Songtao Huang, Yunpeng Ji, Thomas Repplinger, Gabriel G. T. Assumpção, Jianyi Chen, Grant L. Schumacher, Franklin J. Vivanco, Hadrien Kurkjian, Nir Navon
Landau’s Fermi-liquid (FL) theory has been successful at the phenomenological description of the normal phase of many different Fermi systems. Using a dilute atomic Fermi fluid with tunable interactions, we investigate the microscopic basis of Landau’s theory with a system describable from first principles. We study transport properties of an interacting Fermi gas by measuring its density response to a periodic external perturbation. In an ideal Fermi gas, we measure for the first time the celebrated Lindhard function. As the system is brought from the collisionless to the hydrodynamic regime, we observe the emergence of sound and find that the experimental observations are quantitatively understood with a first-principle transport equation for the FL. When the system is more strongly interacting, we find deviations from such predictions. Finally, we measure the momentum-space shape of the quasiparticle excitations and see how it evolves from the collisionless to the collisional regime. Our study establishes this system as a clean platform for studying Landau’s theory of the FL and paves the way for extending the theory to more exotic conditions, such as nonlinear dynamics and FLs with strong correlations in versatile settings.
Landau’s Fermi-liquid (FL) theory has been successful at the phenomenological description of the normal phase of many different Fermi systems. Using a dilute atomic Fermi fluid with tunable interactions, we investigate the microscopic basis of Landau’s theory with a system describable from first principles. We study transport properties of an interacting Fermi gas by measuring its density response to a periodic external perturbation. In an ideal Fermi gas, we measure for the first time the celebrated Lindhard function. As the system is brought from the collisionless to the hydrodynamic regime, we observe the emergence of sound and find that the experimental observations are quantitatively understood with a first-principle transport equation for the FL. When the system is more strongly interacting, we find deviations from such predictions. Finally, we measure the momentum-space shape of the quasiparticle excitations and see how it evolves from the collisionless to the collisional regime. Our study establishes this system as a clean platform for studying Landau’s theory of the FL and paves the way for extending the theory to more exotic conditions, such as nonlinear dynamics and FLs with strong correlations in versatile settings.
Abstract At low temperature, a normal gas of unpaired spin‐1/2 fermions is one of the cleanest realizations of a Fermi liquid. It is described by Landau's theory, where no phenomenological parameters are needed as the quasiparticle interaction function can be computed perturbatively in powers of the scattering length , the sole parameter of the short‐range interparticle interactions. Obtaining an accurate solution of the transport equation nevertheless requires a careful treatment of the collision kernel, as the uncontrolled error made by the relaxation time approximations increases when the temperature drops below the Fermi temperature. Here, sound waves in the hydrodynamic regime are studied up to second order in the Chapman‐Enskog's expansion. It is found that the frequency of the sound wave is shifted above its linear departure as where and are the speed and wavenumber of the sound wave and the typical collision time scales as . Besides the shear viscosity, the coefficient is described by a single second‐order collision time, which is computed exactly from an analytical solution of the transport equation, resulting in a positive dispersion . The results suggest that ultracold atomic Fermi gases are an ideal experimental system for quantitative tests of second‐order hydrodynamics.
This article follows up on arxiv:2511.15938, in which we developed an Hamiltonian renormalization scheme to construct a quantized theory of Fermi liquids. Here, we apply this formalism to a low-temperature atomic Fermi gas where the short-range interactions are fully parametrized by the s-wave scattering length a. We benchmark our renormalized theory by recovering known perturbative results on the static properties of the Fermi gas, such as the Lee-Huang-Yang expansion of the equation of state, the Galitskii expansion of the momentum distribution, and the Gor'kov-Melik Barkhudarov preexponential correction to the critical temperature. We then turn to the transport dynamics and demonstrate the presence of a preexponential correction to the speed of zero sound when including corrections of second order in a. Finally, we develop an efficient numerical method to solve the transport equation exactly, and we apply it to study the crossover from the collisionless to the hydrodynamic regime in the density and polarisation response functions.
