Motivated by the recent experimental observation of quantum oscillations in the underdoped cuprates, we study the cyclotron and infrared Hall effective masses in an anisotropic Fermi liquid characterized by an angle-dependent quasiparticle residue Z_q, which models an arc-shaped Fermi surface. Our primary motivation is to explain the relatively large value of the cyclotron effective mass observed experimentally and its relation with the effective Hall mass. In the framework of a phenomenological model of an anisotropic Fermi liquid, we find that the cyclotron mass is enhanced by a factor <1/Z_q>, while the effective Hall mass is proportional to <Z_q> / <Z_q^2>, where <...> implies an averaging over the Fermi surface. We conclude that if the Z-factor becomes small in some part of the Fermi surface (e.g., in the case of a Fermi arc), the cyclotron mass is enhanced sharply while the infrared Hall mass may remain small. Possible future experiments are discussed.
We consider a model self-energy consisting of an isotropic Fermi liquid term and a Marginal Fermi liquid term which is anisotropic over the Fermi surface, vanishing in the same directions as the superconducting gap and the pseudogap. This model self-energy gives a consistent description of experimental results from Angle-Dependent Magneto-Resistance (ADMR), specific heat, de Haas-van Alphen, and measurements of the quasi-particle dispersion near the Fermi surface from photoemission. In particular, we reconcile the strongly doping dependent anomalous scattering rate observed in ADMR with the al…
Linear spin wave theory shows that ring exchange induces a quantum disordered region in the phase diagram of the title model. Spin wave spectra show that this is a direct manifestation of competing classical orders. A spin liquid is found in the `Goldilocks zone' of frustration, where the quantum fluctuations are large enough to cause strong competition between different classical orderings but not strong enough to stabilize spiral order. We note that the spin liquid phases of $κ$-(BEDT-TTF)${_2}X$ and $Y$[Pd(dmit)$_2$]$_2$ are found in this Goldilocks zone.
We study the problem of the crossover from one- to higher-dimensional metals by considering an array of Luttinger liquids (one-dimensional chains) coupled by a weak interchain hopping {\tp.} We evaluate the exact asymptotic low-energy behavior of the self-energy in the anisotropic infinite-dimension limit. This limit extends the dinamical mean field concept to the case of a chain embedded in a self-consistent medium. The system flows to a Fermi-liquid fixed point for energies below the dimensional crossover temperature, and the anomalous exponent $\al$ renormalizes to zero, in the case of equa…
In this work, we argue that an anisotropic interaction potential may stabilize anisotropic liquid phases of electrons even in a strong magnetic field regime where normally one expects to see only isotropic quantum Hall or isotropic Fermi liquid states. We use this approach to support a theoretical framework that envisions the possibility of an anisotropic liquid crystalline state of electrons in the lowest Landau level. In particular, we argue that an anisotropic liquid state of electrons may stabilize in the lowest Landau level close to the liquid-solid transition region at filling factor $ν=…
Formal but exact DC conductivity formulae for anisotropic Fermi liquids are reviewed. One is the Maebashi-Fukuyama formula based on the Fermi-surface harmonics. The other is the Taylor formula based on the scattering eigenfunction. In comparison to these two formulae the current-vertex-correction in the fluctuation-exchange approximation is shown to be a bad vision caused by an inconsistent approximation.
We show using bosonization techniques, that strong forward scattering interactions between one dimensional spinless Luttinger liquids (LL) can stabilize a phase where charge-density wave, superconducting and transverse single particle hopping perturbations are irrelevant. This new phase retains its LL like properties in the directions of the chains, but with relations between exponents modified by the transverse interactions, whereas, it is a perfect insulator in the transverse direction. The mechanism that stabilizes this phase are strong transverse charge density wave fluctuations at incomme…
Dynamical magnetic correlations in the geometrically frustrated Nd$\_3$Ga$\_5$SiO$\_{14}$ compound were probed by inelastic neutron scattering on a single crystal. A scattering signal with a ring shape distribution in reciprocal space and unprecedented dispersive features was discovered. Comparison with calculated static magnetic scattering from models of correlated spins suggests that the observed phase is a spin liquid inherent to an antiferromagnetic kagomé-like lattice of anisotropic Nd moments.
We analyze the deformations of the Fermi surface induced by electron-electron interactions in anisotropic two dimensional systems. We use perturbation theory to treat, on the same footing, the regular and singular regions of the Fermi surface. It is shown that, even for weak local coupling, the self-energy presents a nontrivial behavior showing momentum dependence and interplay with the Fermi surface shape. Our scheme gives simple analytical expressions based on local features of the Fermi surface.
