The influence of topological phase transition on the superfluid density of overdoped copper oxides

We show that a topological quantum phase transition, generating flat bands and altering Fermi surface topology, is a primary reason for the exotic behavior of the overdoped high-temperature superconductors represented by $\rm La_{2-x}Sr_xCuO_4$, whose superconductivity features differ from what is described by the classical Bardeen-Cooper-Schrieffer theory [J.I. Bo\^zovi\'c, X. He, J. Wu, and A. T. Bollinger, Nature 536, 309 (2016)]. We demonstrate that 1) at temperature $T=0$, the superfluid density $n_s$ turns out to be considerably smaller than the total electron density; 2) the critical temperature $T_c$ is controlled by $n_s$ rather than by doping, and is a linear function of the $n_s$…

The Topological Phase Transitions Related to Fermion Condensate

In this chapter, we consider so-called topological phase transitions, taking place in normal Fermi liquid. In other words, here we are dealing with different instabilities of normal Fermi liquids relative to several kinds of perturbations of initial quasiparticle spectrum \(\varepsilon (p)\) and occupation numbers \(n(p)\) associated with the emergence of a multi-connected Fermi surface. Depending on the parameters and analytical properties of the Landau interaction, such instabilities lead to several possible types of restructuring of initial Landau Fermi liquid ground state. This restructuring generates topologically distinct phases. One of them is the FC discussed above, another one belo…

Energy scales and magnetoresistance at a quantum critical point

The magnetoresistance (MR) of CeCoIn_5 is notably different from that in many conventional metals. We show that a pronounced crossover from negative to positive MR at elevated temperatures and fixed magnetic fields is determined by the scaling behavior of quasiparticle effective mass. At a quantum critical point (QCP) this dependence generates kinks (crossover points from fast to slow growth) in thermodynamic characteristics (like specific heat, magnetization etc) at some temperatures when a strongly correlated electron system transits from the magnetic field induced Landau Fermi liquid (LFL) regime to the non-Fermi liquid (NFL) one taking place at rising temperatures. We show that the abov…

Asymmetrical tunneling in heavy fermion metals as a possible probe for their non-Fermi liquid peculiarities

Tunneling conductivity and point contact spectroscopy between heavy fermion metal and a simple metallic point contact may serve as a convenient probing tool for non-Fermi liquid behavior. Landau Fermi liquid theory predicts that the differential conductivity is a symmetric function of voltage bias. This symmetry, in fact, holds if so called particle–hole symmetry is preserved. Here, we show that the situation can be different when one of the two metals is a heavy fermion one whose electronic system is a heavy fermion liquid. When the heavy fermion liquid undergoes fermion condensation quantum phase transition, the particle–hole symmetry in the excitation spectra is violated making both the …

Violation of the Time-Reversal and Particle-Hole Symmetries in Strongly Correlated Fermi Systems: A Review

In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals and high Tc superconductors exhibit C and T symmetries violation due to so-called non-Fermi liquid (NFL) behavior. In these systems, tunneling differential conductivity (or resistivity) is a very sensitive tool to experimentally test the above symmetry break. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition (FCQPT), it exhibits t…

Magnetic-field-induced reentrance of Fermi-liquid behavior and spin-lattice relaxation rates in

Abstract A strong departure from Landau–Fermi liquid (LFL) behavior have been recently revealed in observed anomalies in both the magnetic susceptibility χ and the muon and 63Cu nuclear spin-lattice relaxation rates 1 / T 1 of YbCu 5 − x Au x ( x = 0.6 ). We show that the above anomalies along with magnetic-field-induced reentrance of LFL properties are indeed determined by the dependence of the quasiparticle effective mass M ∗ on magnetic field B and temperature T and demonstrate that violations of the Korringa law also come from M ∗ ( B , T ) dependence. We obtain this dependence theoretically utilizing our approach based on fermion condensation quantum phase transition (FCQPT) notion. Ou…

