Landau Fermi Liquid Theory Research Articles

Critical Exponents of Quark Matter

I investigate the ferromagnetic phase transition inside strong quark matter (SQM) with one gluon exchange interaction between strong quarks. I use a variational method and the Landau-Fermi liquid theory and obtain the thermodynamics quantities of SQM. In the low temperature limit, the equation of state (EOS) and critical exponents for the second-order phase transition (ferromagnetic phase transition) in SQM are analytically calculated. The results are in agreement with the Ginzberg-Landau theory.

Non-Fermi-liquid d-wave metal phase of strongly interacting electrons

Developing a theoretical framework for conducting electronic fluids qualitatively distinct from those described by Landau's Fermi-liquid theory is of central importance to many outstanding problems in condensed matter physics. One such problem is that, above the transition temperature and near optimal doping, high-transition-temperature copper-oxide superconductors exhibit 'strange metal' behaviour that is inconsistent with being a traditional Landau Fermi liquid. Indeed, a microscopic theory of a strange-metal quantum phase could shed new light on the interesting low-temperature behaviour in the pseudogap regime and on the d-wave superconductor itself. Here we present a theory for a specific example of a strange metal--the 'd-wave metal'. Using variational wavefunctions, gauge theoretic arguments, and ultimately large-scale density matrix renormalization group calculations, we show that this remarkable quantum phase is the ground state of a reasonable microscopic Hamiltonian--the usual t-J model with electron kinetic energy t and two-spin exchange J supplemented with a frustrated electron 'ring-exchange' term, which we here examine extensively on the square lattice two-leg ladder. These findings constitute an explicit theoretical example of a genuine non-Fermi-liquid metal existing as the ground state of a realistic model.

Fermi Liquid in a Torsional Oscillator

We study the transverse acoustic impedance of normal Fermi liquid inside a torsionally oscillating cylindrical container. We use Landau's Fermi liquid theory, and our approach is applicable to both normal 3He and mixtures of 3He in superfluid 4He. The fluid causes dissipation and a change of the resonant frequency of the oscillator. Usually, a liquid medium increases the moment of inertia of the oscillator, but we show that for a suitable choice of container radius and driving frequency, the Fermi liquid can actually decrease the inertia and increase the resonant frequency. Results of numerical calculations for all values of mean free path ℓ are shown and comparison is made to both hydrodynamic theory and simple kinetic theory in the ballistic limit.

Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

In a three-dimensional Fermi liquid, quasiparticles near the Fermi surface may possess a Berry curvature. We show that if the Berry curvature has a nonvanishing flux through the Fermi surface, the particle number associated with this Fermi surface has a triangle anomaly in external electromagnetic fields. We show how Landau's Fermi liquid theory should be modified to take into account the Berry curvature. We show that the "chiral magnetic effect" also emerges from the Berry curvature flux.

Fluctuations in finite density holographic quantum liquids

We study correlators of the global U(1) currents in holographic models which involve N=4 SYM coupled to the finite density matter in the probe brane sector. We find the spectral density associated with the longitudinal response to be exhausted by the zero sound pole and argue that this could be consistent with the behavior of Fermi liquid with vanishing Fermi velocity. However the transversal response shows an unusual momentum independent behavior. Inclusion of magnetic field leads to a gap in the dispersion relation for the zero sound mode propagating in the plane of magnetic field. For small values of the magnetic field B the gap in the spectrum scales linearly with B, which is consistent with Kohn's theorem for nonrelativistic fermions with pairwise interaction. We do not find signatures of multiple Landau levels expected in Landau Fermi liquid theory. We also consider the influence of generic higher derivative corrections on the form of the spectral function.

