N-site Simple Update (#339)

* Introduce `TrotterMPOs`

* Remove `force_3site`

* Introduce `TrotterGates`

* Improve _get_bond_term; introduce _get_site_term

* Allow one-site terms in Hamiltonian for time evolution

* Cleanups

* Restore force_3site

* More cleanups

* Fix SU gauge fixing

* Generalize gate_to_mpo to any number of sites

* Multi-site simple update

* Use sequential CTMRG to improve convergence in test

* Make `trotterize` more universal

* Fix trivial SU gauge fixing

* Change Hubbard SU test for MPO gate

* Option for second order Trotter

* Tweak SU log message and docstrings

* Tweak Hubbard MPO-SU test

* Minor cleanup

* Fix logic in Hubbard MPO-SU test

* Merge _su_xbond, _su_ybond

* Enable bipartite mode for 2-site MPO gates

* Try fixing LAPACKException in tf_ising_finiteT

* Add `lattice` field to TrotterGates

* Fix SU gauge fixing again

* Undo changes to hubbard_model

* Update `trotterize` docstrings

Author: Yue-Zhengyuan

src/PEPSKit.jl

@@ -105,7 +105,6 @@ include("algorithms/truncation/fullenv_truncation.jl")
 include("algorithms/truncation/bond_truncation.jl")
 
 include("algorithms/time_evolution/trotter_gate.jl")
-include("algorithms/time_evolution/trotter_mpo.jl")
 include("algorithms/time_evolution/apply_gate.jl")
 include("algorithms/time_evolution/apply_mpo.jl")
 include("algorithms/time_evolution/time_evolve.jl")

src/algorithms/time_evolution/apply_gate.jl

@@ -1,3 +1,23 @@
+"""
+Apply 1-site `gate` on the PEPS or PEPO tensor `a`.
+"""
+function _apply_sitegate(
+        a::PEPSTensor, gate::AbstractTensorMap{T, S, 1, 1}; purified::Bool = true
+    ) where {T, S}
+    @assert purified
+    return gate * a
+end
+
+function _apply_sitegate(
+        a::PEPOTensor, gate::AbstractTensorMap{T, S, 1, 1}; purified::Bool = true
+    ) where {T, S}
+    @plansor a′[p1 p2; n e s w] := gate[p1; p] * a[p p2; n e s w]
+    if !purified
+        @plansor a′[p1 p2; n e s w] := a′[p1 p; n e s w] * gate[p; p2]
+    end
+    return a′
+end
+
 """
 $(SIGNATURES)
 

src/algorithms/time_evolution/apply_mpo.jl

@@ -283,17 +283,6 @@ e.g. Cluster in PEPS with `gate_ax = 1`:
         g1 -←-- g2 -←-- g3
         ↓       ↓       ↓
 ```
-
-In the cluster, the axes of each tensor use the MPS order
-```
-    PEPS:           PEPO:
-           3             3  4
-          ╱              | ╱
-    1 -- M -- 5     1 -- M -- 6
-       ╱ |             ╱ |
-      4  2            5  2
-    M[1 2 3 4; 5]  M[1 2 3 4 5; 6]
-```
 """
 function _apply_gatempo!(
         Ms::Vector{T1}, gs::Vector{T2}; gate_ax::Int = 1

src/algorithms/time_evolution/gaugefix_su.jl

@@ -17,22 +17,18 @@ $(TYPEDFIELDS)
     maxiter::Int = 100
 end
 
-"""
-A LocalOperator consisting of identity gates on all nearest neighbor bonds.
-"""
 function _trivial_gates(elt::Type{<:Number}, lattice::Matrix{S}) where {S <: ElementarySpace}
-    terms = []
-    for site1 in CartesianIndices(lattice)
+    Nr, Nc = size(lattice)
+    gates = map(Iterators.product(1:2, 1:Nc, 1:Nr)) do (d, c, r)
+        site1 = CartesianIndex(r, c)
+        site2 = (d == 1) ? CartesianIndex(r, c + 1) : CartesianIndex(r - 1, c)
         r1, c1 = mod1.(Tuple(site1), size(lattice))
-        for d in (CartesianIndex(1, 0), CartesianIndex(0, 1))
-            site2 = site1 + d
-            r2, c2 = mod1.(Tuple(site2), size(lattice))
-            V1, V2 = lattice[r1, c1], lattice[r2, c2]
-            h = TensorKit.id(elt, V1 ⊗ V2)
-            push!(terms, (site1, site2) => h)
-        end
+        r2, c2 = mod1.(Tuple(site2), size(lattice))
+        V1, V2 = lattice[r1, c1], lattice[r2, c2]
+        h = TensorKit.id(elt, V1 ⊗ V2)
+        return [site1, site2] => h
     end
-    return LocalOperator(lattice, terms...)
+    return TrotterGates(lattice, vec(gates))
 end
 
 """