We present a unified theory of strongly correlated electron systems with a fermion condensate. This theoretical framework facilitates quantitative analysis and explanation, on an equal footing, of (i) non-Fermi-liquid behavior of high- T c superconductors in which the critical temperature for superconductivity is proportional to the Fermi energy T F and (ii) the so-called quantum electron solid state in the two-dimensional electron liquid of MOSFETs and SiGe/Si/SiGe quantum wells. In this framework, low-temperature chaotic-like behavior that is documented in experimental studies of these systems is attributed to a spontaneous topological rearrangement of the conventional Landau state, quite in contrast to models in which the chaotic element is introduced deliberately in terms of a chaotic distribution of interaction matrix elements.
We present a unified theory of strongly correlated electron systems with a fermion condensate. This theoretical framework facilitates quantitative analysis and explanation, on an equal footing, of (i) non-Fermi-liquid behavior of high- T c superconductors in which the critical temperature for superconductivity is proportional to the Fermi energy T F and (ii) the so-called quantum electron solid state in the two-dimensional electron liquid of MOSFETs and SiGe/Si/SiGe quantum wells. In this framework, low-temperature chaotic-like behavior that is documented in experimental studies of these systems is attributed to a spontaneous topological rearrangement of the conventional Landau state, quite in contrast to models in which the chaotic element is introduced deliberately in terms of a chaotic distribution of interaction matrix elements.
In framework of eigen-functional bosonization method, we introduce an imaginary phase field to uniquely represent electron correlation, and demonstrate that the Landau Fermi liquid theory and the Tomonaga-Luttinger liquid theory can be unified. It is very clear in this framework that the Tomonaga-Luttinger liquid behavior of one-dimensional interacting electron gases originates from their Fermi structure, and the non-Landau-Fermi liquid behavior of 2D interacting electron gases is induced by the long-range electron interaction, while 3D interacting electron gases generally show the Landau Fermi liquid behavior. Typeset using REVTEX 1 Since the discovery of high Tc cuprate superconductors [1], the strongly correlated electron systems has been extensively studied theoretically [2–10]. Now a common consensus is reached that the low energy physics properties of cuprate superconductors, such as anomalous normal state behavior and high superconducting transition temperature, are determined
Abstract Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high- T c superconductors belong to that class of quantum many-body systems for which Landau Fermi-liquid (LFL) theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal ( T ) and particle-hole ( C ) invariance. Measurements of tunneling conductance provide a powerful experimental tool for detecting violations of these basic symmetries inherent to LFLs, which guarantee that the measured differential conductivity d I /d V , where I is the current and V the bias voltage, is a symmetric function of V . Thus, it has been predicted that the conductivity becomes asymmetric for HF metals such as CeCoIn 5 and YbRh 2 Si 2 . In these systems, the background electron liquid is considered to undergo a transformation that renders a portion of its excitation spectrum dispersionless, giving rise to so-called flat bands. The presence of a flat band indicates that the system is close to a special quantum critical point, namely a topological fermion-condensation quantum phase transition . An essential aspect of the behavior of a system hosting a flat band is that application of a magnetic field can restore its normal Fermi-liquid properties, including T - and C -invariance, with the differential conductivity again becoming a symmetric function of V . This behavior has been observed in recent measurements of tunneling conductivity in both YbRh 2 Si 2 and graphene. Also within the FC framework, we describe and explain recent empirical observations of scaling properties related to universal linear-temperature resistivity for a large number of strongly correlated high-temperature superconductors. We show that the observed scaling is explained by the emergence of flat bands formed by fermion condensation.
The Landau theory of phase and phase transition, which describes the state of matter by the spontaneous symmetry breaking, and the Fermi liquid theory of interacting Fermi systems are the two corner stones of contemporary condensed matter physics. They act as our starting points to understand the structure, excitations and phase transitions of any condensed matter system. According to such a Landau paradigm, an interacting Fermi system will behave just as non-interacting Fermi gas system at sufficient low energy, if the interaction is not strong enough to induce a symmetry breaking phase transition in the system. In such a case, the perturbation expansion in the interaction strength is assumed to converge and the low energy excitation can be connected to that of a Fermi gas system adiabatically. In strongly correlated electron systems, such as the high temperature superconductors and quantum antiferromagnets, a pertubative picture on the interaction effect usually fails. The correlation effect between the electrons can induce new forms of order that are beyond the Landau symmetry breaking paradigm. Non-Fermi liquid behavior can emerge in the fully symmetric correlated phases. The Mott insulating phase and the quantum spin liquid phase are the most prominent example of such exotic state of matter. After about three decades of intensive studies, people find that the quantum non-locality effect is at the heart of such new forms of order. The quantum non-locality effect manifests itself in the emergence of gauge degree of freedom in the low energy physics of such strongly correlated system. Such emergent gauge filed is not only important for the characterization and classification of the ground state structure, but is also directly responsible for the non-Fermi liquid behavior of the system. The Landau paradigm should be extended to accommodate such new forms of order and the related new form of excitations and new universal class of phase transitions. Such an extension will elevate our understanding of the structure of matter to the level of quantum wave function. Unlike the conventional symmetry breaking order, which is characterized by the correlation functions between local physical observables, the new form of orders, which are commonly called quantum order (with the topological order as one of its typical example), can be better characterized by the entanglement property in the quantum wave function. From a mathematical point of view, the new form of order is closely related to the projective representation theory of the symmetry group, while the conventional symmetry breaking order is well described by the linear representation theory of the symmetry group.