Entropy excess in strongly correlated Fermi systems near a quantum critical point

A system of interacting, identical fermions described by standard Landau Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if the correlations grow sufficiently strong, as occurs at a quantum critical point where the effective mass diverges. As yet, this phenomenon defies full understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior observed beyond the quantum critical point are still accessible within the general framework of the Landau quasiparticle picture. Self-consistent solutions of the coupled Landau equations for the quasiparticle momentum distribution n(p) and quasiparticle energy spectrum ϵ(p) are shown to exist in two distinct classes, depending on coupling strength and on whether the quasiparticle interaction is regular or singular at zero momentum transfer. One class of solutions maintains the idempotency condition n2(p)=n(p) of standard FL theory at zero temperature T while adding pockets to the Fermi surface. The other solutions are characterized by a swelling of the Fermi surface and a flattening of the spectrum ϵ(p) over a range of momenta in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The latter, non-idempotent solution is revealed by analysis of a Poincaré mapping associated with the fundamental Landau equation connecting n(p) and ϵ(p) and validated by solution of a variational condition that yields the symmetry-preserving ground state. Significantly, this extraordinary solution carries the burden of a large temperature-dependent excess entropy down to very low temperatures, threatening violation of the Nernst Theorem. It is argued that certain low-temperature phase transitions, notably those involving Cooper-pair formation, offer effective mechanisms for shedding the entropy excess. Available measurements in heavy-fermion compounds provide concrete support for such a scenario.

Holographic spectral function in nonequilibrium states

We develop holographic prescriptions for obtaining spectral functions in non-equilibrium states and space-time dependent non-equilibrium shifts in the energy and spin of quasi-particle like excitations. We reproduce strongly coupled versions of aspects of non-equilibrium dynamics of Fermi surfaces in Landau's Fermi-liquid theory. We find that the incoming wave boundary condition at the horizon does not suffice to obtain a well-defined perturbative expansion for non-equilibrium observables. Our prescription, based on analysis of regularity at the horizon, allows such a perturbative expansion to be achieved nevertheless and can be precisely formulated in a universal manner independent of the non-equilibrium state, provided the state thermalizes. We also find that the non-equilibrium spectral function furnishes information about the relaxation modes of the system. Along the way, we argue that in a typical non-supersymmetric theory with a gravity dual, there may exist a window of temperature and chemical potential at large N, in which a generic non-equilibrium state can be characterized by just a finitely few operators with low scaling dimensions, even far away from the hydrodynamic limit.

Stability of the Landau–Fermi Liquid Theory

The stability of the Landau–Fermi liquid theory is investigated. It has been shown that if the interaction function of the Fermi system is a finite function of the angle between the momenta of two particles at the Fermi surface, then the liquid can be stable. We have shown that the absolute value of the expansion coefficients of the interaction functions in Legendre polynomials are decreasing function of the coefficients indices. We solve the stability condition for one photon exchange (OPE) in an electron gas. The results show that we must use the massive boson propagator (higher order corrections to the photon propagator). Similar to previous works (Abrikosov et al. in Method of Quantum Field Theory in Statistical Physics, Pergamon, Elmsford, 1965), our result is proportional to g2. The density and temperature dependence of results is occulted in the effective mass of the system.

Magnetic aspects of QCD at finite density and temperature

Some magnetic aspects of QCD are discussed at finite density and temperature. Possibility of spontaneous magnetization is studied within Landau Fermi-liquid theory, and the important roles of the screening effects for gluon propagation are elucidated. Static screening for the longitudinal gluons improves the infrared singularities, while the transverse gluons receive only dynamic screening. The latter property gives rise to a novel non-Fermi-liquid behaviour for the magnetic susceptibility. Appearance of a density-wave state is also discussed in relation to chiral transition, where pseudoscalar condensate as well as scalar one takes a spatially non-uniform form in a chirally invariant way. Accordingly magnetization of quark matter oscillates like spin density wave. A hadron-quark continuity is suggested in this aspect, remembering pion condensation in hadronic phase.

Model of a Fermi liquid using gauge-gravity duality

We use gauge-gravity duality to model the crossover from a conformal critical point to a confining Fermi liquid, driven by a change in fermion density. The short-distance conformal physics is represented by an anti--de Sitter geometry, which terminates into a confining state along the emergent spatial direction. The Luttinger relation, relating the area enclosed by the Fermi surfaces to the fermion density, is shown to follow from Gauss's law for the bulk electric field. We argue that all low energy modes are consistent with Landau's Fermi liquid theory. An explicit solution is obtained for the Fermi liquid for the case of hard-wall boundary conditions in the infrared.

