Added the reference and test of classical XY model

docs/src/assets/tnrkit.bib

@@ -233,3 +233,17 @@ @article{homma2024a
   number  = {4},
   doi     = {10.1103/PhysRevResearch.6.043102}
 }
+
+@article{Yu_2014,
+  title     = {Tensor renormalization group study of classical XY model on the square lattice},
+  volume    = {89},
+  ISSN      = {1550-2376},
+  url       = {http://dx.doi.org/10.1103/PhysRevE.89.013308},
+  DOI       = {10.1103/physreve.89.013308},
+  number    = {1},
+  journal   = {Physical Review E},
+  publisher = {American Physical Society (APS)},
+  author    = {Yu, J. F. and Xie, Z. Y. and Meurice, Y. and Liu, Yuzhi and Denbleyker, A. and Zou, Haiyuan and Qin, M. P. and Chen, J. and Xiang, T.},
+  year      = {2014},
+  month     = {jan}
+}

src/TNRKit.jl

@@ -89,7 +89,7 @@ export classical_ising, classical_ising_symmetric, ising_βc, f_onsager, ising_c
     classical_ising_triangular, classical_ising_triangular_symmetric,
     ising_βc_triangular, f_onsager_triangular,
     classical_ising_honeycomb, classical_ising_honeycomb_symmetric,
-    ising_βc_honeycomb, f_onsager_honeycomb
+    ising_βc_honeycomb, f_onsager_honeycomb, XY_βc
 
 include("models/gross-neveu.jl")
 export gross_neveu_start

src/models/XY.jl

@@ -1,4 +1,4 @@
-function algebraic_initialization(m::TensorMap, bond::TensorMap)
+function algebraic_initialization(m::AbstractTensorMap{E, S, 1, 2}, bond::AbstractTensorMap{E, S, 1, 1}) where {E, S}
     @tensor opt = true T[l u; d r] :=
         m[u; Au Bu] *
         bond[Au; Ad] *
@@ -11,6 +11,8 @@ function algebraic_initialization(m::TensorMap, bond::TensorMap)
     return T
 end
 
+const XY_βc = 1.1199 # This is an approximation!
+
 """
 $(SIGNATURES)
 
@@ -23,6 +25,9 @@ and charge truncation `charge_trunc`.
     classical_XY_U1_symmetric(0.9, 6)
 ```
 
+### References
+* [Yu et. al. 10.1103/PhysRevE.89.013308 (2014)](@cite Yu_2014)
+
 See also: [`classical_XY_O2_symmetric`](@ref).
 """
 function classical_XY_U1_symmetric(beta::Float64, charge_trunc::Int)
@@ -52,6 +57,9 @@ and charge truncation `charge_trunc`.
     classical_XY_O2_symmetric(0.9, 6)
 ```
 
+### References
+* [Yu et. al. 10.1103/PhysRevE.89.013308 (2014)](@cite Yu_2014)
+
 See also: [`classical_XY_U1_symmetric`](@ref).
 """
 function classical_XY_O2_symmetric(beta::Float64, charge_trunc::Int)

test/models.jl

@@ -28,3 +28,41 @@ model_temp_answer = [
         @test free_energy(data, temp) ≈ answer rtol = 1.0e-3
     end
 end
+
+@testset "LoopTNR - 2D XY model" begin
+    @info "Central charge of KT phase with U(1) symmetry"
+    T_KT = classical_XY_U1_symmetric(XY_βc + 0.1, 8)
+    scheme = LoopTNR(T_KT)
+    data = run!(scheme, truncrank(16), maxiter(20))
+    cft = cft_data(scheme, [sqrt(2), 2 * sqrt(2), 0])
+    central_charge = cft["c"]
+    @test central_charge ≈ 1.0 atol = 1.0e-2
+    @info "Obtained central charge:\n$central_charge."
+
+    @info "Central charge of symmetric phase with U(1) symmetry"
+    T_sym = classical_XY_U1_symmetric(XY_βc - 0.1, 8)
+    scheme = LoopTNR(T_sym)
+    data = run!(scheme, truncrank(16), maxiter(20))
+    cft = cft_data(scheme, [sqrt(2), 2 * sqrt(2), 0])
+    central_charge = cft["c"]
+    @test central_charge ≈ 0.0 atol = 1.0e-13
+    @info "Obtained central charge:\n$central_charge."
+
+    @info "Central charge of KT phase with O(2) symmetry"
+    T_KT = classical_XY_O2_symmetric(XY_βc + 0.1, 8)
+    scheme = LoopTNR(T_KT)
+    data = run!(scheme, truncrank(16), maxiter(20))
+    cft = cft_data(scheme, [sqrt(2), 2 * sqrt(2), 0])
+    central_charge = cft["c"]
+    @test central_charge ≈ 1.0 atol = 1.0e-2
+    @info "Obtained central charge:\n$central_charge."
+
+    @info "Central charge of symmetric phase with O(2) symmetry"
+    T_sym = classical_XY_O2_symmetric(XY_βc - 0.1, 8)
+    scheme = LoopTNR(T_sym)
+    data = run!(scheme, truncrank(16), maxiter(20))
+    cft = cft_data(scheme, [sqrt(2), 2 * sqrt(2), 0])
+    central_charge = cft["c"]
+    @test central_charge ≈ 0.0 atol = 1.0e-13
+    @info "Obtained central charge:\n$central_charge."
+end