Phase diagram of strongly correlated Fermi systems

Phase transitions caused by the redistribution of quasiparticle occupation numbers n(p) in homogeneous Fermi systems with particle repulsion are analyzed. The phase diagram of a strongly correlated Fermi system, when drawn in the coordinates “density ρ-dimensionless coupling constant η,” resembles a Washington pie for a rather broad class of interactions. Its upper part is “filled” with Fermi condensate, and the bottom part is filled with normal Fermi liquid. Both parts are separated by a narrow interlayer of Lifshitz phase with a multiply connected Fermi surface.     

Destruction of the Fermi surface due to pseudogap fluctuations in strongly correlated systems

We generalize the dynamical-mean field theory (DMFT) by including into the DMFT equations dependence on the correlation length of the pseudogap fluctuations via the additional (momentum dependent) self-energy Σ_k. This self-energy describes nonlocal dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures, these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT + Σ_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbor hopping. The effective single impurity problem is solved by using a numerical renormalization group (NRG). Both types of strongly correlated metals, namely, (i) doped Mott insulator and (ii) the case of the bandwidth W ? U (U-value of local Coulomb interaction) are considered. By calculating profiles of the spectral densities for different parameters of the model, we demonstrate the qualitative picture of Fermi surface destruction and formation of Fermi arcs due to pseudogap fluctuations in qualitative agreement with the ARPES experiments. Blurring of the Fermi surface is enhanced with the growth of the Coulomb interaction.     

Universal behavior of the collision rate in strongly correlated Fermi systems

Low temperature transport phenomena in strongly collision rate τ(T) is evaluated in closed form and applied to the calculation of the resistivity ρ(T). The ratio of ρ(T) to the square of the specific heat C _V(T) is shown to be a nearly universal function independent of the effective interaction between particles in medium. The result is found to be close to the well known Kadowaki-Woods ratio deduced from available experimental data on heavy fermion systems.     

Fermi surface reconstruction in strongly correlated Fermi systems as a first-order phase transition

A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point has been studied using the Fermi liquid approach. The transition takes place between topologically equivalent states with three Fermi surface sheets, but one of them is characterized by a quasiparticle halo in the quasiparticle momentum distribution n(p), and the other one is characterized by a hole pocket. It has been found that the transition between these states is a first-order phase transition for the interaction constant g and temperature T. The phase diagram in the vicinity of this transition has been constructed.     

Evolution of spin susceptibility from the Pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ～T^?1 appears in the expression for the spin susceptibility χ_ac(T) of the system after the transition point at finite temperatures. The behavior of χ_ac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature T _f is close to zero is discussed. The results are compared with the available experimental data.     

Energetics of a strongly correlated Fermi gas

The energy of the two-component Fermi gas with the s-wave contact interaction is a simple linear functional of its momentum distribution:

     

强关联费米气体的高温热力学性质

文章首先简要评述了目前强关联超冷费米原子体系的研究现状.由于缺少严格解和小相互作用参数,强关联的量子气体一直缺乏清晰的理解.在该项研究工作中,文章作者提出了一种系统的维里级数展开方法来研究强相互作用费米气体在高温下的热力学行为.方法中的控制小参量是易逸度,即exp(μ/kBT),其中μ是体系的化学势.文章提出了一种实用的方法去计算均匀或势阱束缚下的费米气体的维里展开系数,并首次精确得到了第三维里系数.文章将计算得到的热力学状态方程与最近的实验测量及量子蒙特卡罗模拟结果进行了比较.     

Large momentum part of a strongly correlated Fermi gas

It is well known that the momentum distribution of the two-component Fermi gas with large scattering length has a tail proportional to 1/k⁴ at large k. We show that the magnitude of this tail is equal to the adiabatic derivative of the energy with respect to the reciprocal of the scattering length, multiplied by a simple constant. This result holds at any temperature (as long as the effective interaction radius is negligible) and any large scattering length; it also applies to few-body cases. We then show some more connections between the 1/k⁴ tail and various physical quantities, including the pressure at thermal equilibrium and the rate of change of energy in a dynamic sweep of the inverse scattering length.     

Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases

A strongly correlated Fermi system plays a fundamental role in very different areas of physics, from neutron stars, quark–gluon plasmas, to high temperature superconductors. Despite the broad applicability, it is notoriously difficult to be understood theoretically because of the absence of a small interaction parameter. Recent achievements of ultracold trapped Fermi atoms near a Feshbach resonance have ushered in enormous changes. The unprecedented control of interaction, geometry and purity in these novel systems has led to many exciting experimental results, which are to be urgently understood at both low and finite temperatures. Here we review the latest developments of virial expansion for a strongly correlated Fermi gas and their applications on ultracold trapped Fermi atoms. We show remarkable, quantitative agreements between virial predictions and various recent experimental measurements at about the Fermi degenerate temperature. For equations of state, we discuss a practical way of determining high-order virial coefficients and use it to calculate accurately the long-sought third-order virial coefficient, which is now verified firmly in experiments at ENS and MIT. We discuss also virial expansion of a new many-body parameter—Tan’s contact. We then turn to less widely discussed issues of dynamical properties. For dynamic structure factors, the virial prediction agrees well with the measurement at the Swinburne University of Technology. For single-particle spectral functions, we show that the expansion up to the second order accounts for the main feature of momentum-resolved rf-spectroscopy for a resonantly interacting Fermi gas, as recently reported by JILA. In the near future, more practical applications with virial expansion are possible, owing to the ever-growing power in computation.     

Spin degrees of freedom and flattening of the spectra of single-particle excitations in strongly correlated Fermi systems

The impact of long-range spin-spin correlations on the structure of a flat portion in single-particle spectra ξ(p), which emerges beyond the point where the Landau state loses its stability, is studied. We supplement the well-known Nozieres model of a Fermi system with limited scalar long-range forces by a similar long-range spin-dependent term and calculate the spectra versus its strength g. It is found that Nozieres' results hold as long as g>0. However, with g changing its sign, the spontaneous magnetization is shown to arise at any nonzero g. The increase in the strength |g| is demonstrated to result in shrinkage of the domain in momentum space, occupied by the flat portion of ξ(p), and, eventually, in its vanishing.     

Phase behaviors of strongly correlated Fermi gases in one-dimensional confinements

We report on the ground state of models for strongly correlated one-dimensional Fermi systems by means of theoretical studies of two-component atomic Fermi gases in highly anisotropic harmonic traps. In this context, we consider (i) the Gaudin-Yang model for a Luttinger liquid with repulsive interactions, including an analysis of the emergence of Wigner molecules in the 2k _F → 4k _F crossover, and (ii) the lattice Hubbard model yielding Luttinger liquid and Mott insulator or band-insulator phases for repulsive interactions and the Luther-Emery phase for attractive interactions, including in the former case an analysis of the role of disorder. Our calculations use novel versions of density and spin-density functional theory and a density-matrix renormalization-group technique. We also discuss preliminary results and future perspectives in the study of nonsymmetric two-component Fermi gases.     

Incremental approach to strongly correlated many-body finite systems

The transition and the Green operators of an interacting N body system are obtained from the solutions of the N-M body problem where M = 1,2,ellipsis,N-2. This is achieved via the development of a cumulative, nonperturbative approach that makes use of existing knowledge on the system when the number of interacting particles is reduced. The method is applied to four interacting Coulomb particles where the Green operator is expressed as a sum of Green operators of all three body subsystems that can be combined within the four body system. The calculated four particle continuum spectrum is in a remarkable agreement with recent experimental findings.     

Born-Green-Yvon equations for strongly interacting Fermi systems

A subset of the Fermi-Born-Green-Yvon equations for extended Fermi systems is investigated numerically. We present results for nuclear matter, neutron matter, and normal liquid³He at zero temperature. A comparison with the (alternative) Fermi-Hypernetted-Chain theory demonstrates the Fermi-Born-Green-Yvon equations to be of comparable accuracy.     

Many-body theories of density response for a strongly correlated Fermi gas

Recent breakthroughs in the creation of ultracold atomic gases in the laboratory have ushered in major changes in physical science. Many novel experiments are now possible, with an unprecedented control of interaction, geometry and purity. Quantum many-body theory is facing severe challenges in quantitatively understanding new experimental results. Here, we review some recently developed theoretical techniques that provide successful predictions for density response of a strongly correlated atomic Fermi gas. These include the strong-coupling random-phase approximation theory, hightemperature quantum virial expansion, and asymptotically exact Tan relations applicable at large momentum.     

Low-temperature collapse of the Fermi surface and phase transitions in correlated Fermi systems

A topological crossover, associated with the collapse of the Fermi surface in strongly correlated Fermi systems, is examined. It is demonstrated that in these systems, the temperature domain where standard Ferrai liquid results hold dramatically narrows, because the Landau regime is replaced by a classical one. The impact of the collapse of the Fermi surface on pairing correlations is analyzed. In the domain of the Lifshitz phase diagram where the Fermi surface collapses, splitting of the BCS superconducting phase transition into two different ones of the same symmetry is shown to occur.