The low temperature dependence of the spin and charge susceptibilities of an anisotropic electron system in two dimensions is analyzed. It is shown that the presence of inflection points at the Fermi surface leads, generically, to a $ T \log T $ dependence, and a more singular behavior, $χ\sim T ^{3/4} \log T$, is also possible. Applications to quasi two-dimensional materials are discussed.
We report detailed Knight shift measurements of the two indium sites in the heavy fermion compound CeIrIn$_5$ as a function of temperature and field orientation. We find that the Knight shift anomaly is orientation-dependent, with a crossover temperature $T^*$ that varies by 50% as the field is rotated from (001) to (100). This result suggests that the hybridization between the Ce 4f states and the itinerant conduction electrons is anisotropic, a result that reflects its collective origin, and may lead to anisotropic Kondo liquid behavior and unconventional superconductivity.
We present a numerical study on non-Fermi liquid behaviour of a three dimensional system. The Hubbard model in a cubic lattice is simulated by the dynamical cluster approximation, in particular the quasi-particle weight is calculated at finite dopings for a range of temperatures. Near the putative quantum critical point, we find evidence of a separatrix at a finite doping which separates the Fermi liquid from non-Fermi liquid as the doping increases. Our results suggest that a marginal Fermi liquid and possibly a quantum critical point should exist in the three dimensions interacting Fermi sys…
A continuous unitary transformation is introduced which realizes Landau's mapping of the elementary excitations (quasi-particles) of an interacting Fermi liquid system to those of the system without interaction. The conservation of the number of quasi-particles is important. The transformation is performed numerically for a one-dimensional system, i.e. the worst case for a Fermi liquid approach. Yet evidence for Luttinger liquid behavior is found. Such an approach may open a route to a unified description of Fermi and Luttinger liquids on all energy scales.
We study Fermi liquids with a Fermi surface that lacks continuous rotational invariance, and in the presence of an arbitrary quartic interaction. We obtain the expressions of the generalized static susceptibilities that measure the linear response of a generic order parameter to a perturbation of the Hamiltonian. We apply our formulae to the spin and charge susceptibilities. Based on the resulting expressions, we make a proposal for the definition of the Landau parameters in non-isotropic Fermi liquid.
Using series expansions and spin-wave theory we calculate the spin-stiffness anisotropy $ρ_{sx}/ρ_{sy}$ in Heisenberg models on the square lattice with anisotropic couplings $J_x,J_y$. We find that for the weakly anisotropic spin-half model ($J_x\approx J_y$), $ρ_{sx}/ρ_{sy}$ deviates substantially from the naive estimate $ρ_{sx}/ρ_{sy} \approx J_x/J_y$. We argue that this deviation can be responsible for pinning the electronic liquid crystal direction, a novel effect recently discovered in YBCO. For completeness, we also study the spin-stiffness for arbitrary anisotropy $J_x/J_y$ for spin-hal…
Based on exact diagonalization and density matrix renormalization group (DMRG) method, we show that an anisotropic triangle lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an exponentially-decaying spin correlator along the weaker coupling direction and a quasi-one-dimensional spin structure factor along the chain direction, in agreement with experiments on the Cs2CuCl4 compounds. In the obtained phase diagram, the spin liquid phase is found to persist up to a relati…
We have studied the low energy spin dynamics between 4.6K and 0.07K in a Tb2Ti2O7 single crystal sample, by means of inelastic neutron scattering experiments. The spectra consist in a dual response, with a static and an inelastic contribution, showing striking Q-dependences. We propose an interpretation involving an anisotropic exchange interaction in combination with a breaking of the threefold symmetry at the rare earth site. Simulations of the Q-dependent scattering in the Random Phase Approximation account well for the inelastic response.
