Holographic Fermi arcs and a d-wave gap

We study fermion correlators in a holographic superfluid with a d-wave (spin two) order parameter. We find that, with a suitable bulk Majorana coupling, the Fermi surface is anisotropically gapped. At low temperatures the gap shrinks to four nodal points. At high temperatures the Fermi surface is partially gapped generating four Fermi arcs.     

Numerical renormalization group study of the O(3)-symmetric Anderson model

We use the numerical renormalization group method to study the O(3)-symmetric version of the impurity Anderson model of Coleman and Schofield. This model is of general interest because it displays both Fermi liquid and non-Fermi liquid behaviour, and in the large U limit can be related to the compactified two channel Kondo model of Coleman, Ioffe and Tsvelik. We calculate the thermodynamics for a parameter range which covers the full range of behaviour of the model. We find a non-Fermi liquid fixed point in the isotropic case which is unstable with respect to channel anisotropy.     

Supersymmetric approach to heavy-fermion systems

We present a new supersymmetric approach to the Kondo lattice model in order to describe simultaneously the quasiparticle excitations and the low-energy magnetic fluctuations in heavy-Fermion systems. This approach mixes the fermionic and the bosonic representation of the spin following the standard rules of superalgebra. Our results show the formation of a bosonic band within the hybridization gap reflecting the spin collective modes. The density of states at the Fermi level is strongly renormalized while the Fermi surface sum rule includes n _c + 1 states. The dynamical susceptibility is made of a Fermi liquid superimposed on a localized magnetism contribution.     

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.     

A fractional-spin phase in the power-law Kondo model

We consider a Kondo impurity coupled to a fermionic host with a power-law density of states near the Fermi level, ρ(ε) ∼ |ε|^r, with exponent r < 0. Using both perturbative renormalization group (poor man's scaling) and numerical renormalization group methods, we analyze the phase diagram of this model for ferromagnetic and antiferromagnetic Kondo coupling. Both sectors display non-trivial behavior with several stable phases separated by continuous transitions. In particular, on the ferromagnetic side there is a stable intermediate-coupling fixed point with universal properties corresponding to a fractional ground-state spin. Received 18 February 2002 Published online 31 July 2002     

Fermi surface and antiferromagnetism in the Kondo lattice: an asymptotically exact solution in d>1 dimensions

Interest in the heavy fermion metals has motivated us to examine the quantum phases and their Fermi surfaces within the Kondo lattice model. We demonstrate that the model is soluble asymptotically exactly in any dimension d>1, when the Kondo coupling is small compared with the RKKY interaction and in the presence of antiferromagnetic ordering. We show that the Kondo coupling is exactly marginal in the renormalization group sense, establishing the stability of an ordered phase with a small Fermi surface AFS. Our results have implications for the global phase diagram of the heavy fermion metals, suggesting a Lifshitz transition inside the antiferromagnetic region and providing a new perspective for a Kondo-destroying antiferromagnetic quantum critical point.     

Flow to strong coupling in the two-dimensional Hubbard model

We extend the analysis of the renormalization group flow in the two-dimensional Hubbard model close to half-filling using the recently developed temperature flow formalism. We investigate the interplay of d-density wave and Fermi surface deformation tendencies with those towards d-wave pairing and antiferromagnetism. For a ratio of next nearest to nearest neighbor hoppings, t'/t = - 0.25, and band fillings where the Fermi surface is inside the Umklapp surface, only the d-pairing susceptibility diverges at low temperatures. When the Fermi surface intersects the Umklapp surface close to the saddle points, d-wave pairing, d-density wave, antiferromagnetic and, to a weaker extent, d-wave Fermi surface deformation susceptibilities grow together when the interactions flow to strong coupling. We interpret these findings as indications for a non-trivial strongly coupled phase with short-ranged superconducting and antiferromagnetic correlations, in close analogy with the spin liquid ground state in the well-understood two-leg Hubbard ladder. Received 23 January 2002     

Slave fermion formalism for the tetrahedral spin chain

We use the SU(2) slave fermion approach to study a tetrahedral spin 1/2 chain, which is a one-dimensional generalization of the two dimensional Kitaev honeycomb model. Using the mean field theory, coupled with a gauge fixing procedure to implement the single occupancy constraint, we obtain the phase diagram of the model. We then show that it matches the exact results obtained earlier using the Majorana fermion representation. We also compute the spin-spin correlation in the gapless phase and show that it is a spin liquid. Finally, we map the one-dimensional model in terms of the slave fermions to the model of 1D p-wave superconducting model with complex parameters and show that the parameters of our model fall in the topological trivial regime and hence does not have edge Majorana modes.     

