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In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors. Their transport properties are defined by strong inter-particle interaction forming flat bands in these compounds. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit the linear in temperature resistivity, $\rho(T)\propto T$. We analyze the magnetoresistance and show that it under the application of magnetic field becomes negative. It is shown that near a quantum phase transition, when the density of electronic states diverges, semiclassical physics remains applicable to describe the resistivity $\rho$ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when $T$ exceeds the extremely low Debye temperature $T_D$, the resistivity $\rho(T)$ changes linearly with $T$, since the mechanism of formation of the $T$-dependence $\rho(T)$ is similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of $T$-linear resistance, electron-phonon scattering leads to a lifetime of $\tau$ quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant $\hbar$ to the Boltzmann constant constant $k_B$, $T\tau\sim \hbar/k_B$. We explain that due to the non-Fermi-liquid behavior the real part of the frequency-dependent optical conductivity $\sigma^R_{opt}(\omega)$ exhibits a scaling behavior, and demonstrates the unusual power law behavior $\sigma^R_{opt}(\omega)\propto\omega^{-1}$, rather than the well-known one shown by conventional metals, $\sigma^R_{opt}(\omega)\propto\omega^{-2}$., Comment: 14 pages, 12 figures

Condensed-matter community is involved in hot debate on the nature of quantum critical points (QCP) governing the low-temperature properties of heavy fermion metals. The smeared jump like behavior revealed both in the residual resistivity $\rho_0$ and the Hall resistivity $R_H$, along with the violation of the time invariance symmetry $\mathcal{T}$ and the charge invariance $\mathcal{C}$, including the violation of quasiparticle-hole symmetry, and providing vital clues on the origin of both the non-Fermi-liquid behavior and QCP. For the first time, based on a number of important experimental data, we show that these experimental observations point out unambiguously that QCP of $\rm CeCoIn_5$ is accompanied by the symmetry violation, and QCP itself is represented by the topological fermion-condensation quantum phase transition (FCQPT) connecting two Fermi surfaces of different topological charges., Comment: 7 pages, 8 figures

Landau's quasiparticle formalism is generalized to describe a wide class of strongly correlated Fermi systems, in addition to conventional Fermi liquids. This class includes (i) so-called marginal exemplars and (ii) systems that harbor interaction-driven flat bands, in both of which manifestations of non-Fermi-liquid behavior are well documented. Specifically, the advent of such flat bands is attributed to a spontaneous topological rearrangement of the Landau state that supplements the conventional Landau quasiparticle picture with a different set of quasiparticles, the so-called fermion condensate, whose single-particle spectrum is dispersionless. The celebrated Landau-Luttinger theorem is extended to marginal Fermi liquids, in which the density of the augmented quasiparticle system is shown to coincide with the particle density. On the other hand, the total density of a system hosting an interaction-driven flat band turns out to be the sum of the densities of the two quasiparticle subsystems: the Landau-like component and the fermion condensate. We demonstrate that within the framework of the scenario proposed, a long-standing problem faced by theories of $D$-wave superconductivity in cuprates, namely a consistent explanation of the so-called Uemera plot, can be naturally resolved., Comment: 15 pages, 3 figures

P. W. Phillips, N. E. Hussey, P. Abbamonte (Review Article, 8 July 2022, eabh4273) consider heavy fermion (HF) metals and high-$T_c$ superconductors naming them strange metals. They analyze such features of strange metals as quantum criticality, Planckian dissipation and recently observed fundamental link between the high-$T_c$ superconductivity and strange metals, and conclude that these problems can be possibly resolved within the framework of theories based on gravity, etc. In this comment we discuss that this claim is not correct and the successful description of the quantum criticality, Planckian dissipation and recently observed fundamental link between the high-$T_c$ superconductivity and strange metals has been given within the framework of the fermion condensation theory., Comment: 3 pages, 3 figures

