Supported Lattices

Lattices.jl provides lattices showed below. In each figure, left side shows lattice shape, and right side shows definition of unit cells.

Square lattice

The most fundamental 2D bipartite lattice with coordination number $z=4$. It has a single site per unit cell and does not exhibit geometric frustration. Often used as a standard benchmark for 2D quantum many-body algorithms.

Triangular lattice

A lattice consisting of equilateral triangles with coordination number $z=6$. It is a prototypical example of a geometrically frustrated lattice (non-bipartite), famous for the $120^\circ$ magnetic order in the Heisenberg model.

Honeycomb lattice

A hexagonal lattice structure found in Graphene. It is a bipartite lattice with coordination number $z=3$ and contains 2 sites (sublattices A and B) in the unit cell.

Kagome lattice

A lattice consisting of corner-sharing triangles with coordination number $z=4$. It contains 3 sites in the unit cell. Known for strong geometric frustration and as a candidate host for Quantum Spin Liquids (QSL).

Lieb lattice

A lattice formed by removing the center sites from a $2 \times 2$ cluster of the square lattice, or decorating the edges of a square lattice. It is a bipartite lattice characterized by a flat band in its energy spectrum and ferrimagnetic ground states (Lieb's theorem).

Shastry-Sutherland lattice

A square lattice with additional orthogonal diagonal bonds (dimers). It is geometrically frustrated and realized in the material $\text{SrCu}_2(\text{BO}_3)_2$. The model is famous for having an exact dimer-singlet ground state in a certain parameter region.