Bosonization predicts that the specific heat, C(T), of a one-dimensional interacting Fermi system is a sum of the specific heats of free collective charge and spin excitations, plus the term with the running backscattering amplitude which flows to zero logarithmically with decreasing T. We verify whether this result is reproduced in the g-ology model. Of specific interest are the anomalous terms in C(T) that depend on the bare backscattering amplitude. We show that these terms can be incorporated into a renormalized spin velocity. We do this by proving the equivalence of the results for C(T) obtained within the g-ology model and by bosonization with velocities obtained by the numerical solution of the Bethe-ansatz equations for the Hubbard model.
We study the Fermi surface topological transition of the pocket-opening type in a two dimensional Fermi liquid with spin-orbit coupling of Rashba type. We find that the interactions, far from instabilities, drive the transition first order at zero temperature surprisingly in a more pronounced way than in the case of interacting Fermi liquid without spin-orbit coupling. We first gain insight from second order perturbation theory in the self-energy. We then extend the results to stronger interaction, using the self-consistent fluctuation approximation. We discuss existing experimental work on th…
Fermions in the Fermi gas obey the Pauli exclusion principle restricting any two fermions from filling the same quantum state. Strong interaction between fermions can completely change the properties of the Fermi gas. In our theoretical study we find a new exotic quantum phase in strongly interacting Fermi gases constrained to a certain condition imposed on the Fermi surfaces which we call the Fermi surface resonance. The new phase is quantum critical which can be identified by the power-law frequency tail of the spectral density and divergent static susceptibilities. An especially striking fe…
Recent experimental and numerical evidence suggest an intriguing universal relationship between the Fermi surface anisotropy of the non-interacting parent two-dimensional electron gas and the strongly correlated composite Fermi liquid formed in a strong magnetic field close to half-filing. Inspired by these observations, we explore more generally the question of anisotropy renormalization in interacting 2D Fermi systems. Using a recently developed non-perturbative and numerically-exact projective quantum Monte Carlo simulation as well as other numerical and analytic techniques, only for Dirac …
Reply to the Comment by Galanakis \textit{et al} on the paper \textquotedblleft Exact bosonization for an interacting Fermi gas in arbitrary dimensions"
Momentum space entanglement entropy probes quantum correlations in interacting fermionic phases. It is very sensitive to interactions, obeying volume-law scaling in general, while vanishing in the Fermi gas. We show that the Rényi entropy in momentum space has a systematic expansion in terms of the phase space volume of the partition, which holds at all orders in perturbation theory. This permits, for example, the controlled computation of the entropy of thin shells near the Fermi wavevector in isotropic Fermi liquids and BCS superconductors. In the Fermi liquid, the thin shell entropy is a un…
We study depletion dynamics of an open system of weakly interacting fermions with two-body random interactions. In this model fermions are escaping from the high-energy one-particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra-low temperatures. It is shown that due to dynamical thermalization the system instantaneously adjusts to the new chemical potential and temperature, so that occupation numbers of the one-particle orbitals always obey the Fermi-Dirac distribution. In this way we are able to describe the evaporation p…
Transport of strongly interacting fermions governs modern materials -- from the high-$T_c$ cuprates to bilayer graphene --, but also nuclear fission, the merging of neutron stars and the expansion of the early universe. Here we observe a universal quantum limit of diffusivity in a homogeneous, strongly interacting Fermi gas of atoms by studying sound propagation and its attenuation via the coupled transport of momentum and heat. In the normal state, the sound diffusivity ${D}$ monotonically decreases upon lowering the temperature $T$, in contrast to the diverging behavior of weakly interacting…
Many-body \textit{T}-matrix theory of a strongly interacting spin-orbit coupled Fermi gas: Momentum-resolved radio-frequency spectroscopy and fermionic pairing
