Effective Ising model for correlated systems with charge ordering

TL;DR

This paper derives an effective bosonic Ising model for charge ordering in correlated electronic systems, simplifying the description of complex many-body phenomena like charge order and magnetism.

Contribution

It introduces a new effective bosonic Ising model for charge degrees of freedom in the extended Hubbard model, linking complex correlations to a classical Ising Hamiltonian.

Findings

Derived an effective bosonic action for charge degrees of freedom.

Identified a regime where the action reduces to a classical Ising model.

Provides a simplified framework for studying charge ordering phenomena.

Abstract

Collective electronic fluctuations in correlated materials give rise to various important phenomena, such as existence of the charge ordering, superconductivity, Mott insulating and magnetic phases, plasmon and magnon modes, and other interesting features of such systems. Unfortunately, description of these correlation effects requires significant efforts, since they almost entirely rely on strong local and nonlocal electron-electron interactions. Some collective phenomena, such as magnetism, can be sufficiently described by a simple Heisenberg-like models that are formulated in terms of bosonic variables. This fact suggests that other many-body excitations can also be described by simple bosonic models in spirit of the Heisenberg theory. Here we derive an effective bosonic action for charge degrees of freedom for the extended Hubbard model and define a physical regime where the obtained action reduces to a classical Hamiltonian of an effective Ising model.