Flat bands and strongly correlated Fermi systems

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which Landau Fermiliquid (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 dI/dV, 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 …

Baryon Asymmetry Resulting from FCQPT in the Early Universe

This Chapter does not follow the main line of the book that is the theory of HF compounds but illustrates how the ideas of FC may be applicable to describe a very dissimilar system. Namely, here we consider a novel mechanism for explaining the matter-antimatter asymmetry of the universe. We assume that the universe starts from completely symmetric state and then, as it cools down, it undergoes a quantum phase transition, which in turn causes an asymmetry between matter and anti-matter. As we shall see the quantum phase transition is represented by FCQPT. The mechanism does not require the baryon number violating interactions or \({\textit{CP}}\) violation at a microscopic level. The state F…

Thermodynamic, dynamic and transport properties of quantum spin liquid in herbertsmithite from experimental and theoretical point of view

In our review we focus on the quantum spin liquid, defining the thermodynamic, transport and relaxation properties of geometrically frustrated magnets (insulators) represented by herbertsmithite $\rm ZnCu_{3}(OH)_6Cl_2$.

Highly Correlated Fermi Liquid in Heavy-Fermion Metals: Magnetic Properties

In this chapter we show how the FCQPT theory works, when describing the behavior of HF metals under the application of magnetic field. We show that a large body of experimental data regarding the thermodynamic, transport and relaxation properties collected in measurements on HF metals can be well explained. It is demonstrated that the experimental data exhibit the scaling behavior.

Quantum critical point in high-temperature superconductors

Recently, in high-T_c superconductors (HTSC), exciting measurements have been performed revealing their physics in superconducting and pseudogap states and in normal one induced by the application of magnetic field, when the transition from non-Fermi liquid to Landau Fermi liquid behavior occurs. We employ a theory, based on fermion condensation quantum phase transition which is able to explain facts obtained in the measurements. We also show, that in spite of very different microscopic nature of HTSC, heavy-fermion metals and 2D 3He, the physical properties of these three classes of substances are similar to each other.

Theory of Heavy-Fermion Compounds : Theory of Strongly Correlated Fermi-Systems

Landau Fermi Liquid Theory and Beyond

In this chapter we consider the Landau theory of the Fermi liquid that has a long history and remarkable results in describing a numerous properties of the electron liquid in ordinary metals and Fermi liquids of the \(^3\)He type. The theory is based on the assumption that elementary excitations determine the physics at low temperatures, resembling that of weakly interacting Fermi gas. These excitations behave as quasiparticles with a certain effective mass. The effective mass \(M^*\) exhibits a simple universal behavior, for it is independent of the temperature, pressure, and magnetic field strength and is a parameter of the theory. Microscopically deriving the equation determining the eff…

Quantum Criticality of Heavy-Fermion Compounds

Chapter 17 is devoted to the quantum criticality of quantum spin liquids. In this chapter we continue to consider the nature of quantum criticality in HF compounds. The quantum criticality induced by the fermion condensation quantum phase transition extends over a wide range in the \(T-B\) phase diagram. As we shall see, the quantum criticality in all such different HF compounds, as high-\(T_c\) superconductors, HF metals, compounds with quantum spin liquids, quasicrystals, and 2D quantum liquids, is of the same nature. This challenging similarity between different HF compounds expresses universal physics that transcends the microscopic details of the compounds. This uniform behavior, induc…

Universal behavior of two-dimensional 3He at low temperatures.

On the example of two-dimensional (2D) 3He we demonstrate that the main universal features of its experimental temperature T - density x phase diagram [see M. Neumann, J. Ny\'{e}ki, J. Saunders, Science 317, 1356 (2007)] look like those in the heavy-fermion metals. Our comprehensive theoretical analysis of experimental situation in 2D 3He allows us to propose a simple expression for effective mass M^*(T,x), describing all diverse experimental facts in 2D 3He in unified manner and demonstrating that the universal behavior of M^*(T,x) coincides with that observed in HF metals.