The energetics and transport properties of the polaron in the anisotropic surface over liquid helium are investigated. The localization radii and the energy of the ground and excited states are calculated using the variational method within the hydrodynamic model of the polaron. In particular, we have considered maximal anisotropy which corresponds to the system of electrons in quasi-one-dimensional channels over liquid helium. The polaron binding energy is found and the temperature for the polaron formation is estimated below 0.1 K. Solving the hydrodynamic equations for fluid velocities, the…
The spin-1/2 J1-J2 antiferromagnet is a prototypical model for frustrated magnetism and one possible candidate for a realization of a spin liquid phase. The generalization of this system on the anisotropic square lattice is given by the J1-J2-J1'-J2' Heisenberg model, which can be treated by a renormalization group (RG) analysis of coupled frustrated chains. The J1-J2-J1'-J2'-model shows an interesting interplay of Néel order, dimerization, and spin liquid behavior. The analytical findings supported by numerical results indicate that for the isotropic model the phase at intermediate coupling s…
Umklapp scattering determines the conductivity of clean metals. In typical quasi one-dimensional Fermi liquids with an open Fermi surface, certain pseudo-momenta do not decay by 2-particle collisions even in situations where Umklapp scattering relaxes the momentum of the quasi particles efficiently. Due to this approximate conservation of pseudo-momentum, a certain fraction of the electrical current decays very slowly and a well-pronounced low-frequency peak emerges in the optical conductivity. We develop simple criteria to determine under what conditions approximate pseudo-momentum conservati…
We present the electron tunneling transport and spectroscopic characters of a superconducting {\it Josephson} junction with a barrier of single anisotropic Kitaev quantum spin liquid (QSL) layer. We find that the dynamical spin correlation features are well reflected in the direct-current differential conductance $dI^{c}/dV$ of the single-particle tunneling, including the unique spin gap and dressed itinerant Majorana dispersive band, in addition to an energy shift $2Δ$ of two-lead superconducting gaps. From the spectral characters, we identify different topological quantum phases of the aniso…
We explore spin-1/2 triangular antiferromagnets with both easy-plane and lattice exchange anisotropies by employing a dual vortex mapping followed by a fermionization of the vortices. Over a broad range of exchange anisotropy, this approach leads naturally to a ``critical'' spin liquid--the algebraic vortex liquid--which appears to be distinct from other known spin liquids. We present a detailed characterization of this state, which is described in terms of non-compact QED3 with an emergent SU(4) symmetry. Descendant phases of the algebraic vortex liquid are also explored, which include the Ka…
We explore the effect of the third nearest-neighbors on the magnetic properties of the Heisenberg model on an anisotropic triangular lattice. We obtain the phase diagram of the model using Schwinger-boson mean-field theory. Competition between Néel, spiral and collinear magnetically ordered phases is found as we vary the on the ratios of the nearest, J1, next-nearest, J2, and third-nearest, J_3, neighbor exchange couplings. A spin liquid phase is stabilized between the spiral and collinear ordered states when J2/J1 < 1.8 for rather small J3/J1 < 0.1. The lowest energy two-spinon dispersions re…
We use a recently proposed perturbative numerical renormalization group algorithm to investigate ground-state properties of a frustrated three dimensional Heisenberg model on an anisotropic lattice. We analyze the ground state energy, the finite size spin gap and the static magnetic structure factor. We find in two dimensions a frustration-induced gapless spin liquid state which separates two magnetically ordered phases. In the spin liquid state, the magnetic structure factor shows evidence that this state is made of nearly disconnected chains. This spin liquid state is unstable against unfrus…
We study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters t and t' in different spatial directions and is relevant for layered organic charge-transfer salts. By using a variational approach that includes spiral magnetic order, we provide solid evidence that a spin-liquid phase is stabilized in the strongly-correlated regime and close to the isotropic limit t'/t=1. Otherwise, a magnetically ordered spiral state is found, connecting the (collinear) Néel and the (coplanar) 120° phases. …
We consider the low-energy region of an array of Luttinger liquids coupled by a weak interchain hopping. The leading logarithmic divergences can be re-summed to all orders within a self-consistent perturbative expansion in the hopping, in the large-dimension limit. The anomalous exponent scales to zero below the one-particle crossover temperature. As a consequence, coherent quasiparticles with finite weight appear along the whole Fermi surface. Extending the expansion self-consistently to all orders turns out to be crucial in order to restore the correct Fermi-liquid behavior.
We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems $k$-Fermi liquids. We show how Fermi liquid, Luttinger liquid (or Fermi liquid with exclusion statistics) and spin-charge separation arises from this framework. Two exactly solvable $k$-Fermi liquid models with spin-charge separation are discussed as examples.
Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductivity--anyon superconductor. Such exotic state has been sought for more than twenty years, however it remains unclear whether it can exist in realistic system where time-reversal symmetry is breaking (T-breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model (KHM), which has spontaneously T-breaking. We find that…
We investigate the anisotropic triangular lattice that interpolates from decoupled one-dimensional chains to the isotropic triangular lattice and has been suggested to be relevant for various quasi-two-dimensional materials, such as Cs$_2$CuCl$_4$ or $κ$-(ET)$_2$Cu$_2$(CN)$_3$, an organic material that shows intriguing magnetic properties. We obtain an excellent accuracy by means of a novel representation for the resonating valence bond wave function with both singlet and triplet pairing. This approach allows us to establish that the magnetic order is rapidly destroyed away from the pure trian…
We study the repulsive Hubbard model on an anisotropic honeycomb lattice within a mean-field and a slave-rotor treatment. In addition to the known semi-metallic and band-insulating phases, obtained for very weak interactions, and the anti-ferromagnetic phase at large couplings, various insulating spin-liquid phases develop at intermediate couplings. Whereas some of these spin liquids have gapless spinon excitations, a gapped one occupies a large region of the phase diagram and becomes the predominant phase for large hopping anisotropies. This phase can be understood in terms of weakly-coupled …
Haldane's geometrical description of fractional quantum Hall states is generalized to compressible states. It is shown that anisotropy in the composite fermion Fermi surface is a direct reflection of this intrinsic geometry. A simple model is introduced in which the geometric parameter can be obtained exactly from other parameters including electron mass anisotropy. Our results compare favorably with recent measurements of anisotropy in composite fermion Fermi surface [D. Kamburov, Y. Liu, M. Shayegan, L. N. Pfeiffer, K. W. West, and K. W. Baldwin, Phys. Rev. Lett. 110, 206801 (2013)]. Broader…
We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the $d_{r^2-3z^2}$-type in three dimensions and of the $d_{x^2-y^2}$-type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tri-diagonal Landau interaction matrices in the dipol…
It is well-known that, generically, the one-dimensional interacting fermions cannot be described in terms of the Fermi liquid. Instead, they present different phenomenology, that of the Tomonaga-Luttinger liquid: the Landau quasiparticles are ill-defined, and the fermion occupation number is continuous at the Fermi energy. We demonstrate that suitable fine-tuning of the interaction between fermions can stabilize a peculiar state of one-dimensional matter, which is dissimilar to both the Tomonaga-Luttinger and Fermi liquids. We propose to call this state a quasi-Fermi liquid. Technically speaki…
We clarify the new concept of gravitationally dressed Fermi liquids we have proposed to describe the normal state of high Tc superconductors. In this note we distinguish between weakly gravitationally dressed Fermi liquids which fall in the class of the canonical Fermi liquid theory (with quasiparticle excitations), and strongly gravitationally dressed Fermi liquids (with quasiunparticle excitations) which represent the high dimensional generalization of Luttinger liquids, with specific features. Such weakly or strongly gravitationally dressed Fermi liquids lead naturally to the previously pro…
We study non-Fermi liquid states that arise at the quantum critical points associated with the spin density wave (SDW) and charge density wave (CDW) transitions in metals with twofold rotational symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in $3-ε$ dimensional momentum space. In three dimensions, quasilocal marginal Fermi liquids arise both at the SDW and CDW critical points : the speed of the collective mode along the ordering wavevector is logarithmically renormalized to zero compared to that of Fermi velocity. Below three dimensio…
Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excita…
$α$-YbAlB$_4$ is the locally isostructural polymorph of $β$-YbAlB$_4$, the first example of an Yb-based heavy fermion superconductor which exhibits pronounced non-Fermi-liquid behavior above $T_{\rm c}$. Interestingly, both $α$-YbAlB$_4$ and $β$-YbAlB$_4$ have strongly intermediate valence. Our single crystal study of the specific heat, magnetization and resistivity has confirmed the Fermi liquid ground state of $α$-YbAlB$_4$ ~in contrast with the quantum criticality observed in $β$-YbAlB$_4$. Both systems exhibit Kondo lattice behavior with the characteristic temperature scale $T^* \sim$ 8 K …
We present a study of longitudinal thermal transport in the Kitaev spin model on the honeycomb lattice, focusing on the role of anisotropic exchange to cover both, gapless and gapped phases. Employing a complementary combination of exact diagonalization on small systems and an average gauge configuration approach for up to $\sim O(10^4)$ spinful sites, we report results for the dynamical energy current auto-correlation function as well as the dc thermal conductivity over a wide range of temperatures and exchange anisotropies. Despite a pseudogap in the current correlation spectra, induced by e…
