Quasi-particle approach for general lattice Hamiltonians

TL;DR

This paper introduces a systematic quasi-particle method for general lattice Hamiltonians with large coordination numbers, expanding in 1/Z, applicable to various spin, Bose, and Fermi systems.

Contribution

It presents a new expansion-based approach for quasi-particle approximations in lattice models with large Z, demonstrating broad applicability.

Findings

Effective for large Z systems

Applicable to spin, Bose, and Fermi models

Provides a controlled approximation method

Abstract

In many condensed-matter systems, it is very useful to introduce a quasi-particle approach, which is based on some sort of linearization around a suitable background state. In order to be a systematic and controlled approximation, this linearization should be justified by an expansion into powers of some small control parameter. Here, we present a method for general lattice Hamiltonians with large coordination numbers Z >> 1, which is based on an expansion into powers of 1/Z. In order to demonstrate the generality of our method, we apply it to various spin systems, as well as the Bose and Fermi Hubbard model.