FERMION CONDENSATION, T -LINEAR RESISTIVITY AND PLANCKIAN LIMIT

We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition (FCQPT). We emphasize that so - called Planckian limit, widely used to explain the above universal scatteri…

Quasiparticles and quantum phase transition in universal low-temperature properties of heavy-fermion metals

We demonstrate, that the main universal features of the low temperature experimental $H-T$ phase diagram of CeCoIn5 and other heavy-fermion metals can be well explained using Landau paradigm of quasiparticles. The main point of our theory is that above quasiparticles form so-called fermion-condensate state, achieved by a fermion condensation quantum phase transition (FCQPT). When a heavy fermion liquid undergoes FCQPT, the fluctuations accompanying above quantum critical point are strongly suppressed and cannot destroy the quasiparticles. The comparison of our theoretical results with experimental data on CeCoIn5 have shown that the electronic system of above substance provides a unique opp…

Asymmetric Conductivity of Strongly Correlated Compounds

In this chapter, we show that the FC solutions for distribution function \(n_0(\mathbf{p})\) generate NFL behavior, and violate the particle-hole symmetry inherent in LFL. This, in turn, yields dramatic changes in transport properties of HF metals, particularly, the differential conductivity becomes asymmetric. As it is demonstrated in Sect. 3.1, Fermi quasiparticles can behave as Bose one. Such a state is viewed as possessing the supersymmetry (SUSY) that interchanges bosons and fermions eliminating the difference between them. In the case of asymmetrical conductivity it is the emerging SUSY that violates the time invariance symmetry. Thus, restoring one important symmetry, the FC state vi…

Violation of the Wiedemann-Franz Law in HF Metals

Experimental observations of the much-studied compounds CeCoIn\(_5\) and YbRh\(_2\)Si\(_2\) at vanishing temperatures carefully probe the nature of their magnetic-field-tuned QCPs. The violation of Wiedemann-Franz (WF) law, along with jumps revealed both in the residual resistivity \(\rho _0\) and the Hall resistivity \(R_H\), provide vital clues to the origin of their non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with FC forming flat bands.

High Magnetic Fields Thermodynamics of Heavy Fermion Metals

In this chapter, we present the comprehensive theoretical analysis of thermodynamics of HF compounds at high magnetic fields. Such analysis permits to gain a deeper insight into the interplay of high magnetic field and temperature in suppressing and retrieving the Landau Fermi liquid state in these substances. Our analysis shows that although high magnetic fields and temperatures alter the properties of ordinary Landau quasiparticles, they survive, generating the experimentally observable anomalies in the thermodynamical quantities of HF compounds. We illustrate our theoretical findings by the example of the HF compound \(\mathrm{{YbRh_2Si_2}}\).

Asymmetric Tunneling Conductance and the non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the nonFermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau– Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V . This is because the particle-hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle-hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V . Th…

Metals with a Strongly Correlated Electron Liquid

In this chapter, we consider the main properties of strongly correlated Fermi systems, which are formed by the fermion condensate leading to the emergence of flat bands. Namely, we consider the residual entropy \(S_0\) related to the flat bands that leads to the violation of the quasiparticle—hole symmetry. The presence of \(S_0\) has a profound impact on the universality of second order phase transitions. In that case under the application of magnetic field the curve of the second order AF phase transitions passes into a curve of the first order ones at the tricritical point, thus leading to a violation of the critical universality of the fluctuation theory. We demonstrate that a jump in t…

Flat Bands and Salient Experimental Features Supporting the Fermion Condensation Theory of Strongly Correlated Fermi

