lattice

Simple Lattice/Graph Library

Main functions

• Access to information of lattice structure (sites, bonds, etc)
• Construct lattice from unitcell, span vector of supercell, and boundary conditions
• Construct lattice by adding sites and bonds one by one
• Reading and writing ALPS Lattice XML file

Prerequisites

• C++-14 compiler
• CMake to build tests and examples
• Eigen3
• [optional] Boost Library (Property Tree) for reading and writing XML files

How to build tests and examples and run tests

mkdir build
cd build
cmake ..
make
make test

Classes/types

• lattice::basis

  Helper class that contains the shape, i.e. the set of basis vectors, of the unit cell.

• lattice::unitcell

  Helper class that contains the structure, i.e. sites and bonds, of the unit cell.

• lattice::graph

  This class contains the structure of the whole lattice structure. It provides various information of sites (vertices) and bonds (edges) via the following member functions:

  member functions	description
  std::size_t dimension() const;	dimension of the lattice
  std::size_t num_sites() const;	total number of sites
  std::size_t site_type(std::size_t s) const;	type of site s
  const coordinate_t& coordinate(std::size_t s) const;	coordinate of site s
  std::size_t num_neighbors(std::size_t s) const;	number of neighboring sites of site s
  std::size_t neighbor(std::size_t s, std::size_t k) const;	k-th neighbor site of site s
  std::size_t neighbor_bond(std::size_t s, std::size_t k) const;	bond connecting site s and its k-th neighbor site
  std::size_t num_bonds() const;	total number of bonds
  int bond_type(std::size_t b) const;	type of bond s
  std::size_t source(std::size_t b) const;	start point (site) of bond b
  std::size_t target(std::size_t b) const;	end point (site) of bond b

How to construct lattices

• periodic chain lattice of 16 sites

  • simplest interface

    lattice::graph lat = lattice::graph::simple(1, 16);
    

  • most generic interface

    lattice::basis_t bs(1, 1); bs << 1; // 1x1 matrix
    lattice::basis basis(bs);
    lattice::unitcell unitcell(1);
    unitcell.add_site(lattice::coordinate(0), 0);
    unitcell.add_bond(0, 0, lattice::offset(1), 0);
    lattice::span_t span(1, 1); span << 16; // 1x1 matrix
    std::vector<lattice::boundary_t> boundary(1, lattice::boundary_t::periodic);
    lattice::graph lat(basis, unitcell, span, boundary);
    

• periodic square lattice of 4 x 4 sites

  • simplest interface

    lattice::graph lat = lattice::graph::simple(2, 4);
    

  • most generic interface

    lattice::basis_t bs(2, 2); bs << 1, 0, 0, 1; // 2x2 matrix
    lattice::basis basis(bs);
    lattice::unitcell unitcell(2);
    unitcell.add_site(lattice::coordinate(0, 0), 0);
    unitcell.add_bond(0, 0, lattice::offset(1, 0), 0);
    unitcell.add_bond(0, 0, lattice::offset(0, 1), 0);
    lattice::span_t span(2, 2); span << 4, 0, 0, 4; // 2x2 matrix
    std::vector<lattice::boundary_t> boundary(2, lattice::boundary_t::periodic);
    lattice::graph lat(basis, unitcell, span, boundary);
    

  • reading basis and unitcell from XML file

    std::string file = "lattices.xml";
    std::ifstream is(file);
    boost::property_tree::ptree pt;
    read_xml(is, pt);
    lattice::basis bs;
    read_xml(pt, "square lattice", bs);
    lattice::unitcell cell;
    read_xml(pt, "simple2d", cell);
    lattice::graph lat(bs, cell, lattice::extent(4, 4));
    

• fully connected lattice of 10 sites

  lattice::graph lat = lattice::graph::fully_connected(10);