The quasiparticle formalism invented by Lev Landau for description of conventional Fermi liquids is generalized to exotic superconductivity attributed to Cooper pairing, whose measured properties defy explanation within the standard BCS-Fermi Liquid description. We demonstrate that in such systems the quasiparticle number remains equal to particle number, just as in common Fermi liquids. We are then able to explain the puzzling relationship between the variation with doping $x$ of two key properties of the family La$_{2-x}$Sr$_x$Cu0$_4$ of exotic superconductors, namely the $T=0$ superfluid density $\rho_{s0}(x)$ and the coefficient $A_1(x)$ in the linear-in-$T$ component of the normal-state low-$T$ resistivity $\rho(T)=\rho_0+A_1T+A_2T^2$, in terms of the presence of interaction-induced flat bands in the ground states of these metals., Comment: 6 pages, 2 figures

We address the intervention of classical-like behavior, well documented in experimental studies of strongly correlated electron systems of solids that emerges at temperatures $T$ far below the Debye temperature $T_D$. We attribute this unexpected phenomenon to spontaneous rearrangement of the conventional Landau state beyond a critical point at which the topological stability of this state breaks down, leading to the formation of an interaction-induced flat band adjacent to the nominal Fermi surface. We demonstrate that beyond the critical point, the quasiparticle picture of such correlated Fermi systems still holds, since the damping of single-particle excitations remains small compared with the Fermi energy $T_F=p^2_F/2m_e$. A Pitaevskii-style equation for determination of the rearranged quasiparticle momentum distribution $n_*({\bf p})$ is derived, which applies to explanation of the linear-in-$T$ behavior of the resistivity $\rho(T)$ found experimentally., Comment: 5 pages, 3 figures, Supplemental Material

Landau's theory of the Fermi liquid is adapted to analyze the impact of electron-electron ($e-e$) interactions on the deficit of the superfluid density $\rho_{s0}=\rho_s(T=0)$ in dirty superconducting electron systems in which the damping $\gamma$ of single-particle excitations exceeds the zero temperature BCS gap $\Delta_0$. In the dirty strong-coupling limit $\gamma/\Delta_0\gg 1,m^*/m_e\gg 1$, the formula derived for $\rho_{s0}$ is shown to coincide with the well-known empirical Uemura relation provided pair-breaking contributions are nonexistent. The roles of the crystal lattice and magnetic pair-breaking effects in the observed decline of the zero-temperature superfluid density $\rho_{s0}$ in overdoped LSCO compounds are also discussed. Our method is also applied to elucidation of results from the pioneering experimental studies performed recently by Bozovi\`c and collaborators in overdoped LSCO compounds., Comment: 9 pages, 1 figure

The structure of the joint phase diagram demonstrating high-$T_c$ superconductivity of copper oxides is studied on the basis of the theory of interaction-induced flat bands. Prerequisites of an associated topological rearrangement of the Landau state are established, and related non-Fermi-liquid (NFL) behavior of the normal states of cuprates is investigated. We focus on manifestations of this behavior in the electrical resistivity $\rho(T)$, especially the observed gradual crossover from normal-state $T$-linear behavior $\rho(T,x)=A_1(x)T$ at doping $x$ below the critical value $x_c^h$ for termination of superconductivity, to $T$-quadratic behavior at $x>x_c^h$, which is incompatible with predictions of the conventional quantum-critical-point scenario. It is demonstrated that at $x

Superconducting electron systems of solids hosting flat bands are studied, with a view to improved understanding of the fundamental physics giving rise to high-temperature superconductivity. We present a modified form of the set of Gor'kov equations of BCS theory that incorporates a Mott-like gap in the single-particle spectrum. Such a quantity is emergent in systems with flat bands having interactions repulsive in the Cooper channel, provided particle-hole symmetry is broken. The equations so obtained are applied to the elucidation of features of the two-gap structure of single-particle spectra of underdoped high-$T_c$ superconductors, as revealed in angle-resolved photoemission spectrometry., Comment: The paper has been withdrawn by the author due to a crucial error in Equation 7