The physics of strongly correlated Fermi systems, being the mainstream topic for more than half a century, still remains elusive. Recent advancements in experimental techniques permit to collect important data, which, in turn, allow us to make the conclusive statements about the underlying physics of strongly correlated Fermi systems. Such systems are close to a special quantum critical point represented by topological fermion-condensation quantum phase transition which separates normal Fermi liquid and that with a fermion condensate, forming flat bands. Our review paper considers recent exciting experimental observations of universal scattering rate related to linear temperature dependence…

Highly Correlated Fermi Liquid in Heavy-Fermion Metals: The Scaling Behavior

In this chapter we show how the FCQPT theory works. We do that on the base of experimentally relevant examples. Namely, as noted in the Introduction (Chap. 1), the challenge for the theories is to explain the scaling behavior of the normalized effective mass \(M^*_N(y)\) displayed in Fig. 1.3. The theories analyzing only the critical exponents characterizing \(M^*_N(y)\) at \(y\gg 1\) consider only a part of the problem. In this section we analyze and derive the scaling behavior of the normalized effective mass near QCP as reported in Fig. 1.3. We start with describing magnetic field dependence of the quasiparticle effective mass in Sect. 6.1. Quasiparticle damping and the temperature depen…

Quasi-classical Physics Within Quantum Criticality in HF Compounds

In this chapter, we explore how the fermion condensation paves the road for quasi-classical physics in HF compounds. This means simply that systems with FC admit partly the quasi-classical description of their thermodynamic and transport properties. This, in turn, simplifies a lot not only of their description but permits to gain more insights both in the puzzling NFL physics of HF compounds and of the physics of FC itself. The quasi-classical physics starts to be applicable near FCQPT, at which FC generates flat bands and quantum criticality, and makes the density of electron states in strongly correlated metals diverge. As we shall see, due to the formation of flat bands the strongly corr…

Identification of strongly correlated spin liquid in herbertsmithite

Exotic quantum spin liquid (QSL) is formed with such hypothetic particles as fermionic spinons carrying spin 1/2 and no charge. Here we calculate its thermodynamic and relaxation properties. Our calculations unveil the fundamental properties of QSL, forming strongly correlated Fermi system located at a fermion condensation quantum phase transition. These are in a good agreement with experimental data and allow us to detect the behavior of QSL as that observed in heavy fermion metals. We predict that the thermal resistivity of QSL under the application of magnetic fields at fixed temperature demonstrates a very specific behavior. The key features of our findings are the presence of spin-char…

Theoretical and experimental developments in quantum spin liquid in geometrically frustrated magnets: a review

The exotic substances have exotic properties. One class of such substances is geometrically frustrated magnets, where correlated spins reside in the sites of triangular or kagome lattice. In some cases, such magnet would not have long-range magnetic order. Rather, its spins tend to form kind of pairs, called valence bonds. At $$T \rightarrow 0$$ these highly entangled quantum objects condense in the form of a liquid, called quantum spin liquid (QSL). The observation of a gapless QSL in actual materials is of fundamental significance both theoretically and technologically, as it could open a path to creation of topologically protected states for quantum information processing and computation…

Magnetoresistance in the HF Metal at Zero Temperature

In this chapter we consider the paradoxical behavior of the residual resistivity \(\rho _0\) of HF metals in magnetic fields and under pressure. Our consideration is based on the idea of flattening of the single-particle spectrum \(\varepsilon (\mathbf{p})\) that profoundly effects on the specific heat \(C\), thermal expansion coefficient \(\alpha \) and magnetic susceptibility \(\chi \) in the normal state, the jump of \(C\) at the point of superconducting phase transition etc. We show that FC associated with flat bands contributes to the residual resistivity \(\rho _0\), while the application of the magnetic field or pressure to the system with a flat band removes the flat band and leads …

