Magnetic Properties of the Second Mott Lobe in Pairing Hamiltonians

TL;DR

This paper investigates the magnetic properties of the second Mott lobe in bosonic pairing Hamiltonians, revealing a quantum phase transition in the Ising universality class and potential observation of the E8 spectrum.

Contribution

It provides a detailed analysis of the magnetic quantum phase transition in the second Mott lobe using analytical and numerical methods, linking to the 1D quantum Ising and anisotropic Heisenberg models.

Findings

Identification of a magnetic quantum phase transition in the second Mott lobe.

Observation of the potential for E8 mass spectrum in the critical Ising model.

Demonstration of tunable ferromagnetic and antiferromagnetic interactions.

Abstract

We explore the Mott insulating state of single-band bosonic pairing Hamiltonians using analytical approaches and large scale density matrix renormalization group calculations. We focus on the second Mott lobe which exhibits a magnetic quantum phase transition in the Ising universality class. We use this feature to discuss the behavior of a range of physical observables within the framework of the 1D quantum Ising model and the strongly anisotropic Heisenberg model. This includes the properties of local expectation values and correlation functions both at and away from criticality. Depending on the microscopic interactions it is possible to achieve either antiferromagnetic or ferromagnetic exchange interactions and we highlight the possibility of observing the E8 mass spectrum for the critical Ising model in a longitudinal magnetic field.