Informative recent measurements on the heavy-fermion metal $\rm \beta-YbAlB_4$ performed with applied magnetic field and pressure as control parameters are analyzed with the goal of establishing a sound theoretical explanation for the inferred scaling laws and non-Fermi-liquid (NFL) behavior, which demonstrate some unexpected features. Most notably, the robustness of the NFL behavior of the thermodynamic properties and of the anomalous $T^{3/2}$ temperature dependence of the electrical resistivity under applied pressure $P$ in zero magnetic field $B$ is at variance with the fragility of the NFL phase under application of a field. We show that a consistent topological basis for this combination of observations, as well as the empirical scaling laws, may be found within fermion-condensation theory in the emergence and destruction of a flat band, and explain that the paramagnetic NFL phase takes place without magnetic criticality, thus not from quantum critical fluctuations. Schematic $T-B$ and $T-P$ phase diagrams are presented to illuminate this scenario., Comment: 6 pages, 6 figures, added references

We introduce and analyze two different scenarios for violation of the Wiedemann-Franz law in strongly correlated electron systems of solids, close to a topological quantum critical point (TQCP) where the density of states $N(0)$ diverges. The first, applicable to the Fermi-liquid (FL) side of the TQCP, involves a transverse zero-sound collective mode that opens a new channel for the thermal conductivity, thereby enhancing the Lorenz number $L(0)$ relative to the value $L_0=\pi^2k^2_B/3e^2$ dictated by conventional FL theory. The second mechanism for violation of the WF law, relevant to the non-Fermi-liquid (NFL) side of the TQCP, involves the formation of a flat band and leads instead to a reduction of the Lorenz number., Comment: 7 pages, 1 figure

We show that the disappearance of the chemical potential jumps over the range of perpendicular magnetic fields at fixed integer filling factor in a double quantum well with a tunnel barrier is caused by the interaction-induced level merging. The distribution function in the merging regime is special in that the probability to find an electron with energy equal to the chemical potential is different for the two merged levels.

The phenomenon of flat bands pinned to the Fermi surface is analyzed on the basis of the Landau-Pitaevskii relation, which is applicable to electron systems of solids. It is shown that the gross properties of normal states of high-$T_c$ superconductors, frequently called strange metals, are adequately explained within the flat-band scenario. Most notably, we demonstrate that in electron systems moving in a two-dimensional Brillouin zone, superconductivity may exist in domains of the Lifshitz phase diagram lying far from lines of critical antiferromagnetic fluctuations, even if the effective electron-electron interaction in the Cooper channel is repulsive., Comment: 6 pages, 2 figures. arXiv admin note: text overlap with arXiv:1502.05659

The authors of a recent paper evidently take the view that the whole of progress made toward a theoretical understanding of the physics of quantum spin liquids (QSL) is associated with models of the kind proposed and applied in their present work. As motivation for this work, they observe that in contrast to existing theoretical models of both gapped and gapless spin liquids, which give rise to sharp dispersive features in the dynamic structure factor, the measured dynamic structure factor reveals an excitation continuum that is remarkably flat as a function of frequency. They go on to assert that "so far, the only theoretical model for a spin liquid state on the kagome lattice which naturally gives rise to a flat excitation band at low energies consists of the $Z_2$ spin liquids". Here we point out that there already exists a different and demonstrably successful approach to the QSL problem that does naturally feature a flat band., Comment: 2 pages

We show that the merging of the spin- and valley-split Landau levels at the chemical potential is an intrinsic property of a strongly-interacting two-dimensional electron system in silicon. Evidence for the level merging is given by available experimental data.

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the $nn$ pairing interaction is provided by a realistic bare $nn$ potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density where the pairing constant $\lambda$, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where $\lambda$ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei., Comment: The paper is dedicated to S.T.Belyaev on the occasion of his 90th birthday

Understanding the nature of field-tuned metamagnetic quantum criticality in the ruthenate Sr3Ru2O7 has presented a significant challenge within condensed matter physics. It is known from experiments that the entropy within the ordered phase forms a peak, and is unexpectedly higher than that outside, while the magnetoresistivity experiences steep jumps near the ordered phase. We find a challenging connection between Sr3Ru2O7 and heavy-fermion metals expressing universal physics that transcends microscopic details. Our construction of the T-B phase diagram of Sr3Ru2O7 permits us to explain main features of the experimental one, and unambiguously implies an interpretation of its extraordinary low-temperature thermodynamic in terms of fermion condensation quantum phase transition leading to the formation of a flat band at the restricted range of magnetic fields B. We show that it is the flat band that generates both the entropy peak and the resistivity jumps at the QCPs., Comment: 8 pages, 4 figures, revised following comments from colleagues, typos corrected, some references and comments added