The quantum spin-1/2 antiferromagnetic Heisenberg model on a two dimensional triangular lattice geometry with spatial anisotropy is relevant to describe materials like ${\rm Cs_2 Cu Cl_4}$ and organic compounds like {$κ$-(ET)$_2$Cu$_2$(CN)$_3$}. The strength of the spatial anisotropy can increase quantum fluctuations and can destabilize the magnetically ordered state leading to non conventional spin liquid phases. In order to understand these intriguing phenomena, quantum Monte Carlo methods are used to study this model system as a function of the anisotropic strength, represented by the ratio…
We study the scaling behaviour of the optical conductivity $(σ)$, free energy density $(F)$, and shear viscosity of the quantum critical point associated with the spin density wave phase transition for a two-dimensional metallic system with $C_2$ symmetry. A non-Fermi liquid behaviour emerges at two pairs of isolated points on the Fermi surface, due to the coupling of a bosonic order parameter to fermionic excitations at those so-called ``hot-spots''. We find that near the hot-spots, $σ$ and $F$ obey the scalings expected for such an anisotropic system, and the direction-dependent viscosity to…
In the framework of the mean field approach, we provide analytical and numerical solution of the spin-1/2 anisotropic Kondo lattice for arbitrary dimension at half filling. Nontrivial solution for the amplitude of the field opens a gap in the fermion spectrum of an electron liquid in which local moments on the lattice sites are realized. The ground state in the insulator state is determined by a static Z_2 field of local moments, which forms the lattice with a double cell, conduction electrons move in this field. Due to hybridization between electron states a large Fermi surface is formed in t…
Incommensurate order with translationally invariant projected entangled-pair states: Spiral states and quantum spin liquid on the anisotropic triangular lattice
We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-$M$ (where spin symmetry is enlarged to SU$(M)$) study of the normal state to superconductor phase transition. We describe the transition temperature, the sup…
Instability of the Luttinger liquids towards an exotic quantum state of matter with highly degenerate ground states: an anisotropic extension of the ferromagnetic spin-1 biquadratic model
We propose in this paper an effective low-energy theory for interacting fermion systems which supports exclusion statistics. The theory can be viewed as an extension of Landau Fermi liquid theory where besides quasi-particle energy $ξ_{\mathbf{k}}$, the kinetic momentum $\mathbf{k}$ of quasi-particles depends also on quasi-particle occupation numbers as a result of momentum ($k$)-dependent current-current interaction. The dependence of kinetic momentum on quasi-particles excitations leads to change in density of states and exclusion statistics. The properties of this new Fermi liquid state is …
We develop a theory for a generic instability of a Fermi liquid in dimension d>1 against the formation of a Luttinger-liquid-like state. The density of states at the Fermi level is the order parameter for the ensuing quantum phase transition, which is driven by the effective interaction strength. A scaling theory in conjunction with an effective field theoy for clean electrons is used to obtain the critical behavior of observables. In the Fermi-liquid phase the order-parameter susceptibility, which is measurable by tunneling, is predicted to diverge for 1<d<3.
The $S=1/2$ quantum spin ladder system with the anisotropic ferromagnetic exchange interaction on the rung under magnetic field is investigated using the numerical diagonalization and the density matrix renormalization group (DMRG) analyses. It is found that the nematic-spin-correlation-dominant Tomonaga-Luttinger liquid (TLL) appears in some high magnetic field. It is included in the TLL phase where the two-magnon bound state is realized. For some suitable parameters, after the field-induced phase transition from this two-magnon-bound TLL phase to the single-magnon TLL one, the re-entrant tra…
The ruby lattice is a four-valent lattice interpolating between honeycomb and triangular lattices. In this work we investigate the topological spin-liquid phases of a spin Hamiltonian with Kitaev interactions on the ruby lattice using exact diagonalization and perturbative methods. The latter interactions combined with the structure of the lattice yield a model with $\mathbb{Z}_2 \times \mathbb{Z}_2$ gauge symmetry. We mapped out the phase digram of the model and found gapped and gapless spin-liquid phases. While the low energy sector of the gapped phase corresponds to the well-known topologic…
We investigate the effect of ring-exchange on the ground-state properties and magnetic excitations of the $S = 1/2$ Heisenberg model on the anisotropic triangular lattice with ring-exchange at $T = 0$ using linear spin-wave theory. Classically, we find stable Néel, spiral and collinear magnetically ordered phases. Upon including quantum fluctuations to the model, linear spin-wave theory shows that ring exchange induces a large quantum disordered region in the phase diagram, completely wiping out the classically stable collinear phase. Analysis of the spin-wave spectra for each of these three m…
