Functions for Making Lattices

ITensor provides functions which return a vector of LatticeBond objects for conveniently working with various lattices such as the square lattice or triangular lattice.

The source code for these functions can be found in the folder itensor/mps/lattice and are meant to be written in a straightforward style that can be used to develop similar functions for other lattices. If you would like to contribute a lattice function (such as kagome, or next-neighbor triangular) which is currently missing, we would be happy to receive a pull request from you.

Synopsis

int Nx = 10;
int Ny = 10;

auto square_latt = squareLattice(Nx,Ny,{"YPeriodic=",true});
for(auto& bnd : square_latt)
    {
    printfln("Bond from site %d -> %d",bnd.s1,bnd.s2);
    }

auto square_latt_nn = squareNextNeighbor(Nx,Ny,{"YPeriodic=",true});
for(auto& bnd : square_latt_nn)
    {
    if(bnd.type == "1")
        {
        printfln("First-neighbor bond from site %d -> %d",bnd.s1,bnd.s2);
        }
    else if(bnd.type == "2")
        {
        printfln("Second-neighbor bond from site %d -> %d",bnd.s1,bnd.s2);
        }
    }

//Make a Hamiltonian on the triangular lattice using AutoMPO
auto sites = SpinHalf(Nx*Ny);
auto ampo = AutoMPO(sites);
auto tri_latt = triangularLattice(Nx,Ny);
for(auto& bnd : tri_latt)
    {
    ampo += "Sz",bnd.s1,"Sz",bnd.s2;
    ampo += 0.5,"S+",bnd.s1,"S-",bnd.s2;
    ampo += 0.5,"S-",bnd.s1,"S+",bnd.s2;
    }
auto H = toMPO(ampo);

Lattice Functions

• squareLattice(int Nx, int Ny, Args args = Args::global()) -> Lattice
  

  Return a Lattice (vector) of nearest-neighbor bonds of the two-dimensional square lattice of dimensions Nx by Ny.

  This function recognizes the following optional named arguments:

  • "YPeriodic" — (default=false). If true, includes next-neighbor periodic bonds wrapping around the y-direction.

• squareNextNeighbor(int Nx, int Ny, Args args = Args::global()) -> Lattice
  

  Return a Lattice (vector) of both nearest-neighbor and next-nearest-neighbor (second-nearest-neighbor) bonds of the two-dimensional square lattice of dimension Nx by Ny.

  First-neighbor bonds in the returned lattice have the type "1" while second-neighbor bonds have the type "2".

  This function recognizes the following optional named arguments:

  • "YPeriodic" — (default=false). If true, includes next-neighbor periodic bonds wrapping around the y-direction.

• triangularLattice(int Nx, int Ny, Args args = Args::global()) -> Lattice
  

  Return a Lattice (vector) of nearest-neighbor bonds of the two-dimensional triangular lattice of dimension Nx by Ny.

  This function recognizes the following optional named arguments:

  • "YPeriodic" — (default=false). If true, includes next-neighbor periodic bonds wrapping around the y-direction.