We study different scenarios of topological phase transitions in the vicinity of the \pi^0 condensation point in neutron matter. The transitions occur between the Fermi-liquid state and a topologically different one with two sheets of the Fermi surface. Two possibilities of a rearrangement of quasiparticle degrees of freedom are shown: the first-order topological phase transition and the second-order one. The order of the phase transition is found to be strongly dependent on the value of the critical wave vector of the soft \pi^0 mode. The thermodynamics of the system is also studied. It is shown that the topology of the quasiparticle momentum distribution is mainly determined by the neutron matter density, while the temperature T is essential in a narrow density region. A simple explanation of the first-order topological phase transition at T=0 is given., Comment: 8 pages, 11 figures. The English of the text was revised; 2 references were added; minor changes in figures were made; all results remained unchanged

Physicists are engaged in vigorous debate on the nature of the quantum critical points (QCP) governing the low-temperature properties of heavy-fermion (HF) metals. Recent experimental observations of the much-studied compound YbRh2Si2 in the regime of vanishing temperature incisively probe the nature of its magnetic-field-tuned QCP. The jumps revealed both in the residual resistivity rho_0 and the Hall resistivity R_H, along with violation of the Wiedemann-Franz law, provide vital clues to the origin of such non-Fermi-liquid behavior. The empirical facts point unambiguously to association of the observed QCP with a fermion-condensation phase transition. Based on this insight, the resistivities rho_0 and R_H are predicted to show jumps at the crossing of the QCP produced by application of a magnetic field, with attendant violation of the Wiedemann-Franz law. It is further demonstrated that experimentally identifiable multiple energy scales are related to the scaling behavior of the effective mass of the quasiparticles responsible for the low-temperature properties of such HF metals., Comment: 7 pages, 4 figures, revised and accepted by JETP Lett

Renewed interest in 3He physics has been stimulated by experimental observation of non-Fermi-liquid behavior of dense 3He films at low temperatures. Abnormal behavior of the specific heat C(T) of two-dimensional liquid 3He is demonstrated in the occurrence of a T-independent term in C(T). To uncover the origin of this phenomenon, we have considered the group velocity of transverse zero sound propagating in a strongly correlated Fermi liquid. For the first time, it is shown that if two-dimensional liquid 3He is located in the vicinity of the quantum critical point associated with a divergent quasiparticle effective mass, the group velocity depends strongly on temperature and vanishes as T is lowered toward zero. The predicted vigorous dependence of the group velocity can be detected in experimental measurements on liquid 3He films. We have demonstrated that the contribution to the specific heat coming from the boson part of the free energy due to the transverse zero-sound mode follows the Dulong-Petit Law. In the case of two-dimensional liquid 3He, the specific heat becomes independent of temperature at some characteristic temperature of a few mK., Comment: 5 pages, 1 figure

Comment on Zeeman-Driven Lifshitz Transition: A Model for the Experimentally Observed Fermi-Surface Reconstruction in YbRh2Si2 by A. Hackl and M. Vojta, Phys. Rev. Lett. 106, 137002 (2011)., Comment: 1 page

An explanation of paradoxical behavior of the residual resistivity rho_0 of the heavy-fermion metal CeCoIn5 in magnetic fields and under pressure is developed. The source of this behavior is identified as a flattening of the single-particle spectrum, which exerts profound effects on the specific heat, thermal expansion coefficient, and magnetic susceptibility in the normal state, the specific heat jump at the point of superconducting phase transition, and other properties of strongly correlated electron systems in solids. It is shown that application of a magnetic field or pressure to a system possessing a flat band leads to a strong suppression of rho_0. Analysis of its measured thermodynamic and transport properties yields direct evidence for the presence of a flat band in CeCoIn5., Comment: 5 pages, 3 figures, references added, minor corrections made

