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Bulletin of the American Physical Society

Luttinger theorem and Fermi liquid behavior close to a Feshbach resonance

S. Gaudio, Jason Jackiewicz, Kevin S. Bedell

Published Mar 6, 2007• 0 citations
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We present a study of a gas of bosons confined in one dimension with Feshbach-resonant interactions, at zero temperature. Unlike the gas of one-dimensional bosons with non resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses additional features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this regime in detail due to the lack of the appropriate formalism.

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Fermi liquid behavior and Luttinger's theorem close to a diverging scattering length

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We derive the thermodynamic properties of a Fermi gas, deep into the quantum degenerate regime. We show that, if Luttinger's theorem holds, a first-order phase transition occurs in the normal phase as a function of the interaction strength. We also show that a volume change occurs at finite temperatures as we go through a divergence in the s-wave scattering length, in the normal phase. The first-order transition has a critical temperature, T *, above the BCS transition temperature. Also, we show that a paramagnetic system in equilibrium, close to the divergence of the scattering length, on the negative side, screens out any applied magnetic field.

arXiv:cond-mat/0703722•The Philosophical Magazine A Journal of Theoretical Experimental and Applied Physics•Jun 20, 2009•2 citations
We present a study of a gas of bosons confined in one dimension with Feshbach-resonant interactions, at zero temperature. Unlike the gas of one-dimensional bosons with non resonant interactions, which is known to be equivalent to a system of interacting spinless fermions and can be described using the Luttinger liquid formalism, the resonant gas possesses additional features. Depending on its parameters, the gas can be in one of three possible regimes. In the simplest of those, it can still be described by the Luttinger liquid theory, but its Fermi momentum cannot be larger than a certain cutoff momentum dependent on the details of the interactions. In the other two regimes, it is equivalent to a Luttinger liquid at low density only. At higher densities its excitation spectrum develops a minimum, similar to the roton minimum in helium, at momenta where the excitations are in resonance with the Fermi sea. As the density of the gas is increased further, the minimum dips below the Fermi energy, thus making the ground state unstable. At this point the standard ground state gets replaced by a more complicated one, where not only the states with momentum below the Fermi points, but also the ones with momentum close to that minimum, get filled, and the excitation spectrum develops several branches. We are unable so far to study this regime in detail due to the lack of the appropriate formalism.
We derive the thermodynamic properties of a Fermi gas, deep into the quantum degenerate regime. We show that, if Luttinger's theorem holds, a first-order phase transition occurs in the normal phase as a function of the interaction strength. We also show that a volume change occurs at finite temperatures as we go through a divergence in the s-wave scattering length, in the normal phase. The first-order transition has a critical temperature, T *, above the BCS transition temperature. Also, we show that a paramagnetic system in equilibrium, close to the divergence of the scattering length, on the negative side, screens out any applied magnetic field.