On non-Fermi liquid quantum critical points in heavy fermion metals

Heavy electron metals on the verge of a quantum phase transition to magnetism show a number of unusual non-Fermi liquid properties which are poorly understood. This article discusses in a general way various theoretical aspects of this phase transition with an eye toward understanding the non-Fermi liquid phenomena. We suggest that the non-Fermi liquid quantum critical state may have a sharp Fermi surface with power law quasiparticles but with a volume not set by the usual Luttinger rule. We also discuss the possibility that the electronic structure change associated with the possible Fermi surface reconstruction may diverge at a different time/length scale from that associated with magnetic phenomena.     

Numerical evidence of Luttinger liquid to Fermi liquid transformation in lithium doped trans-polyacetylene chain

We report on the first direct numerical evidence of doping-induced transformation of Tomonaga-Luttinger liquid to Fermi liquid in quasi-one-dimensional lithium doped trans-polyacetylene chain. Using density functional theoretical calculation, an analysis of density of states near the Fermi energy reveals a power-law scaling factor of Tomonaga-Luttinger liquid at low dopant concentration in the metallic regime. As soon as the doping level reaches 0.0763e/C, normal power-law scaling factor of Fermi liquid has been realized as a special case of Luttinger liquid in one dimension. The variation of density-density correlation is consistent with the present theoretical prediction.     

Equilibration of a one-dimensional quantum liquid

We review some of the recent results on equilibration of one-dimensional quantum liquids. The low-energy properties of these systems are described by the Luttinger liquid theory, in which the excitations are bosonic quasiparticles. At low temperatures, the relaxation of the gas of excitations toward full equilibrium is exponentially slow. In electronic Luttinger liquids, these relaxation processes involve backscattering of electrons and give rise to interesting corrections to the transport properties of one-dimensional conductors. We focus on the phenomenological theory of the equilibration of a quantum liquid and obtain an expression for the relaxation rate in terms of the excitation spectrum.     

Generalization of Luttinger’s theorem for strongly correlated electron systems

By on the analyzing the general structure of the Green function of a strongly correlated electron system, it is shown that, for the regime of strong correlations, Luttinger’s theorem should be generalized in the following way: the volume of the Fermi surface of the system of noninteracting particles is equal to that of the quasiparticles in the strongly correlated system with due regard for the spectral weight of the quasiparticles. An investigation of the t-J model and of the Hubbard model, as applied to the paramagnetic nonsuperconducting phase, shows that the generalized Luttinger theorem is valid for these models.     

Renormalization group and Fermi liquid theory

We give a Hamiltonian-based interpretation of microscopic Fermi liquid theory within a renormalization group framework. The Fermi liquid fixed-point Hamiltonian with its leading-order corrections is identified and we show that the mean field calculations for this model correspond to the Landau phenomenological approach. This is illustrated first of all for the Kondo and Anderson models of magnetic impurities which display Fermi liquid behaviour at low temperatures. We then show how these results can be deduced by a reorganization of perturbation theory, in close parallel to that for the renormalized φ⁴ field theory. The Fermi liquid results follow from the two lowest order diagrams of the renormalized perturbation expansion. The calculations for the impurity models are simpler than for the general case because the self-energy depends on frequency only. We show, however, that a similar renormalized expansion can be derived also for the case of a translationally invariant system. The parameters specifying the Fermi liquid fixed-point Hamiltonian are related to the renormalized vertices appearing in the perturbation theory. The collective zero sound modes appear in the quasiparticle-quasihole ladder sum of the renormalized perturbation expansion. The renormalized perturbation expansion can in principle be used beyond the Fermi liquid regime to higher temperatures. This approach should be particularly useful for heavy fermions and other strongly correlated electron systems, where the renormalization of the single-particle excitations are particularly large.

