Fermi surfaces and Luttinger’s theorem in paired fermion systems

Subir Sachdev,Kun Yang

doi:10.1103/physrevb.73.174504

Abstract

We discuss ground state properties of a mixture of two fermion species which can bind to form a molecular boson. When the densities of the fermions are unbalanced, one or more Fermi surfaces can appear: we describe the constraints placed by Luttinger's theorem on the volumes enclosed by these surfaces in such Bose-Fermi mixtures. We also discuss the nature of the quantum phase transitions involving changes in the number of Fermi surfaces.

Highlights

Recent experiments [1, 2] on trapped ultracold atoms have refocused theoretical attention on pairing between distinct fermion species, in situations in which the densities of the two species are unequal
On one side of the resonance the fermions bind to form a bosonic molecule which can condense into a BoseEinstein condensate (BEC), while on the other side they experience a weak attractive interaction which leads to formation of Cooper pairs in a Bardeen-Cooper-Schrieffer (BCS) state
This paper will describe the constraints that Luttinger’s theorem places on the volumes enclosed by Fermi surfaces under such conditions. Such constraints are distinct in different phases, and we will describe the quantum phase transitions across which the statement of Luttinger’s theorem changes. We note that these Fermi surface volume constraints are exact, and apply even in strongly interacting regimes where the fermions fluctuate into bosonic molecular states at short scales

Summary

INTRODUCTION

Recent experiments [1, 2] on trapped ultracold atoms have refocused theoretical attention on pairing between distinct fermion species, in situations in which the densities of the two species are unequal. In these experiments unequal numbers of two hyperfine states of fermionic 6Li atoms were mixed and scanned across a Feshbach resonance. Such constraints are distinct in different phases, and we will describe the quantum phase transitions across which the statement of Luttinger’s theorem changes We note that these Fermi surface volume constraints are exact, and apply even in strongly interacting regimes where the fermions fluctuate into bosonic molecular states at short scales. We use nonperturbative arguments similar to those of Yamanaka, Oshikawa and Affleck [6] to establish analogous results in one dimension

HAMILTONIAN AND PHASE DIAGRAM

LUTTINGER’S THEOREM

ONE DIMENSIONAL SYSTEMS

QUANTUM PHASE TRANSITIONS

Multicritical point M

Multicritical point L