The paradigm of Landau Fermi liquid theory has successfully described the low-energy behavior of numerous metallic systems. However, a growing number of experimental observations in strongly correlated electron materials, such as high-temperature superconductors and heavy fermion compounds, defy this conventional description, exhibiting what is known as non-Fermi liquid (NFL) behavior. These exotic states lack well-defined quasiparticle excitations, displaying anomalous scaling laws and transport properties. Ultracold atomic gases have emerged as highly controllable quantum simulators for strongly correlated matter, offering unprecedented access to tunable interaction strengths, dimensionality, and lattice geometries. This paper explores the potential of ultracold fermionic gases to unveil and characterize NFL behavior. We review the theoretical underpinnings of Landau Fermi liquid theory and its breakdown, survey prominent theoretical models for NFL states, and highlight experimental techniques in ultracold atomic systems pertinent to their detection. Specific attention is given to phenomena such as the BCS-BEC crossover, quantum criticality, and pseudogap phases in ultracold fermions, where strong interactions are expected to lead to deviations from quasiparticle descriptions. We discuss experimental signatures like anomalous spectral functions, linear-in-temperature resistivity analogs, and deviations in thermodynamic properties, proposing how these could be observed and analyzed in current and future ultracold atom platforms. This research aims to leverage the purity and tunability of atomic gases to gain fundamental insights into the nature of NFL states, contributing to a broader understanding of quantum many-body physics beyond the conventional quasiparticle picture.
We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme introduces an energy cutoff Λ to remove the resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau function f, the pair interaction g responsible for superfluidity, and the collision amplitude A responsible for transport and equilibration. Studying the flow equation that results from infinitesimal variations of the cutoff, we recover the Bethe-Salpeter relation between f and the forward limit of A, and we demonstrate an analogue relation between g and the frontal limit of A. We show that our effective theory captures all the low-energy phenomena of Fermi liquids, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to the calculation of non-Fermi liquid corrections to the quasiparticle lifetime. This publication is continued by arXiv:2607.07041 where we apply the effective theory to a Fermi fluid of ultracold atoms.
Abstract This chapter analyses Landau’s Fermi liquid theory. A fundamental postulate of Landau’s Fermi liquid theory is that quasiparticle energies are a function of the momentum, p, and that the momentum, pF, corresponding to the Fermi energy continues to be given by a free particle expression. Thus, the quasiparticle states are in one-to-one correspondence with those of an ideal Fermi gas and each quasiparticle has a spin quantum number, σ ± 1/2. The remainder of the chapter deals with the quasiparticle interaction function; sum rules; and collisionless collective modes, which are defined as a collective mode as a time- (or frequency) and space- (or wave vector) dependent oscillation of the fluid involving a coordinated motion of its constituent particles. Sample problems are also provided at the end of the chapter.
We use kinetic-theory methods to analyze Landau Fermi-liquid theory, and in particular to investigate the number and nature of modes in Fermi liquids that are soft in the long-wavelength limit, both in the hydrodynamic and the collisionless regimes. In the hydrodynamic regime we show that Fermi-liquid theory is consistent with Navier-Stokes hydrodynamics at all temperatures, as expected. The soft modes are the ones familiar from classical hydrodynamics that are controlled by the five conservation laws; namely, two first-sound modes, two shear diffusion modes, and one heat diffusion mode. These modes have a particle-like spectrum and are soft, or scale invariant, at all temperatures. In the collisionless regime we show that the entire single-particle distribution function is soft with a continuous part of the spectrum. This continuous soft mode, which is well known but often not emphasized, has important physical consequences, e.g., for certain quantum phase transitions. In addition, there are the well-known soft zero-sound excitations that describe angular fluctuations of the Fermi surface; their spectra are particle-like. They are unrelated to conservation laws, acquire a mass at any nonzero temperature, and their number depends on the strength of the quasiparticle interaction. We also discuss the fates of these two families of soft modes as the temperature changes. With increasing temperature the size of the collisionless regime shrinks, the damping of the modes grows, and eventually all of the collisionless modes become overdamped. In their stead the five hydrodynamic modes appear in the hydrodynamic regime at asymptotically low frequencies. The two families of soft modes are unrelated and have very different physical origins. In charged Fermi liquids the first-sound modes in the hydrodynamic regime and the $\ensuremath{\ell}=0$ zero-sound modes in the collisionless regime get replaced by plasmons, all other modes remain soft.