The appearance of the fermion condensation, which can be compared to the Bose-Einstein condensation, in different Fermi liquids is considered; its properties are discussed; and a large amount of experimental evidence in favor of the existence of the fermion condensate (FC) is presented. We show that the appearance of FC is a signature of the fermion condensation quantum phase transition (FCQPT), which separates the regions of normal and strongly correlated liquids. Beyond the FCQPT point, the quasiparticle system is divided into two subsystems, one containing normal quasiparticles and the other, FC, localized at the Fermi level. In the superconducting state, the quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by effective masses M FC * and M L * and intersecting near the binding energy E 0, which is of the order of the superconducting gap. The same quasiparticle picture and the energy scale E 0 persist in the normal state. We demonstrate that fermion systems with FC have features of a “quantum protectorate” and show that strongly correlated systems with FC, which exhibit large deviations from the Landau Fermi liquid behavior, can be driven into the Landau Fermi liquid by applying a small magnetic field B at low temperatures. Thus, the essence of strongly correlated electron liquids can be controlled by weak magnetic fields. A reentrance into the strongly correlated regime is observed if the magnetic field B decreases to zero, while the effective mass M* diverges as $$M^ * \propto {1 \mathord{\left/ {\vphantom {1 {\sqrt B }}} \right. \kern-\nulldelimiterspace} {\sqrt B }}$$ . The regime is restored at some temperature T∗∝B . The behavior of Fermi systems that approach FCQPT from the disordered phase is considered. This behavior can be viewed as a highly correlated one, because the effective mass is large and strongly depends on the density. We expect that FCQPT takes place in trapped Fermi gases and in low-density neutron matter, leading to stabilization of the matter by lowering its ground-state energy. When the system recedes from FCQPT, the effective mass becomes density independent and the system is suited perfectly to be conventional Landau Fermi liquid.
Experiments on strongly correlated quasi-two-dimensional electronic materials---for example, the high-temperature cuprate superconductors and the putative quantum spin liquids kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2---routinely reveal highly mysterious quantum behavior which cannot be explained in terms of weakly interacting degrees of freedom. Theoretical progress thus requires the introduction of completely new concepts and machinery beyond the traditional framework of the band theory of solids and its interacting counterpart, Landau's Fermi liquid theory. In full two dimensions, controlled and reliable analytical approaches to such problems are severely lacking, as are numerical simulations of even the simplest of model Hamiltonians due to the infamous fermionic sign problem.Here, we attempt to circumvent some of these difficulties by studying analogous problems in quasi-one dimension. In this lower dimensional setting, theoretical and numerical tractability are on much stronger footing due to the methods of bosonization and the density matrix renormalization group, respectively. Using these techniques, we attack two problems: (1) the Mott transition between a Fermi liquid metal and a quantum spin liquid as potentially directly relevant to the organic compounds kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2 and (2) non-Fermi liquid metals as strongly motivated by the strange metal phase observed in the cuprates. In both cases, we are able to realize highly exotic quantum phases as ground states of reasonable microscopic models. This lends strong credence to respective underlying slave-particle descriptions of the low-energy physics, which are inherently strongly interacting and also unconventional in comparison to weakly interacting alternatives.Finally, working in two dimensions directly, we propose a new slave-particle theory which explains in a universal way many of the intriguing experimental results of the triangular lattice organic spin liquid candidates kappa-(BEDT-TTF)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2. With use of large-scale variational Monte Carlo calculations, we show that this new state has very competitive trial energy in an effective spin model thought to describe the essential features of the real materials.
The rearrangement of single-particle degrees of freedom of a dilute two-dimensional electron gas in the vicinity of the quantum critical point is examined within a microscopic approach. It is shown that just beyond the critical point, the Landau state undergoes self-consistent rearrangement of the quasiparticle spectrum and momentum distribution. At very low temperatures, there emerges a multi-connected quasiparticle momentum distribution. With increasing temperature, two crossovers occur: a fermion condensate appears in the first and disappears in the second, giving way to universal non-Fermi-liquid behavior. Manifestations of these crossovers in thermodynamic properties of the electron gas are studied and characterized. The four quasiparticle phases predicted to exist in the vicinity of the critical point are collected in a schematic phase diagram.