Kondo stripes in an Anderson-Heisenberg model of heavy fermion systems

We study the interplay between the spin-liquid and Kondo physics, as related to the nonmagnetic part of the phase diagram of heavy fermion materials. Within the unrestricted mean-field treatment of the infinite-U 2D Anderson-Heisenberg model, we find that there are two topologically distinct nondegenerate uniform heavy Fermi liquid states that may form as a consequence of the Kondo coupling between spinons and conduction electrons. For certain carrier concentrations, the uniform Fermi liquid becomes unstable with respect to the formation of a new kind of anharmonic "Kondo stripe" state with inhomogeneous Kondo screening strength and the charge density modulation. These features are experimentally measurable and thus may help to establish the relevance of the spin-liquid correlations to heavy fermion materials.     

Triplet superconductivity vs. easy-plane ferromagnetism in a 1D itinerant electron system with transverse spin anisotropy

In this paper we study the ground state phase diagram of a one-dimensional t-U-J model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin- XY model takes place.Received: 6 February 2004, Published online: 9 April 2004PACS: 71.10.Hf Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems - 71.10.Fd Lattice fermion models (Hubbard model, etc.) - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Pq Spin chain modelsG.I. Japaridze: Permanent address: Andronikashvili Institute of Physics, Georgian Academy, Tamarashvili 6, Tbilisi 380077, Georgia     

Effect of relevant umklapp process on the two-leg Hubbard ladder with a half-filled band under pressure

By means of perturbative renormalization approach we study the effect of relevant umklapp process on dimensional crossover caused by interladder one particle hopping in weakly coupled two-leg Hubbard ladders with a half filled-band. We found that a crossover takes place at a finite value which increases as the amplitude of umklapp process increases. For the system undergoes a phase transition to the spin density wave phase (SDW) via the two particle hopping process, while for the system undergoes a crossover to the two dimensional Fermi liquid phase via one particle hopping process. Received 25 December 1998     

Breakdown of Fermi liquid behavior near the hot spots in a two-dimensional model: A two-loop renormalization group analysis

Motivated by a recent experimental observation of a nodal liquid on both single crystals and thin films of Bi₂Sr₂CaCu₂O_8 + δ by Chatterjee et al. [Nature Phys. 6 (2010) 99], we perform a field-theoretical renormalization group (RG) analysis of a two-dimensional model such that only eight points located near the “hot spots” on the Fermi surface are retained, which are directly connected by spin density wave ordering wavevector. We derive RG equations up to two-loop order describing the flow of renormalized couplings, quasiparticle weight, several order-parameter response functions, and uniform spin and charge susceptibilities of the model. We find that while the order-parameter susceptibilities investigated here become non-divergent at two loops, the quasiparticle weight vanishes in the low-energy limit, indicating a breakdown of Fermi liquid behavior at this RG level. Moreover, both uniform spin and charge susceptibilities become suppressed in the scaling limit which indicate gap openings in both spin and charge excitation spectra of the model.     

A Lie algebraic approach to the Kondo problem

The Kondo problem is approached using the unitary Lie algebra of spin-singlet fermion bilinears. In the limit when the number of values of the spin N goes to infinity the theory approaches a classical limit, which still requires a renormalization. We determine the ground state of this renormalized theory. Then we construct a quantum theory around this classical limit, which amounts to recovering the case of finite N.     