A system of interacting, identical fermions described by standard Landau Fermi-liquid (FL) theory can experience a rearrangement of its Fermi surface if the correlations grow sufficiently strong, as occurs at a quantum critical point where the effective mass diverges. As yet, this phenomenon defies full understanding, but salient aspects of the non-Fermi-liquid (NFL) behavior observed beyond the quantum critical point are still accessible within the general framework of the Landau quasiparticle picture. Self-consistent solutions of the coupled Landau equations for the quasiparticle momentum distribution $n(p)$ and quasiparticle energy spectrum $\epsilon(p)$ are shown to exist in two distinct classes, depending on coupling strength and on whether the quasiparticle interaction is regular or singular at zero momentum transfer. One class of solutions maintains the idempotency condition $n^2(p)=n(p)$ of standard FL theory at zero temperature $T$ while adding pockets to the Fermi surface. The other solutions are characterized by a swelling of the Fermi surface and a flattening of the spectrum $\epsilon(p)$ over a range of momenta in which the quasiparticle occupancies lie between 0 and 1 even at T=0. The latter, non-idempotent solution is revealed by analysis of a Poincar\'e mapping associated with the fundamental Landau equation connecting $n(p)$ and $\epsilon(p)$ and validated by solution of a variational condition that yields the symmetry-preserving ground state. Paradoxically, this extraordinary solution carries the burden of a large temperature-dependent excess entropy down to very low temperatures, threatening violation of the Nernst Theorem. It is argued that certain low-temperature phase transitions offer effective mechanisms for shedding the entropy excess. Available measurements in heavy-fermion compounds provide concrete support for such a scenario., Comment: 34 pages, 6 figures

A quasiparticle pattern advanced in Landau's first article on Fermi liquid theory is adapted to elucidate the properties of a class of strongly correlated Fermi systems characterized by a Lifshitz phase diagram featuring a quantum critical point (QCP) where the density of states diverges. The necessary condition for stability of the Landau Fermi Liquid state is shown to break down in such systems, triggering a cascade of topological phase transitions that lead, without symmetry violation, to states with multi-connected Fermi surfaces. The end point of this evolution is found to be an exceptional state whose spectrum of single-particle excitations exhibits a completely flat portion at zero temperature. Analysis of the evolution of the temperature dependence of the single-particle spectrum yields results that provide a natural explanation of classical behavior of this class of Fermi systems in the QCP region., Comment: 26 pages, 14 figures. Dedicated to 100th anniversary of A.B.Migdal birthday

A quantum phase transition in strongly correlated Fermi systems beyond the topological quantum critical point is studied within the Fermi liquid approach. The transition occurs between two topologically equivalent states, each with three sheets of the Fermi surface. One of these states possesses a quasiparticle halo in the quasiparticle momentum distribution $n(p)$, while the other, the hole pocket. The transition is found to be of the first order with respect to both the coupling constant $g$ and the temperature $T$. The phase diagram of the system in the vicinity of this transition is constructed., Comment: 6 pages, 7 figures

We study the temperature evolution of the single-particle spectrum $\epsilon(p)$ and quasiparticle momentum distribution $n(p)$ of homogeneous strongly correlated Fermi systems beyond a point where the necessary condition for stability of the Landau state is violated, and the Fermi surface becomes multi-connected by virtue of a topological crossover. Attention is focused on the different non-Fermi-liquid temperature regimes experienced by a phase exhibiting a single additional hole pocket compared with the conventional Landau state. A critical experiment is proposed to elucidate the origin of NFL behavior in dense films of liquid $^3$He., Comment: 7 pages, 6 figures

