ALPS Model Definitions

As part of the ALPS project we need to describe quantum lattice models in a common XML format, independent of the lattice they run on (see Lattice Definitions for that half of an ALPS input file). This section builds that format up in stages: from the model library file and its overall <MODEL>/<SITEBASIS>/<BASIS>/<HAMILTONIAN> structure, through the basis of a single site and of the full lattice, to the quantum operators and Hamiltonian terms built from them.

Introduction

An overview of the ALPS model library file (lib/xml/models.xml), the built-in models it provides (spin, boson/fermion Hubbard, t-J, Kondo lattice, and more) with a glossary of their parameters and citations to the original papers, and the four-part <MODEL>/<SITEBASIS>/<BASIS>/<HAMILTONIAN> structure used to define a custom model.

Site Basis

How to describe the Hilbert space of a single site with one or more <QUANTUMNUMBER> elements, including fermionic vs. bosonic quantum numbers, parametrized ranges and defaults, and models such as the t-J model where several equivalent choices of quantum numbers are possible.

Lattice Basis

How to combine single-site bases into the basis of the whole lattice with <BASIS>, covering lattices with more than one site per unit cell (including the # wildcard shortcut for per-type parameters), and how to restrict the basis with a <CONSTRAINT> on a summed quantum number (e.g. total Sz).

Quantum Operators

How to define the operators the Hamiltonian is built from: simple site operators with an explicit matrix element and quantum-number <CHANGE> (e.g. Splus, bdag, cdag_up), complex <SITEOPERATOR>s built from simpler ones (e.g. Sx), and two-site <BONDOPERATOR>s (e.g. exchange, fermion_hop).

Hamiltonian Descriptions

How to assemble a <HAMILTONIAN> from <PARAMETER> defaults, a <BASIS> reference, and <SITETERM>/<BONDTERM> elements — including type-dependent couplings, either via an explicit type attribute or the # wildcard.