• Parallel and CUDA
• Minor bugs fixed
• New UI

Windows 10 Home

Wolfram Mathematica 10.2

• Wick expand of operators
  • Symetric expand
  • Antisymetric expand
  • User-defined (Not implemented)
• Vacuum average of creation and annihilation operators
• Simulate arbitrary Hamiltonian and initial state
  • Hamiltonian
    • Single term
    • Basic arithmetics
    • Infinite sum
    • Periodic boundary condition (Not implemented)
  • Initial state
    • Single term
    • Basic arithmetics
    • Infinite sum (Not implemented)
  • Partical type
    • Boson
    • Fermion
    • Hard-core Boson (Not implemented)

Assume the package file (SQQW.wl) is in the same category of your notebook.

Clear["Global`*"];
Get[NotebookDirectory[] <> "SQQW.wl"]
SQQWInitialize[];

H1 = SQHamiltonian[
  -HInfiniteSum[Subscript[SuperDagger[a], l + 1] ** Subscript[a, l] + Subscript[SuperDagger[a], l] ** Subscript[a, l + 1], {l}]
  +5 HInfiniteSum[Subscript[n, l + 1] ** Subscript[n, l], {l}]
   ];

This may seems odd here but in Mathematica it is displayed in the way of writing phyiscs equations.

Note that the double stars mean non-commutable multiplication.

Initial = SQInitial[0.5 InitialTerm[{0, 1}] + 0.5 InitialTerm[{2, 3}]];

This means the initial state is a superposition.

particalType = "Boson";

Currently, Boson and Fermion are supported.

base = Subscript[SuperDagger[a], l1] ** Subscript[SuperDagger[a], l2];

{{fe, fd}, H1Base, H1WaveFunction} = 
  SQHamiltonialEvolve[
    H1, 
    particalType, 
    Initial, 
    base, 
    {l1, l2}, {{l1, -10, 10}, {l2, l1, 10}}
  ];

A progress bar will show when constructing Hamiltonian matrix.

After calculation, fe and fd will be assigned to a encoding and decoding function which can be ignored. H1Base is assigned to a vector of bases. H1WaveFunction is assigned to the coresponding wave function under that base. Note that H1WaveFunction is a function of time.

H1CorrelationHalf[t_] := 
  Abs[Normal[
    SparseArray[
      Thread[Rule[
        Map[# + {10 + 1, 10 + 1} &, H1Base], 
        H1WaveFunction[t]
        ]],
    {2 10 + 1, 2 10 + 1}
  ]]]^2;
H1Correlation[t_] := (# + Transpose[#]) &[H1CorrelationHalf[t]];

Manipulate[
 MatrixPlot[
  Chop@H1Corelation[t],
  DataReversed -> {True, False},
  ColorFunction -> (Hue[(1 - #)^0.23*0.83] &),
  FrameTicks -> {Table[{i + 10 + 1, i}, {i, -10, 10, 5}], Table[{i + 10 + 1, i}, {i, -10, 10, 5}]}
  ],
{t, 0, 4}]