Luttinger theorem and imbalanced Fermi systems

Pieri, P.; Strinati, G. C.

doi:10.1140/epjb/e2017-80071-2

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…Quantum phase transitions are associated with the change in the number of Fermi surfaces when the system parameters are varied. In a recent article [85], the validity of the Luttinger's theorem was proven for any approximate theory based on a conserving approximation in case of spindensity imbalance. In the FFLO state, pairing occurs in such a way that the minority Fermi surface can be thought of as shifted by the FFLO wave vector q.…”

Section: 10luttinger's Theorem and Fermi Surfacesmentioning

confidence: 99%

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

et al. 2018

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We review the concepts and the present state of theoretical studies of spin-imbalanced superfluidity, in particular the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in the context of ultracold quantum gases. The comprehensive presentation of the theoretical basis for the FFLO state that we provide is useful also for research on the interplay between magnetism and superconductivity in other physical systems. We focus on settings that have been predicted to be favourable for the FFLO state, such as optical lattices in various dimensions and spin-orbit coupled systems. These are also the most likely systems for near-future experimental observation of the FFLO state. Theoretical bounds, such as Bloch's and Luttinger's theorems, and experimentally important limitations, such as finite-size effects and trapping potentials, are considered. In addition, we provide a comprehensive review of the various ideas presented for the observation of the FFLO state. We conclude our review with an analysis of the open questions related to the FFLO state, such as its stability, superfluid density, collective modes and extending the FFLO superfluid concept to new types of lattice systems.

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Section: 10luttinger's Theorem and Fermi Surfacesmentioning

confidence: 99%

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

et al. 2018

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“…These methods were applied to study the finite temperature BCS-BEC crossover, in particular the phase diagram of non-polarized [43,44] and polarized [45] gases. In [46], it was shown that within the Luttinger-Ward formalism, the Luttinger theorem is exactly fulfilled with the full Dyson equation.…”

Section: Discussionmentioning

confidence: 99%

Application of the renormalized random-phase approximation to polarized Fermi gases

Durel

Urban

2020

Phys. Rev. A

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We consider a spin imbalanced Fermi gas at zero temperature in the normal phase on the BCS side of the BCS-BEC crossover and around unitarity. We compute the critical polarization for pairing, the correlated occupation numbers and the contact in an extension of particle-particle RPA (also called non self-consistent T -matrix approach or ladder approximation). The so-called renormalized RPA consists in computing the T matrix with self-consistently determined occupation numbers. The occupation numbers are determined either by keeping the self-energy only to first order or by resumming the Dyson equation. In this way, the result for the critical polarization, strongly overestimated in standard RPA, is clearly improved. We also discuss some problems of this approach. arXiv:1908.00530v2 [cond-mat.quant-gas]

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Necessary and sufficient conditions for the validity of Luttinger’s theorem

Heath

Bedell

2020

New J. Phys.

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We derive the minimum requirements for the application of Luttinger's Theorem to a general manybody fermionic system of arbitrary interaction strength. By redefining the Fermi surface to include zero solutions of the interacting Green's function (i.e., "Luttinger surfaces"), we show that the only requirement that must be observed for the applicability of a "hard" Luttinger's theorem with trivial Luttinger count is the existence of a (D − 1)-dimensional manifold of gapless chiral excitations. Examples of systems with Luttinger surfaces that obey Luttinger's theorem are given, and the explicit dependence of Luttinger's theorem on the momentum and frequency dependence of the self energy is discussed.

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Luttinger theorem and imbalanced Fermi systems

Cited by 7 publications

References 23 publications

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

The Fulde–Ferrell–Larkin–Ovchinnikov state for ultracold fermions in lattice and harmonic potentials: a review

Application of the renormalized random-phase approximation to polarized Fermi gases

Necessary and sufficient conditions for the validity of Luttinger’s theorem

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