A semi-microscopic model for nucleon pairing in nuclei is presented starting from the ab intio BCS gap equation with Argonne v18 force and the self-consistent Energy Density Functional Method basis characterized with the bare nucleon mass. The BCS theory is formulated in terms of the model space S0 with the effective pairing interaction calculated from the first principles in the subsidiary space S0. This effective interaction is supplemented with a small phenomenological addendum containing one phenomenological parameter universal for all medium and heavy atomic nuclei. We consider the latter as a phenomenological way to take into account both the many-body corrections to the BCS theory and the effective mass effects. For protons, the Coulomb interaction is introduced directly. Calculations made for several isotopic and isotonic chains of semi-magic nuclei confirm the validity of the model. The role of the self-consistent basis is stressed., Comment: 22 pages, 9 figures, 3 tables

The low-temperature kinetics of the strongly correlated electron liquid inhabiting a solid is analyzed. It is demonstrated that a softly damped branch of transverse zero sound emerges when several bands cross the Fermi surface simultaneously near a quantum critical point at which the density of states diverges. Suppression of the damping of this branch occurs due to a mechanism analogous to that affecting the phonon mode in solids at room temperature, giving rise to a classical regime of transport at extremely low temperatures in the strongly correlated Fermi system., Comment: 4 pages

A brief review of recent microscopic calculations of nuclear pairing gap is given. A semi-microscopic model is suggested in which the ab-initio effective pairing interaction is supplemented with a small phenomenological addendum. It involves a parameter which is universal for all medium and heavy nuclei. Calculations for several isotopic and isotonic chains of semi-magic nuclei confirm the relevance of the model., Comment: 16 pages, 6 figs

The Fermi liquid approach is applied to the problem of spontaneous violation of the four-fold rotational point-group symmetry ($C_4$) in strongly correlated two-dimensional electronic systems on a square lattice. The symmetry breaking is traced to the existence of a topological phase transition. This continuous transition is triggered when the Fermi line, driven by the quasiparticle interactions, reaches the van Hove saddle points, where the group velocity vanishes and the density of states becomes singular. An unconventional Fermi liquid emerges beyond the implicated quantum critical point., Comment: 6 pages, 4 figures

Motivated by recent observations of $C_4$ symmetry breaking in strongly correlated two-dimensional electron systems on a square lattice, we analyze this phenomenon within an extended Fermi liquid approach. It is found that the symmetry violation is triggered by a continuous topological phase transition associated with exchange of antiferromagnetic fluctuations. In contrast to predictions of mean-field theory, the structure of a part of the single-particle spectrum violating $C_4$ symmetry is found to be highly anisotropic, with a peak located in the vicinity of saddle points., Comment: 7 pages, 3 figures; extended version, added figure

Competing scenarios for quantum critical points (QCPs) of strongly interacting Fermi systems signaled by a divergent density of states at zero temperature are contrasted. The conventional scenario, which enlists critical fluctuations of a collective mode and attributes the divergence to a coincident vanishing of the quasiparticle strength $z$, is shown to be incompatible with identities arising from conservation laws prevailing in the fermionic medium. An alternative scenario, in which the topology of the Fermi surface is altered at the QCP, is found to explain the non-Fermi-liquid thermodynamic behavior observed experimentally in Yb-based compounds close to the QCP. It is suggested that combination of the topological scenario with the theory of quantum phase transitions will provide a proper foundation for analysis of the extended QCP region., Comment: 4 pages, minor changes

Spatial correlation characteristics of the anomalous density matrix $\kappa$ in a slab of nuclear matter with the Paris and Argonne v18 forces are calculated. A detailed comparison with predictions of the effective Gogny force is made. It is found that the two realistic forces lead to very close results which are qualitatively similar to those for the Gogny force. At the same time, the magnitude of $\kappa$ for realistic forces is essentially smaller than the one for the Gogny force. The correlation characteristics are practically independent of the magnitude of $\kappa$ and turn out to be quite close for the three kinds of the force. In particular, all of them predict a small value of the local correlation length at the surface of the slab and a big one, inside. These results are in agreement with those obtained recently by Pillet at al. for finite nuclei with the Gogny force., Comment: 19 pages, 13 figures

