Effective models for gapped phases of strongly correlated quantum lattice models

TL;DR

This paper introduces a non-perturbative scheme combining graph theory and continuous unitary transformations to derive effective models for gapped quantum lattice systems, accurately capturing low-energy physics.

Contribution

It presents a novel, robust method (gCUT) for deriving effective models in gapped quantum lattice models, applicable in both quasi-particle and low-energy regimes.

Findings

Successfully applied to 1D and 2D models with convincing thermodynamic limit results.

Shows the spin liquid in the Hubbard model on honeycomb lattice is outside strong-coupling perturbation.

Provides extensions and perspectives for the gCUT method.

Abstract

We present a robust scheme to derive effective models non-perturbatively for quantum lattice models when at least one degree of freedom is gapped. A combination of graph theory and the method of continuous unitary transformations (gCUTs) is shown to efficiently capture all zero-temperature fluctuations in a controlled spatial range. The gCUT can be used either for effective quasi-particle descriptions or for effective low-energy descriptions in case of infinitely degenerate subspaces. We illustrate the method for 1d and 2d lattice models yielding convincing results in the thermodynamic limit. We find that the recently discovered spin liquid in the Hubbard model on the honeycomb lattice lies outside the perturbative strong-coupling regime. Various extensions and perspectives of the gCUT are discussed.