We briefly look at the breakdown of Fermi liquid theory from a renormalized perturbation theory point of view. We show how a modified version of the approach can be used in some situations, such as the spinless Luttinger model, where Fermi liquid theory is not applicable. Other examples of systems where the Fermi liquid theory breaks down are also briefly discussed.     

Transition in a Luttinger liquid with two-level impurities to the fermi-liquid state

The mechanisms leading to instability of the non-Fermi-liquid state of a Luttinger liquid with two-level impurities are proposed. Since exchange scattering in 1D systems is two-channel scattering in a certain range of parameters, several types of non-Fermi-liquid excitations with different quantum numbers exist in the vicinity of the Fermi level. These excitations include, first, charge density fluctuations in the Luttinger liquid and, second, many-particle excitations due to two-channel exchange interaction, which are associated with band-type as well as impurity fermion states. It is shown that mutual scattering of many-particle excitations of various types leads to the emergence of an additional Fermi-liquid singularity in the vicinity of the Fermi level. The conditions under which the Fermi-liquid state with a new energy scale (which is much smaller than the Kondo temperature) is the ground state of the system are formulated.     

Structure of the ground state of a nonsuperfluid dense quark-gluon plasma

The single-particle spectrum and momentum distribution of quasiparticles in a cold dense quark-gluon plasma are calculated within the Fermi liquid approach. It is shown that this system does not behave as a standard Fermi liquid: at zero temperature, the single-particle spectrum has a plateau at the Fermi surface, while the Fermi surface itself has a nonzero volume in momentum space.     

Appearance of fractional charge in the noise of nonchiral Luttinger liquids

The current noise of a voltage biased interacting quantum wire adiabatically connected to metallic leads is computed in the presence of an impurity in the wire. We find that in the weak backscattering limit the Fano factor characterizing the ratio between noise and backscattered current crucially depends on the noise frequency omega relative to the ballistic frequency vF/gL, where vF is the Fermi velocity, g is the Luttinger liquid interaction parameter, and L is the length of the wire. In contrast to chiral Luttinger liquids the noise is not only due to the Poissonian backscattering of fractionally charged quasiparticles at the impurity, but it also depends on Andreev-type reflections at the contacts, so that the frequency dependence of the noise needs to be analyzed to extract the fractional charge e*=eg of the bulk excitations.     

The Microscopic Model of Composite Fermion-Type Excitations for υ = l/m Edge States

We derive a microscopic theory of the composite fermion-type quasiparticles describing the low-lying edge excitations in the fractional quantdm Hall liquid with υ = 1/m. Using the composite fermion transformation, one finds that the edge states of the system in a disc sample are described by the Calogero-Sutherland-like model (CSLM) in the one-dimensional limit. This result presents the consistency between one-dimensional and two-dimensional statistics. It is shown that the low-lying excitations, indeed, have the chiral Luttinger liquid behaviors because there is a gap between the right-and left-moving excitations of the CSLM.     

Density functionals not based on the electron gas: local-density approximation for a Luttinger liquid

By shifting the reference system for the local-density approximation (LDA) from the electron gas to other model systems, one obtains a new class of density functionals, which by design account for the correlations present in the chosen reference system. This strategy is illustrated by constructing an explicit LDA for the one-dimensional Hubbard model. While the traditional ab initio LDA is based on a Fermi liquid (the three-dimensional interacting electron gas), this one is based on a Luttinger liquid. First applications to inhomogeneous Hubbard models, including one containing a localized impurity, are reported.     

On the superconductivity of a Wigner liquid

The disorder effect on the interaction of quasiparticles between each other is discussed. The occurrence of a soft mode is taken as the basic assumption. The interaction through the soft mode results in attraction between Fermi quasiparticles (this is apart from the repulsion that has remained from the initial Coulomb interaction between particles). This attraction (in the vicinity of the Fermi surface) is strengthened with increasing concentration of the scattering centers. Therefore, even if the pure system exhibits no superconductivity, superconductivity could appear in the impurity system.     