By using variational wave functions and quantum Monte Carlo techniques, we investigate the complete phase diagram of the Heisenberg model on the anisotropic triangular lattice, where two out of three bonds have super-exchange couplings $J$ and the third one has instead $J^\prime$. This model interpolates between the square lattice and the isotropic triangular one, for $J^\prime/J \le 1$, and between the isotropic triangular lattice and a set of decoupled chains, for $J/J^\prime \le 1$. We consider all the fully-symmetric spin liquids that can be constructed with the fermionic projective-symmet…
We extend and apply a recent theory of the dynamical spin response of Anderson lattice systems to interpret ESR data on YbRh2Si2. Starting within a semiphenomenological Fermi liquid description at low temperatures T < Tx (a crossover temperature) and low magnetic fields B << Bx, we extend the description to the non-Fermi liquid regime by adopting a quasiparticle picture with effective mass and spin susceptibility varying logarithmically with energy/temperature, as observed in experiment. We find a sharp ESR resonance line slightly shifted from the local f-level resonance and broadened by quasi…
We show that in anisotropic Fermi liquids where momentum-conserving scattering is much faster than momentum-relaxing scattering processes, local imaging of the electric current flow patterns can cleanly distinguish between ballistic, viscous and ohmic flow patterns simultaneously (using a single image). We propose using multi-layer graphene-based heterostructures, including ABA trilayer graphene, as a natural experimental platform where an anisotropic ballistic-to-viscous crossover may be visible in near-term experiments. Such experiments could lead to more direct measurements of momentum-cons…
The two-dimensional Hubbard model on the anisotropic triangular lattice, with two different hopping amplitudes $t$ and $t^\prime$, is relevant to describe the low-energy physics of $κ$-(ET)$_2$X, a family of organic salts. The ground-state properties of this model are studied by using Monte Carlo techniques, on the basis of a recent definition of backflow correlations for strongly-correlated lattice systems. The results show that there is no magnetic order for reasonably large values of the electron-electron interaction $U$ and frustrating ratio $t^\prime/t = 0.85$, suitable to describe the no…
We show that thermodynamics is insufficient to probe the nature of the low energy dynamics of quantum impurity models and a more subtle analysis based on scattering theory is required. Traditionally, quantum impurity models are classified into one of two categories: Fermi liquids and non-Fermi liquids, depending on the analytic properties of the various thermodynamic quntities. We show, however, that even when a quantum impurity model is a Fermi liquid (an incoming electron at the Fermi level scatters elastically off the impurity), one may find singular thermodynamic behavior if characteristic…
We show that the one-dimensional (1D) electron systems can also be described by Landau's phenomenological Fermi-liquid theory. Most of the known results derived from the Luttinger-liquid theory can be retrieved from the 1D Fermi-liquid theory. Exact correspondence between the Landau parameters and Haldane parameters is established. The exponents of the dynamical correlation functions and the impurity problem are also discussed based on the finite size corrections of elementary excitations with the predictions of the conformal field theory, which provides a bridge between the 1D Fermi-liquid an…
We study the longitudinal sound propagation in the electronic nematic Fermi liquid where the Fermi surface is distorted due to the spontaneously broken rotational symmetry. The behavior of the sound wave in the nematic ordered state is dramatically different from that in the isotropic Fermi liquid. The collective modes associated with the fluctuations of the Fermi surface distortion in the nematic Fermi liquid leads to the strong and anisotropic damping of the sound wave. The relevance of the nematic Fermi liquid in doped Mott insulator is discussed.
In these lecture notes, the basic physics of Fermi liquids and Luttinger liquids is presented. Fermi liquids are discussed both from a phenomenological viewpoint, in relation to microscopic approaches, and as renormalization group fixed points. Luttinger liquids are introduced using the bosonization formalism, and their essential differences with Fermi liquids are pointed out. Applications to transport effects, the effect of disorder, quantum spin chains, and spin ladders, both insulating and metallic, are given.
We show that a strongly correlated Fermi system with the fermion condensate, which exhibits strong deviations from Landau Fermi liquid behavior, is driven into the Landau Fermi liquid by applying a small magnetic field $B$ at temperature T=0. This field-induced Landau Fermi liquid behavior provides the constancy of the Kadowaki-Woods ratio. A reentrance into the strongly correlated regime is observed if the magnetic field $B$ decreases to zero, then the effective mass $M^*$ diverges as $M^*\propto 1/\sqrt{B}$. At finite temperatures, the strongly correlated regime is restored at some temperatu…
