Large N Expansion for Strongly-coupled Boson-Fermion Mixtures

TL;DR

This paper develops a large N theoretical framework for strongly-coupled boson-fermion mixtures, revealing controllable quantum fluctuations and predicting BCS superfluidity of composite fermions at low temperatures.

Contribution

It introduces a novel large N expansion for boson-fermion mixtures with O(N) symmetry, enabling systematic analysis of quantum fluctuations and superfluid phases.

Findings

Controlled 1/N expansion for composite fermions.

Derivation of an effective action including next-to-leading order.

Prediction of BCS superfluidity of composite fermions at low temperatures.

Abstract

We study a many-body mixture of an equal number of bosons and two-component fermions with a strong contact attraction. In this system bosons and fermions can be paired into composite fermions. We construct a large N extension where both bosons and fermions have the extra large N degrees of freedom and the boson-fermion interaction is extended to a four-point contact interaction which is invariant under the O(N) group transformation, so that the composite fermions become singlet in terms of the O(N) group. It is shown that such O(N) singlet fields have controllable quantum fluctuations suppressed by 1/N factors and yield a systematic 1/N-expansion in terms of composite fermions. We derive an effective action described by composite fermions up to the next-to-leading-order terms in the large N expansion, and show that there can be the BCS superfluidity of composite fermions at sufficiently low temperatures.