Reprint of : Regular and singular Fermi liquid in triple quantum dots: Coherent transport studies

A system of three coupled quantum dots in a triangular geometry (TQD) with electron–electron interaction and symmetrically coupled to two leads is analyzed with respect to the electron transport by means of the numerical renormalization group. Varying gate potentials this system exhibits extremely rich range of regimes with different many-electron states with various local spin orderings. It is demonstrated how the Luttinger phase changes in a controlled manner which then via the Friedel sum rule formula exactly reproduces the conductance through the TQD system. The analysis of the uncoupled TQD molecule from the leads gives a reliable qualitative understanding of various relevant regimes and an insight into the phase diagram with the regular Fermi liquid and singular-Fermi liquid phases.     

4He Luttinger liquid in nanopores

We study the low-temperature properties of a 4He fluid confined in nanopores, using large-scale quantum Monte Carlo simulations with realistic He-He and He-pore interactions. In the narrow-pore limit, the system can be described by the quantum hydrodynamic theory known as Luttinger liquid theory with a large Luttinger parameter, corresponding to the dominance of solid tendencies and strong susceptibility to pinning by a periodic or random potential from the pore walls. On the other hand, for wider pores, the central region appears to behave like a Luttinger liquid with a smaller Luttinger parameter, and may be protected from pinning by the wall potential, offering the possibility of experimental detection of a Luttinger liquid.     

Junction of Tomonaga–Luttinger liquids

Low-energy physics of one-dimensional electron systems can be generally described in terms of the Tomonaga–Luttinger liquid, instead of the Fermi liquid. We give a nontechnical review for nonspecialists on this intriguing subject. As an example of physical consequences, we discuss junction of two and three Tomonaga–Luttinger liquids.     

Spin susceptibility of interacting electrons in one dimension: Luttinger liquid and lattice effects

The temperature-dependent uniform magnetic susceptibility of interacting electrons in one dimension is calculated using several methods. At low temperature, the renormalization group reveals that the Luttinger liquid spin susceptibility approaches zero temperature with an infinite slope in striking contrast with the Fermi liquid result and with the behavior of the compressibility in the absence of umklapp scattering. This effect comes from the leading marginally irrelevant operator, in analogy with the Heisenberg spin 1/2 antiferromagnetic chain. Comparisons with Monte Carlo simulations at higher temperature reveal that non-logarithmic terms are important in that regime. These contributions are evaluated from an effective interaction that includes the same set of diagrams as those that give the leading logarithmic terms in the renormalization group approach. Comments on the third law of thermodynamics as well as reasons for the failure of approaches that work in higher dimensions are given. Received 2 March 1999     

Experimental evidence for resonant tunneling in a luttinger liquid

We have measured the low-temperature conductance of a one-dimensional island embedded in a single mode quantum wire. The quantum wire is fabricated using the cleaved edge overgrowth technique and the tunneling is through a single state of the island. Our results show that while the resonance line shape fits the derivative of the Fermi function the intrinsic linewidth decreases in a power law fashion as the temperature is reduced. This behavior agrees quantitatively with Furusaki's model for resonant tunneling in a Luttinger liquid.     

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

General interaction quenches in a Luttinger liquid

We discuss a general interaction quench in a Luttinger liquid described by a paired bosonic Hamiltonian.By employing su(1,1)Lie algebra,the post-quench time-evolved wavefunctions are obtained analytically,from which the time evolution of the entanglement in momentum space can be investigated.We note that depending on the choice of Bogoliubov quasiparticles,the expressions of wavefunctions,which describe time-evolved paired states,can take different forms.The correspondence between the largest entanglement eigenvalue in momentum space and the wavefunction overlap in quench dynamics is discussed,which generalizes the results of Dora et al(2016,Phys.Rev.Lett.117,010603).A numerical demonstration on an XXZ lattice model is presented via the exact diagonalization method.