We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is tuned to a critical value are characterized by a dynamic exponent $z$ related to the energy and length scales $\Delta$ and $\xi$. Simple arguments based on an expansion to first order in the effective interaction allow to define an upper-critical dimension $D_{C}=4$ (where $D=d+z$ and $d$ is the spatial dimension) below which mean-field description is no longer valid. We emphasize the role of pertubative renormalization group (RG) approaches and self-consistent renormalized spin fluctuation (SCR-SF) theories to understand the quantum-classical crossover in the vicinity of the quantum critical point with generalization to the Kondo effect in heavy-fermion systems. Finally we quote some recent inelastic neutron scattering experiments performed on heavy-fermions which lead to unusual scaling law in $\omega /T$ for the dynamical spin susceptibility revealing critical local modes beyond the itinerant magnetism scheme and mention new attempts to describe this local quantum critical point.

https://arxiv.org/pdf/cond-mat/0102119.pdf

Quantum Phase Transitions

The realization of superfluidity in a dilute gas of fermionic atoms, analogous to superconductivity in metals, represents a long-standing goal of ultracold gas research. In such a fermionic superfluid, it should be possible to adjust the interaction strength and tune the system continuously between two limits: a Bardeen–Cooper–Schrieffer (BCS)-type superfluid (involving correlated atom pairs in momentum space) and a Bose–Einstein condensate (BEC), in which spatially local pairs of atoms are bound together. This crossover between BCS-type superfluidity and the BEC limit has long been of theoretical interest, motivated in part by the discovery of high-temperature superconductors. In atomic Fermi gas experiments superfluidity has not yet been demonstrated; however, long-lived molecules consisting of locally paired fermions have been reversibly created. Here we report the direct observation of a molecular Bose–Einstein condensate created solely by adjusting the interaction strength in an ultracold Fermi gas of atoms. This state of matter represents one extreme of the predicted BCS–BEC continuum.

Emergence of a molecular Bose-Einstein condensate from a Fermi gas

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Theory Of Simple Liquids

We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold 6Li gas at magnetic fields above a Feshbach resonance, where no stable 6Li2 molecules would exist in vacuum. We accurately determined the position of the resonance to be 822+/-3 G. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.

Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance

When a gas of bosonic particles is cooled below a critical temperature, it condenses into a Bose-Ei…

Bose-Einstein condensation

We present a high-precision determination of the universal contact parameter in a strongly interacting Fermi gas. In a trapped gas at unitarity, we find the contact to be $3.06\ifmmode\pm\else\textpm\fi{}0.08$ at a temperature of 0.08 of the Fermi temperature in a harmonic trap. The contact governs the high-momentum (short-range) properties of these systems, and this low-temperature measurement provides a new benchmark for the zero-temperature homogeneous contact. The experimental measurement utilizes Bragg spectroscopy to obtain the dynamic and static structure factors of ultracold Fermi gases at high momentum in the unitarity and molecular Bose-Einstein condensate regimes. We have also performed quantum Monte Carlo calculations of the static properties, extending from the weakly coupled BCS regime to the strongly coupled Bose-Einstein condensate case, that show agreement with experiment at the level of a few percent.

Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas

We have studied the transition from two to three dimensions in a low temperature weakly interacting $^{6}\mathrm{Li}$ Fermi gas. Below a critical atom number ${N}_{2\mathrm{D}}$ only the lowest transverse vibrational state of a highly anisotropic oblate trapping potential is occupied and the gas is two dimensional. Above ${N}_{2\mathrm{D}}$ the Fermi gas enters the quasi-2D regime where shell structure associated with the filling of individual transverse oscillator states is apparent. This dimensional crossover is demonstrated through measurements of the cloud size and aspect ratio versus atom number.

/pdf/crossover-from-2d-to-3d-in-a-weakly-interacting-fermi-gas-3ltc6wy0dd.pdf

Crossover From 2D to 3D in a Weakly Interacting Fermi Gas

Bragg spectroscopy shows the evolution of gapless Goldstone modes and single-particle-like excitations in an atomic Fermi superfluid as it crosses from a Bardeen–Cooper–Schrieffer superfluid to the Bose–Einstein condensate regime.

Goldstone mode and pair-breaking excitations in atomic Fermi superfluids

Thermodynamic properties of matter are conveniently expressed as functional relations between variables known as equations of state. Here we experimentally determine the compressibility, density, and pressure equations of state for an attractive 2D Fermi gas in the normal phase as a function of temperature and interaction strength. In 2D, interacting gases exhibit qualitatively different features to those found in 3D. This is evident in the normalized density equation of state, which peaks at intermediate densities corresponding to the crossover from classical to quantum behavior.

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.045302

Thermodynamics of an Attractive 2D Fermi Gas.

The contact $\mathcal{I}$, introduced by Tan, has emerged as a key parameter characterizing universal properties of strongly interacting Fermi gases. For ultracold Fermi gases near a Feshbach resonance, the contact depends upon two quantities: the interaction parameter $1/({k}_{F}a)$, where ${k}_{F}$ is the Fermi wave vector and $a$ is the $s$-wave scattering length, and the temperature $T/{T}_{F}$, where ${T}_{F}$ is the Fermi temperature. We present the first measurements of the temperature dependence of the contact in a unitary Fermi gas using Bragg spectroscopy. The contact is seen to follow the predicted decay with temperature and shows how pair-correlations at high momentum persist well above the superfluid transition temperature.

https://researchbank.swinburne.edu.au/file/cd13d754-7941-4410-bf21-424949dfc746/1/PDF (Published version).pdf

Sascha Hoinka

Papers

Precise Determination of the Structure Factor and Contact in a Unitary Fermi Gas

Crossover From 2D to 3D in a Weakly Interacting Fermi Gas

Goldstone mode and pair-breaking excitations in atomic Fermi superfluids

Thermodynamics of an Attractive 2D Fermi Gas.

Temperature dependence of the universal contact parameter in a unitary Fermi gas.