The peculiarities of the phase diagram of heavy fermion metal CeCoIn5

We analyze the low temperature experimental magnetic field–temperature H–T phase diagram of CeCoIn5. We demonstrate that its main features can be well explained within Landau quasiparticle picture incorporating the fact that quasiparticles form so-called fermion-condensate (FC) state emerging behind the fermion condensation quantum phase transition (FCQPT). We show that near FCQPT, the fluctuations are strongly suppressed while FC by itself is “protected” from above fluctuations by the first order phase transition. We demonstrate that the electronic system of CeCoIn5 can be shifted from the ordered towards disordered side of FCQPT by the application of magnetic field therefore giving a uniq…

Quantum critical point in ferromagnet

Abstract The heavy-fermion metal CePd 1 - x Rh x can be tuned from ferromagnetism at x = 0 to non-magnetic state at the critical concentration x c . The non-Fermi liquid behavior at x ≃ x c is recognized by power law dependence of the specific heat C ( T ) given by the electronic contribution, susceptibility χ ( T ) and volume expansion coefficient α ( T ) at low temperatures: C / T ∝ χ ( T ) ∝ α ( T ) / T ∝ 1 / T . We show that this alloy exhibits a universal thermodynamic non-Fermi liquid behavior independent of magnetic ground state. This can be well understood utilizing the quasiparticle picture and the concept of fermion condensation quantum phase transition at the density ρ = p F 3 / …

Fermion Condensation in Finite Systems

Here we consider another example of systems, in which fermion condensation takes place. These are what is called finite Fermi systems, i.e. systems with finite number of fermions, contrary to a solid, where the number of electrons is practically infinite. An example of a finite Fermi system is an atomic nucleus, having finite number of nucleons, protons and neutrons, which are fermions. Here we show that the fermion condensation manifests itself in finite Fermi systems as a forced merger of all, discreet for finite systems, single-particle levels, lying near the Fermi surface. On the first sight, this merger contradicts the standard Landau quasiparticle picture. Nevertheless, similar to inf…

New state of matter: heavy-fermion systems, quantum spin liquids, quasicrystals, cold gases, and high temperature superconductors

We report on a new state of matter manifested by strongly correlated Fermi systems including various heavy-fermion (HF) metals, two-dimensional quantum liquids such as $\rm ^3He$ films, certain quasicrystals, and systems behaving as quantum spin liquids. Generically, these systems can be viewed as HF systems or HF compounds, in that they exhibit typical behavior of HF metals. At zero temperature, such systems can experience a so-called fermion-condensation quantum phase transition (FCQPT). Combining analytical considerations with arguments based entirely on experimental grounds we argue and demonstrate that the class of HF systems is characterized by universal scaling behavior of their ther…

Zero Temperature Magnetoresistance of the HF Metal: Enigma of $$\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}$$

To understand the nature of field-tuned metamagnetic quantum criticality in the ruthenate \(\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}\) is one of the significant challenges in the condensed matter physics. It is established experimentally that the entropy has a peak in the ordered phase. It is unexpectedly higher than that outside latter phase, while the magnetoresistivity varies abruptly near the ordered phase boundary. We demonstrate unexpected similarity between \(\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}\) and HF metals expressing universal physics that transcends microscopic details. Our \(T-B\) phase diagram of \(\mathrm{Sr}_{3}\mathrm{Ru}_{2}\mathrm{O}_{7}\) explains main featu…

Fermi Liquid with Fermion Condensate

Here we discuss the general properties of FCQPT leading to the emergence of FC. We present a microscopic derivation of the main equations of FC, and show that Fermi systems with FC form an entirely new class of Fermi liquids with its own topological structure, protecting the FC state. We construct the phase diagram, and explore the order parameter of these systems. We show that the fermion condensate has a strong impact on the observable physical properties of systems, where it is realized, up to relatively high temperatures of a few tens kelvin. Two different scenarios of the quantum critical point (QCP), a zero-temperature instability of the Landau state, related to the divergence of the …