Competition between Kondo and RKKY correlations in the presence of strong randomness

We propose that competition between Kondo and magnetic correlations results in a novel universality class for heavy fermion quantum criticality in the presence of strong randomness. Starting from an Anderson lattice model with disorder, we derive an effective local field theory in the dynamical mean-field theory approximation, where randomness is introduced into both hybridization and Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions. Performing the saddle-point analysis in the U(1) slave-boson representation, we reveal its phase diagram which shows a quantum phase transition from a spin liquid state to a local Fermi liquid phase. In contrast with the clean limit case of the Anderson lattice model, the effective hybridization given by holon condensation turns out to vanish, resulting from the zero mean value of the hybridization coupling constant. However, we show that the holon density becomes finite when the variance of the hybridization is sufficiently larger than that of the RKKY coupling, giving rise to the Kondo effect. On the other hand, when the variance of the hybridization becomes smaller than that of the RKKY coupling, the Kondo effect disappears, resulting in a fully symmetric paramagnetic state, adiabatically connected to the spin liquid state of the disordered Heisenberg model. We investigate the quantum critical point beyond the mean-field approximation. Introducing quantum corrections fully self-consistently in the non-crossing approximation, we prove that the local charge susceptibility has exactly the same critical exponent as the local spin susceptibility, suggesting an enhanced symmetry at the local quantum critical point. This leads us to propose novel duality between the Kondo singlet phase and the critical local moment state beyond the Landau-Ginzburg-Wilson paradigm. The Landau-Ginzburg-Wilson forbidden duality serves the mechanism of electron fractionalization in critical impurity dynamics, where such fractionalized excitations are identified with topological excitations.     

Anomalous normal-state properties of high-T c superconductors: intrinsic properties of strongly correlated electron systems?

A systematic study of optical and transport properties of the Hubbard model, based on the Metzner-Vollhardt dynamical mean-field approximation, is reviewed. This model shows interesting anomalous properties that are, in our opinion, ubiquitous to single-band strongly correlated systems (for all spatial dimensions greater than one) and also compare qualitatively with many anomalous transport features of the high-T _c cuprates. This anomalous behaviour of the normal-state properties is traced to a ‘collective single-band Kondo effect’, in which a quasiparticle resonance forms at the Fermi level as the temperature is lowered, ultimately yielding a strongly renormalized Fermi liquid at zero temperature.     

Negative tunnel magnetoresistance in a quantum dot induced by interplay of a Majorana fermion and thermal-driven ferromagnetic leads

We investigate the spin-related currents and tunnel magnetoresistance through a quantum dot, which is side-coupled with a Majorana fermion zero mode and two thermal-driven ferromagnetic electrodes. It is found that the interplay of Majorana fermion and electrodes' spin polarization can induce a nonlinear thermal-bias spin current. This interplay also decreases the total magnitude of spin or charge current, in either parallel or antiparallel configuration. In addition, a thermal-driven negative tunnel magnetoresistance is found, which is an unique feature to characterize Majorana fermion.With large temperature difference, a step phenomenon is observed in gate tuned spin-up current. When the coupling between quantum dot and topological superconductor is strong enough, this step will evolve into a linear relation, revealing Majorana fermion's robustness.     

Magnetic quantum criticality in quasi‐one‐dimensional Heisenberg antiferromagnet

We analyze exciting recent measurements [Phys. Rev. Lett. 114 (2015) 037202] of the magnetization, differential susceptibility and specific heat on one dimensional Heisenberg antiferromagnet Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to strong magnetic fields. Using the mapping between magnons (bosons) in CuPzN and fermions, we demonstrate that magnetic field tunes the insulator towards quantum critical point related to so‐called fermion condensation quantum phase transition (FCQPT) at which the resulting fermion effective mass diverges kinematically. We show that the FCQPT concept permits to reveal the scaling behavior of thermodynamic characteristics, describe the experimental results quantitatively, and derive for the first time the (temperature—magnetic field) phase diagram, that contains Landau‐Fermi‐liquid, crossover and non‐Fermi liquid parts, thus resembling that of heavy‐fermion compounds.     

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces. Received 11 April 2001 and Received in final form 6 September 2001