Many-body techniques

Many-body techniques are analytical and computational methods for describing systems of many interacting particles. They include perturbative expansions, diagrammatic methods, and numerical simulations.

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Many-body problem: The problem of predicting a system’s behavior when many particles interact with one another. Many-body techniques are methods designed to make this problem tractable.
Perturbation theory: A family of methods that approximates solutions by expanding around a solvable reference problem. It estimates interaction effects order by order when a suitable reference system exists.
Quantum Monte Carlo: A family of stochastic algorithms for calculating properties of quantum systems. It provides numerical estimates for ground states, thermal states, and correlation functions.
Hartree–Fock method: A self-consistent approximation in which each particle moves in an average field produced by the others. It captures exchange but neglects much of the correlated motion treated by richer methods.
Hamiltonian (quantum mechanics): The operator representing a quantum system’s total energy and governing its time evolution. Most many-body calculations begin by specifying the interacting system’s Hamiltonian.
Feynman diagram: A graphical representation of terms in a perturbative expansion of quantum amplitudes or correlation functions. Diagrams organize the contributions generated by many-body perturbation theory.
Density matrix renormalization group: A variational numerical method especially effective for one-dimensional quantum systems. It accurately treats many interacting particles when entanglement is limited.
Density functional theory: A framework that expresses ground-state properties through the particle density and an exchange-correlation functional. It often replaces explicit many-body wavefunctions with a more economical density description.
Fock space: A Hilbert space that combines sectors with different particle numbers. Creation and annihilation operators act naturally in the representation used by many-body methods.
Dyson equation: An equation relating a full propagator to a reference propagator and its self-energy. It resums interaction effects into a dressed Green’s function.