Heavy fermion spin liquid in herbertsmithite

We analyze recent heat capacity measurements in herbertsmithite $\rm ZnCu_3(OH)_6Cl_2$ single crystal samples subjected to strong magnetic fields. We show that the temperature dependence of specific heat $C_{mag}$ formed by quantum spin liquid at different magnetic fields $B$ resembles the electronic heat capacity $C_{el}$ of the HF metal $\rm YbRh_2Si_2$. We demonstrate that the spinon effective mass $M^*_{mag}\propto C_{mag}/T$ exhibits a scaling behavior like that of $C_{el}/T$. We also show that the recent measurements of $C_{mag}$ are compatible with those obtained on powder samples. These observations allow us to conclude that $\rm ZnCu_3(OH)_6Cl_2$ holds a stable strongly correlated …

Quasi-one-dimensional quantum spin liquid in the $\rm {Cu(C_4H_4N_2)(NO_3)_2}$ insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-one dimensional insulator Cu(C$_4$H$_4$N$_2$)(NO$_3$)$_2$ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic $T-H$ (temperature---magnetic field…

Experimental Manifestations of Fermion Condensation in Strongly Correlated Fermi Systems

Many strongly correlated Fermi systems including heavy-fermion (HF) metals and high-Tc superconductors belong to that class of quantum many-body systems for which the Landau–Fermi liquid theory fails. Instead, these systems exhibit non-Fermi-liquid properties that arise from violation of time-reversal (T) and particle– hole (C) invariance. Here we consider two most recent experimental puzzles, which cannot be explained neither within the Landau–Fermi liquid picture nor can they be made intelligible by the approaches like the Hubbard model and/or the Kondo effect, which are commonly used to spell out the typical non-Fermi-liquid behavior. The first experimental puzzle is the asymmetric (with…

Universal Behavior of Quantum Spin Liquid and Optical Conductivity in the Insulator Herbertsmithite

We analyze optical conductivity with the goal to demonstrate experimental manifestation of a new state of matter, the so-called fermion condensate. Fermion condensates are realized in quantum spin liquids, exhibiting typical behavior of heavy fermion metals. Measurements of the low-frequency optical conductivity collected on the geometrically frustrated insulator herbertsmithite provide important experimental evidence of the nature of its quantum spin liquid composed of spinons. To analyze recent measurements of the herbertsmithite optical conductivity at different temperatures, we employ a model of strongly correlated quantum spin liquid located near the fermion condensation phase transiti…

Magnetic quantum criticality in quasi-one-dimensional Heisenberg antiferromagnet Cu (C4H4N2)( NO 3)2

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 quantitativ…

Appearance of Fermion-Condensation Quantum Phase Transition in Fermi Systems

As high-\(T_c\) superconductors are represented primarily by 2D layered structures, in Sect. 5.1 we discuss the superconducting state of a 2D liquid of heavy electrons, and within the framework of Gor’kov microscopic equations construct the Green functions of the FC state. On the other hand, our study can easily be generalized to the 3D case. To show that there is no fundamental difference between the 2D and 3D cases, we derive Green’s functions for the 3D case in Sect. 5.1.1. In Sect. 5.2, we consider the dispersion law and lineshape of single-particle excitations. Section 5.3 is devoted to the behavior of heavy-electron liquid with FC in magnetic field. In Sect. 5.4, we analyze conditions…

Quantum Criticality of Spin Liquids in Novel Insulators and Magnets

Strongly correlated Fermi systems are among the most intriguing and fundamental systems in physics, whose realization in some compounds is still under consideration. Quantum spin liquids are a promising new phases, where exotic quantum states of matter could be realized. Exotic quantum spin liquid (QSL) made of such hypothetic particles as fermionic spinons which carry spin \(1/2\) and no charge are considered in this chapter. Magnetic insulators with geometrical frustration produce important experimental facts shedding light on the nature of quantum spin liquid composed of spinons. We present a theory of the thermodynamic properties of quantum spin liquids, elucidating how their properties…