Fermi surfaces and gauge-gravity duality

We give a unified overview of the zero temperature phases of compressible quantum matter: i.e., phases in which the expectation value of a globally conserved U(1) density, $\mathcal{Q}$, varies smoothly as a function of parameters. Provided the global U(1) and translational symmetries are unbroken, such phases are expected to have Fermi surfaces, and the Luttinger theorem relates the volumes enclosed by these Fermi surfaces to $⟨\mathcal{Q}⟩$. We survey models of interacting bosons and/or fermions and/or gauge fields which realize such phases. Some phases have Fermi surfaces with the singularities of Landau's Fermi liquid theory, while other Fermi surfaces have non-Fermi liquid singularities. Compressible phases found in models applicable to condensed-matter systems are argued to also be present in models obtained by applying chemical potentials (and other deformations allowed by the residual symmetry at nonzero chemical potential) to the paradigmatic supersymmetric gauge theories underlying gauge-gravity duality: the Aharony-Bergman-Jafferis-Maldacena model in spatial dimension $d=2$, and the $\mathcal{N}=4$ super Yang-Mills theory in $d=3$.

Superfluid 3He—the Early Days

A history is given of liquid 3He research from the time when 3He first became available following World War II through 1972 when the discovery of the superfluid phases was made. The Fermi liquid nature was established early on, and the Landau Fermi liquid theory provided a framework for understanding the interactions between the Fermions (quasiparticles). The theory’s main triumph was to predict zero sound, which was soon discovered experimentally. Experimental techniques are treated, including adiabatic demagnetization, dilution refrigerator technology, and Pomeranchuk cooling. A description of the superfluid 3He discovery experiments using the latter two of these techniques is given. While existing theories provided a basis for understanding the newly discovered superfluid phases in terms of l>0 Cooper pairs, the unexpected stability of the A phase in the high-P, high-T region of the phase diagram needed for its explanation a creative leap beyond the BCS paradigm. The use of sum rules to interpret some of the unusual magnetic resonance in liquid 3He is discussed. Eventually a complete theory of the spin dynamics of superfluid 3He was developed, which predicted many of the exciting phenomena subsequently discovered.

MAGNETIC SUSCEPTIBILITY OF GRAPHENE BY GAUSSIAN CORRECTION

In the present paper, we compute the magnetic susceptibility of graphene by using Gaussian correction. The collective excitations away from Fermi points of graphene are gapless, chiral fermions, with linear dispersion. The system is modeled as N massless Dirac fermions in two spatial dimensions interacting with 1/r Coulomb interactions. We find that the magnetic susceptibility is suppressed by the interaction between these collective excitations. And it has ln T correction due to the long-ranged Coulomb interaction, which is different from Landau Fermi liquid theory.

Renormalization group flow for noncommutative Fermi liquids

Some recent studies of the AdS/CFT correspondence for condensed matter systems involve the Fermi liquid theory as a boundary field theory. Adding $B$-flux to the boundary D-branes leads in a certain limit to the noncommutative Fermi liquid, which calls for a field theory description of its critical behavior. As a preliminary step to more general consideration, the modification of the Landau's Fermi liquid theory due to noncommutativity of spatial coordinates is studied in this paper. We carry out the renormalization of interactions at tree level and one loop in a weakly coupled fermion system in two spatial dimensions. Channels ZS, ZS' and BCS are discussed in detail. It is shown that while the Gaussian fixed-point remains unchanged, the BCS instability is modified due to the space noncommutativity.

Magnetic Aspects of QCD and Compact Stars

Magnetic properties of quark matter are discussed. The possibility of ferromagnetic transition is studied by using the one-gluon-exchange interaction. Magnetic susceptibility is evaluated within Landau Fermi liquid theory, and the important roles of the screening for the gluon propagation are elucidated. Static screening for the longitudinal gluons improves the infrared singularities, while the transverse gluons receive only dynamic screening. The latter property gives rise to a novel non-Fermi-liquid behaviour in the magnetic susceptibility. The critical density is estimated to be around the nuclear density and the Curie temperature several tens MeV. The spin density wave is also discussed at moderate densities, where chiral transition becomes important. Pseudoscalar condensate as well as scalar one takes a spatially non-uniform form in a chirally invariant way. Accordingly magnetization oscillates like spin density wave. These results should have some implications on compact star phenomena.

