eps) = ifelse(iszero(x), eps, ifelse(abs(x) < eps, sign(x) * eps, x))

function guided_vector_modify(value, is_adjoint, eps, guide1, guide2)
    if iszero(guide1) && iszero(guide2)
        return value
    else
        guide1 = _apply_eps(guide1, eps)
        guide2 = _apply_eps(guide2, eps)
        if is_adjoint
            return value * (guide1 / guide2)
        else
            return value * (guide2 / guide1)
        end
    end
end

function get_offdiagonal(h::GuidingVectorSampling{A}, add1, chosen) where A
    add2, matrix_element = get_offdiagonal(h.hamiltonian, add1, chosen)
    guide1 = h.vector[add1]
    guide2 = h.vector[add2]
    return add2, guided_vector_modify(matrix_element, A, h.eps, guide1, guide2)
end

struct GuidingVectorOffdiagonals{
    F,T,A,E,H<:AbstractHamiltonian,D,N<:AbstractOffdiagonals{F,T}
}<:AbstractOffdiagonals{F,T}
    hamiltonian::H
    vector::D
    guide::T
    offdiagonals::N
end

function offdiagonals(h::GuidingVectorSampling{A,T,H,D,E}, a) where {A,T,H,D,E}
    hps = offdiagonals(h.hamiltonian, a)
    guide = h.vector[a]
    return GuidingVectorOffdiagonals{typeof(a),T,A,E,H,D,typeof(hps)}(
        h.hamiltonian, h.vector, guide, hps
    )
end

function Base.getindex(h::GuidingVectorOffdiagonals{F,T,A,E}, i)::Tuple{F,T} where {F,T,A,E}
    add2, matrix_element = h.offdiagonals[i]
    guide1 = h.guide
    guide2 = h.vector[add2]
    return add2, guided_vector_modify(matrix_element, A, E, guide1, guide2)
end

Base.size(h::GuidingVectorOffdiagonals) = size(h.offdiagonals)

"""
    TransformUndoer(k::GuidingVectorSampling, op::AbstractOperator)
    TransformUndoer(k::GuidingVectorSampling)

For a guiding vector similarity transformation ``\\hat{G} = f \\hat{H} f^{-1}``
define the operator ``f^{-1} \\hat{A} f^{-1}``, and special case ``f^{-2}``, in order
to calculate observables. Here ``f`` is a diagonal operator whose entries are
the components of the guiding vector, i.e.``f_{ii} = v_i``.

See [`AllOverlaps`](@ref), [`GuidingVectorSampling`](@ref).
"""
function TransformUndoer(k::GuidingVectorSampling, op::Union{Nothing,AbstractOperator})
    if isnothing(op)
        T = eltype(k)
    else
        T = promote_type(eltype(k), eltype(op))
    end
    return TransformUndoer{T,typeof(k),typeof(op)}(k, op)
end

# methods for general operator `f^{-1} A f^{-1}`
LOStructure(::Type{<:TransformUndoer{<:Any,<:GuidingVectorSampling,A}}) where {A} = LOStructure(A)

function LinearAlgebra.adjoint(s::TransformUndoer{T,<:GuidingVectorSampling,<:AbstractOperator}) where {T}
    a_adj = adjoint(s.op)
    return TransformUndoer{T,typeof(s.transform),typeof(a_adj)}(s.transform, a_adj)
end

function diagonal_element(s::TransformUndoer{<:Any,<:GuidingVectorSampling,<:AbstractOperator}, add)
    guide = s.transform.vector[add]
    diagA = diagonal_element(s.op, add)
    return guided_vector_modify(diagA, true, s.transform.eps, 1., 2 * guide)
end

function num_offdiagonals(s::TransformUndoer{<:Any,<:GuidingVectorSampling,<:Any}, add)
    return num_offdiagonals(s.op, add)
end

function get_offdiagonal(s::TransformUndoer{<:Any,<:GuidingVectorSampling,<:Any}, add1, chosen)
    add2, offd = get_offdiagonal(s.op, add1, chosen)
    # Guiding vector `v` is represented as a diagonal operator `f`
    guide1 = s.transform.vector[add1]
    guide2 = s.transform.vector[add2]
    return add2, guided_vector_modify(offd, true, s.transform.eps, 1., guide1 + guide2)
end

# methods for special case `f^{-2}`
LOStructure(::Type{<:TransformUndoer{<:Any,<:GuidingVectorSampling,Nothing}}) = IsDiagonal()

function diagonal_element(s::TransformUndoer{<:Any,<:GuidingVectorSampling,Nothing}, add)
    guide = s.transform.vector[add]
    return guided_vector_modify(1., true, s.transform.eps, 1., 2 * guide)
end

num_offdiagonals(s::TransformUndoer{<:Any,<:GuidingVectorSampling,Nothing}, add) = 0

