Hubbardlike

Hubbardlike is an adjective used to describe models in theoretical physics that resemble the Hubbard model, a simple lattice model used to study strong correlations in many-body systems. In Hubbardlike models, particles move (hop) between sites of a lattice and interact primarily through local, on-site interactions, capturing the competition between kinetic energy and repulsion that can drive complex collective behavior.

A typical Hubbardlike Hamiltonian has the form H = -t sum_{<i j>, sigma} (c†_{i sigma} c_{j sigma} + h.c.) + U sum_i n_{i up} n_{i down} - mu sum_i n_i, where t is the hopping amplitude and U is the on-site interaction. The model is often studied at or near half-filling. Variants include multi-orbital versions, longer-range hopping, and additional terms such as nearest-neighbor repulsion V, exchange interactions J, or spin-orbit coupling. The Bose-Hubbard model is a closely related bosonic counterpart with analogous physics for bosons.

Applications of Hubbardlike models span condensed matter physics and cold-atom physics. They are used to understand Mott insulating phases, metal-insulator transitions, and magnetic order in correlated electron systems. In ultracold atomic experiments, optical lattices realize Hubbardlike physics with tunable t/U, enabling quantum simulations of lattice magnetism and transport. In the strong-coupling regime, effective models such as the t-J model can describe low-energy spin and charge dynamics after projecting out double occupancy.

Analytical and numerical methods employed include dynamical mean-field theory (DMFT), density-matrix renormalization group (DMRG), variational and auxiliary-field quantum Monte Carlo, and other many-body techniques. Hubbardlike models thus provide a versatile framework for exploring correlation effects across materials and platforms.