Fermi-liquid behavior in an underdoped high-Tcsuperconductor

We use magnetic quantum oscillations in the underdoped high Tc superconductor YBa_2Cu_3O_(6+x) (x=0.56) measured over a broad range of temperatures 100 mK<T<18 K to extract the form of the distribution function describing the low-lying quasiparticle excitations in high magnetic fields. Despite the proximity of YBa_2Cu_3O_(6+x) (x=0.56) to a Mott insulating state, various broken symmetry ground states and/or states with different quasiparticle statistics, we find that our experimental results can be understood in terms of quasiparticle excitations obeying Fermi-Dirac statistics as in the Landau Fermi liquid theory.

Electron liquids and solids in one dimension

Even though bulk metallic systems contain a very large number of strongly interacting electrons, their properties are well described within Landau's Fermi liquid theory of non-interacting quasiparticles. Although many higher-dimensional systems can be successfully understood on the basis of such non-interacting theories, this is not possible for one-dimensional systems. When confined to narrow channels, electron interaction gives rise to such exotic phenomena as spin-charge separation and the emergence of correlated-electron insulators. Such strongly correlated electronic behaviour has recently been seen in experiments on one-dimensional carbon nanotubes and nanowires, and this behaviour challenges the theoretical description of such systems.

Neutrino mean free paths in spin-polarized neutron Fermi liquids

Neutrino mean free paths in magnetized neutron matter are calculated using the Hartree-Fock approximation with effective Skyrme and Gogny forces in the framework of the Landau Fermi Liquid Theory. It is shown that describing nuclear interaction with Skyrme forces and for magnetic field strengths $log_{10} B(G) \gtrsim 17$, the neutrino mean free paths stay almost unchanged at intermediate densities but they largely increase at high densities when they are compared to the field-free case results. However the description with Gogny forces differs from the previous and mean free paths stay almonst unchanged or decrease at densities $[1-2]\rho_0$. This different behaviour can be explained due to the combination of common mild variation of the Landau parameters with both types of forces and the values of the nucleon effective mass and induced magnetization of matter under presence of a strong magnetic field as described with the two parametrizations of the nuclear interaction.

Fermi liquid near Pomeranchuk quantum criticality

We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic $(n=2)$ Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, related to the Landau interaction function. We derive ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor ${Z}_{\ensuremath{\Gamma}}$, related to the single-particle residue $Z$ and effective-mass renormalization ${m}^{\ensuremath{\ast}}/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$, to obtain and solve a set of coupled nonlinear equations for ${Z}_{\ensuremath{\Gamma}}$, $Z$, and ${m}^{\ensuremath{\ast}}/m$. We show that near the transition the system enters a critical FL regime, where ${Z}_{\ensuremath{\Gamma}}\ensuremath{\sim}Z\ensuremath{\propto}{(1+{g}_{c,2})}^{1/2}$ and ${m}^{\ensuremath{\ast}}/m\ensuremath{\approx}1/Z$, where ${g}_{c,2}$ is the $n=2$ charge Landau component which approaches $\ensuremath{-}1$ at the instability. We construct the Landau function of the critical FL and show that all but ${g}_{c,2}$ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\ensuremath{\Sigma}(K)\ensuremath{\propto}\ensuremath{\int}dPG(P)D(K\ensuremath{-}P)$ is asymptotically exact if one identifies the effective interaction $D$ with the RPA form of ${\ensuremath{\Gamma}}^{\ensuremath{\Omega}}$.

Holographic quantum liquids in 1+1 dimensions

In this paper we initiate the study of holographic quantum liquids in 1+1 dimensions. Since the Landau Fermi liquid theory breaks down in 1+1 dimensions, it is of interest to see what holographic methods have to say about similar models. For theories with a gapless branch, the Luttinger conjecture states that there is an effective description of the physics in terms of a Luttinger liquid which is specified by two parameters. The theory we consider is the defect CFT arising due to a probe D3 brane in the AdS Schwarzschild planar black hole background. We turn on a fundamental string density on the worldvolume. Unlike higher dimensional defects, a persistent dissipationless zero sound mode is found. The thermodynamic aspects of these models are considered carefully and certain subtleties with boundary terms are explained which are unique to 1+1 dimensions. Spectral functions of bosonic and fermionic fluctuations are also considered and quasinormal modes are analysed. A prescription is given to compute spectral functions when there is mixing due to the worldvolume gauge field. We comment on the Luttinger conjecture in the light of our findings.