1	"""
2	GuidingVectorSampling
3
4	Wrapper over any [`AbstractHamiltonian`](@ref) that implements guided vector a.k.a. guided
5	wave function sampling. In this importance sampling scheme the Hamiltonian is modified as
6	follows.
7
8	```math
9	\\tilde{H}_{ij} = v_i H_{ij} v_j^{-1}
10	```
11
12	and where `v` is the guiding vector. `v_i` and `v_j` are also thresholded to avoid dividing
13	by zero (see below).
14
15	# Constructors
16
17	* `GuidingVectorSampling(::AbstractHamiltonian, vector, eps)`
18	* `GuidingVectorSampling(::AbstractHamiltonian; vector, eps)`
19
20	`eps` is a thresholding parameter used to avoid dividing by zero; all values below `eps` are
21	set to `eps`. It is recommended that `eps` is in the same value range as the guiding
22	vector. The default value is set to `eps=norm(v, Inf) * 1e-2`
23
24	After construction, we can access the underlying hamiltonian with `G.hamiltonian`, the
25	`eps` parameter with `G.eps`, and the guiding vector with `G.vector`.
26
27	# Example
28
29	```jldoctest
30	julia> H = HubbardReal1D(BoseFS(1,1,1); u=6.0, t=1.0);
31
32	julia> v = DVec(starting_address(H) => 10; capacity=1);
33
34	julia> G = GuidingVectorSampling(H, v, 0.1);
35
36	julia> get_offdiagonal(H, starting_address(H), 4)
37	(BoseFS{3,3}(2, 0, 1), -1.4142135623730951)
38
39	julia> get_offdiagonal(G, starting_address(G), 4)
40	(BoseFS{3,3}(2, 0, 1), -0.014142135623730952)
41	```
42
43	# Observables
44
45	To calculate observables, pass the transformed Hamiltonian `G` to
46	[`AllOverlaps`](@ref) with keyword argument `transform=G`.
47	"""
48	struct GuidingVectorSampling{A,T,H<:AbstractHamiltonian{T},D,E} <: AbstractHamiltonian{T}
49	# The A parameter sets whether this is an adjoint or not.
50	# The E parameter is the epsilon value.
51	hamiltonian::H	14✔
52	vector::D
53	end
54
55	function GuidingVectorSampling(h, v::AbstractDVec, eps=1e-2 * norm(v, Inf))	13✔
56	return GuidingVectorSampling{false,eltype(h),typeof(h),typeof(v),eps}(h, v)	13✔
57	end
58	function GuidingVectorSampling(h; vector, eps=1e-2 * norm(vector, Inf))	2✔
59	return GuidingVectorSampling(h, vector, eps)	1✔
60	end
61
62	starting_address(h::GuidingVectorSampling) = starting_address(h.hamiltonian)	7✔
63	LOStructure(::Type{<:GuidingVectorSampling{<:Any,<:Any,H}}) where {H} = _lo_str(LOStructure(H))	10✔
64
65	function LinearAlgebra.adjoint(h::GuidingVectorSampling{A,T,<:Any,D,E}) where {A,T,D,E}	1✔
66	h_adj = h.hamiltonian'	1✔
67	return GuidingVectorSampling{!A,T,typeof(h_adj),D,E}(h_adj, h.vector)	1✔
68	end
69
70	dimension(h::GuidingVectorSampling, addr) = dimension(h.hamiltonian, addr)	2✔
71
72	Base.getproperty(h::GuidingVectorSampling, s::Symbol) = getproperty(h, Val(s))	4,522✔
73	Base.getproperty(h::GuidingVectorSampling{<:Any,<:Any,<:Any,<:Any,E}, ::Val{:eps}) where E = E	1,443✔
74	Base.getproperty(h::GuidingVectorSampling, ::Val{:hamiltonian}) = getfield(h, :hamiltonian)	170✔
75	Base.getproperty(h::GuidingVectorSampling, ::Val{:vector}) = getfield(h, :vector)	2,909✔
76
77	# Forward some interface functions.
78	num_offdiagonals(h::GuidingVectorSampling, add) = num_offdiagonals(h.hamiltonian, add)	1✔
79	diagonal_element(h::GuidingVectorSampling, add) = diagonal_element(h.hamiltonian, add)	56✔
80
81	_apply_eps(x, eps) = ifelse(iszero(x), eps, ifelse(abs(x) < eps, sign(x) * eps, x))	3,151✔
82
83	function guided_vector_modify(value, is_adjoint, eps, guide1, guide2)	3,577✔
84	if iszero(guide1) && iszero(guide2)	3,577✔
85	return value	2,040✔
86	else
87	guide1 = _apply_eps(guide1, eps)	1,576✔
88	guide2 = _apply_eps(guide2, eps)	1,575✔
89	if is_adjoint	1,537✔
90	return value * (guide1 / guide2)	1,468✔
91	else
92	return value * (guide2 / guide1)	69✔
93	end
94	end
95	end
96
97	function get_offdiagonal(h::GuidingVectorSampling{A}, add1, chosen) where A	13✔
