Lattice

Lattices are very common in both condensed matter physics and statistic physics. We offer a general tiny framework for lattices here.

All lattice types are subtype of AbstractLattice{N}

QMTK.AbstractLattice — Type.

AbstractLattice{N}

Abstract type for lattices. N indicated the dimension of this lattice type.

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We also offers some property tags for lattices. All possible property types are subtype of LatticeProperty.

QMTK.LatticeProperty

Currently we only offer one property: Boundary

QMTK.Boundary — Type.

Boundary <: LatticeTag

Abstract type for boundary conditions.

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There are two kinds of boundary conditions for a lattice

QMTK.Fixed — Type.

Fixed <: Boundary

Fixed boundary tag.

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QMTK.Periodic — Type.

Periodic <: Boundary

Periodic boundary tag.

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Lattice with Boundary Condition

All lattices with a boundary condition is the subtype of

QMTK.BCLattice — Type.

BCLattice{B, N} <: AbstractLattice{N}

Lattice with boundary condition.

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The BCLattice has the following interface

QMTK.isperiodic — Function.

isperiodic(lattice) -> Bool

whether this lattice has periodic boundary.

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QMTK.shape — Function.

shape(lattice) -> Tuple

get the shape of a lattice

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Base.length — Function.

length(lattice) -> Int

get the length (or the product of size in each dimension) of the lattice

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QMTK.sites — Function.

sites(lattice)

get the site iterator of the lattice.

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QMTK.bonds — Function.

bonds(lattice, k)

get the $k$th bond's iterator of the lattice

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To traverse all sites of a certain lattice, you can use it as an iterator.

for each_site in sites(lattice)
    println(each_site)
end

To traverse all bonds of a certain lattice, you can use bonds, the following example traverse 2nd nearest bond on the lattice.

for each_bond in bonds(lattice, 2)
    println(each_bond)
end

Chain Lattice

QMTK.Chain — Type.

Chain{B} <: BCLattice{B, 1}

general chain lattice with boundary condition B.

Chain([Boundary], length)

Construct a chain lattice with boundary (optional, default to be Fixed)

julia> Chain(10)
QMTK.Chain{QMTK.Fixed}(10)

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Square Lattice

QMTK.Square — Type.

Square{B} <: BCLattice{B, 2}

General square lattice with boundary condition B.

Square([Boundary], height, width)
Square([Boundary], shape)

Construct a square lattice. The shape follows the order of Julia's Native Array.

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