98	add2, matrix_element = get_offdiagonal(h.hamiltonian, add1, chosen)	19✔
99	guide1 = h.vector[add1]	26✔
100	guide2 = h.vector[add2]	25✔
101	return add2, guided_vector_modify(matrix_element, A, h.eps, guide1, guide2)	13✔
102	end
103
104	struct GuidingVectorOffdiagonals{
105	F,T,A,E,H<:AbstractHamiltonian,D,N<:AbstractOffdiagonals{F,T}
106	}<:AbstractOffdiagonals{F,T}
107	hamiltonian::H	45✔
108	vector::D
109	guide::T
110	offdiagonals::N
111	end
112
113	function offdiagonals(h::GuidingVectorSampling{A,T,H,D,E}, a) where {A,T,H,D,E}	45✔
114	hps = offdiagonals(h.hamiltonian, a)	69✔
115	guide = h.vector[a]	51✔
116	return GuidingVectorOffdiagonals{typeof(a),T,A,E,H,D,typeof(hps)}(	45✔
117	h.hamiltonian, h.vector, guide, hps
118	)
119	end
120
121	function Base.getindex(h::GuidingVectorOffdiagonals{F,T,A,E}, i)::Tuple{F,T} where {F,T,A,E}	2,134✔
122	add2, matrix_element = h.offdiagonals[i]	2,134✔
123	guide1 = h.guide	2,134✔
124	guide2 = h.vector[add2]	3,528✔
125	return add2, guided_vector_modify(matrix_element, A, E, guide1, guide2)	2,134✔
126	end
127
128	Base.size(h::GuidingVectorOffdiagonals) = size(h.offdiagonals)	45✔
129
130	"""
131	TransformUndoer(k::GuidingVectorSampling, op::AbstractOperator)
132	TransformUndoer(k::GuidingVectorSampling)
133
134	For a guiding vector similarity transformation ``\\hat{G} = f \\hat{H} f^{-1}``
135	define the operator ``f^{-1} \\hat{A} f^{-1}``, and special case ``f^{-2}``, in order
136	to calculate observables. Here ``f`` is a diagonal operator whose entries are
137	the components of the guiding vector, i.e.``f_{ii} = v_i``.
138
139	See [`AllOverlaps`](@ref), [`GuidingVectorSampling`](@ref).
140	"""
141	function TransformUndoer(k::GuidingVectorSampling, op::Union{Nothing,AbstractOperator})	46✔
142	if isnothing(op)	46✔
143	T = eltype(k)	5✔
144	else
145	T = promote_type(eltype(k), eltype(op))	41✔
146	end
147	return TransformUndoer{T,typeof(k),typeof(op)}(k, op)	46✔
148	end
149
150	# methods for general operator `f^{-1} A f^{-1}`
151	LOStructure(::Type{<:TransformUndoer{<:Any,<:GuidingVectorSampling,A}}) where {A} = LOStructure(A)	36✔
152
153	function LinearAlgebra.adjoint(s::TransformUndoer{T,<:GuidingVectorSampling,<:AbstractOperator}) where {T}	×
154	a_adj = adjoint(s.op)	×
155	return TransformUndoer{T,typeof(s.transform),typeof(a_adj)}(s.transform, a_adj)	×
156	end
157
158	function diagonal_element(s::TransformUndoer{<:Any,<:GuidingVectorSampling,<:AbstractOperator}, add)	34✔
159	guide = s.transform.vector[add]	68✔
160	diagA = diagonal_element(s.op, add)	297✔
161	return guided_vector_modify(diagA, true, s.transform.eps, 1., 2 * guide)	34✔
162	end
163
164	function num_offdiagonals(s::TransformUndoer{<:Any,<:GuidingVectorSampling,<:Any}, add)	34✔
165	return num_offdiagonals(s.op, add)	60✔
166	end
167
168	function get_offdiagonal(s::TransformUndoer{<:Any,<:GuidingVectorSampling,<:Any}, add1, chosen)	1,362✔
169	add2, offd = get_offdiagonal(s.op, add1, chosen)	1,368✔
170	# Guiding vector `v` is represented as a diagonal operator `f`
171	guide1 = s.transform.vector[add1]	2,724✔
172	guide2 = s.transform.vector[add2]	2,718✔
173	return add2, guided_vector_modify(offd, true, s.transform.eps, 1., guide1 + guide2)	1,362✔
174	end
175
176	# methods for special case `f^{-2}`
177	LOStructure(::Type{<:TransformUndoer{<:Any,<:GuidingVectorSampling,Nothing}}) = IsDiagonal()	34✔
178
179	function diagonal_element(s::TransformUndoer{<:Any,<:GuidingVectorSampling,Nothing}, add)	34✔
180	guide = s.transform.vector[add]	68✔
181	return guided_vector_modify(1., true, s.transform.eps, 1., 2 * guide)	34✔
182	end
183
UNCOV 184	num_offdiagonals(s::TransformUndoer{<:Any,<:GuidingVectorSampling,Nothing}, add) = 0	×

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