We examine the nature of phase transitions occurring in strongly correlated Fermi systems at the quantum critical point (QCP) associated with a divergent effective mass. Conventional scenarios for the QCP involving collective degrees of freedom are shown to have serious shortcomings. Working within the original Landau quasiparticle picture, we propose an alternative topological scenario for the QCP, in systems that obey standard Fermi liquid (FL) theory in advance of the QCP. Applying the technique of Poincar\'e mapping, we analyze the sequence of iterative maps generated by the Landau equation for the single-particle spectrum at zero temperature. It is demonstrated that the Fermi surface is subject to rearrangement beyond the QCP. If the sequence of maps converges, a multi-connected Fermi surface is formed. If it fails to converge, the Fermi surface swells into a volume that provides a measure of entropy associated with formation of an exceptional state of the system characterized by partial occupation of single-particle states and dispersion of their spectrum proportional to temperature. Based on this dual scenario, the thermodynamics of Fermi systems beyond the QCP exhibits striking departures from the predictions of standard FL theory. Mechanisms for the release of the entropy excess of the exceptional state are discussed., Comment: 20 pages, 11 figures

Ab initio gap equation for ^1S_0 pairing in a nuclear slab is solved for the Argonne v18 NN-potential. The gap function is compared in detail with the one found previously for the separable form of the Paris potential. The difference between the two gaps turned out to be about 10%. Dependence of the gap on the chemical potential mu is analyzed., Comment: 20 pages, 8 figures

The renormalization of the Wiedemann-Franz (WF) ratio in strongly correlated electron systems is analyzed within the Landau quasiparticle picture. We demonstrate that the WF law is violated: (i) at the quantum critical point, where the effective mass diverges, and (ii) beyond a point of fermion condensation, where the single-particle spectrum $\epsilon(p)$ becomes flat. Results of the analysis are compared with available experimental data., Comment: 6 pages, 5 figures, added references

Non-Fermi liquid behavior of strongly correlated Fermi systems is derived within the Landau approach. We attribute this behavior to a phase transition associated with a rearrangement of the Landau state that leads to flattening of a portion of the single-particle spectrum $\epsilon({\bf p})$ in the vicinity of the Fermi surface. We demonstrate that the quasiparticle subsystem responsible for the flat spectrum possesses the same thermodynamic properties as a gas of localized spins. Theoretical results compare favorably with available experimental data. While departing radically from prevalent views on the origin of non-Fermi-liquid behavior, the theory advanced here is nevertheless a conservative one of in continuing to operate within the general framework of Landau theory., Comment: 8 pages, 4 figures, corrected list of authors

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., Comment: 11 pages, 11 figures

We examine the problem of finite Fermi systems having a degenerate single-particle spectrum and show that the Landau approach, applied to such a system, admits the possibility of merging single-particle levels. It is demonstrated that the opportunity for this behavior is widespread in quantum many-body systems. The salient feature of the phenomenon is the occurrence of nonintegral quasiparticle occupation numbers, leading to a radical alteration of the standard quasiparticle picture. Implications of this alteration are considered for nuclear, atomic, and solid-state systems., Comment: 5 pages, 1 figure

Properties of the distribution of single-particle levels adjacent to the Fermi surface in finite Fermi systems are studied, focusing on the case in which these levels are degenerate. The interaction of the quasiparticles occupying these levels lifts the degeneracy and affects the distance between the closest levels on opposite sides of the Fermi surface, as the number of particles in the system is varied. In addition to the familiar scenario of level crossing, a new phenomenon is uncovered, in which the merging of single-particle levels results in the disappearance of well-defined single-particle excitations. Implications of this finding are discussed for nuclear, solid-state, and atomic systems., Comment: 4 pages, 2 figures

Departures of thermodynamic properties of three-dimensional superfluid $^3$He from the predictions of BCS theory are analyzed. Attention is focused on deviations of the ratios $\Delta(T=0)/T_c$ and $[C_s(T_c)-C_n(T_c)]/C_n(T_c)$ from their BCS values, where $\Delta(T=0)$ is the pairing gap at zero temperature, $T_c$ is the critical temperature, and $C_s$ and $C_n$ are the superfluid and normal specific heats. We attribute these deviations to the momentum dependence of the gap function $\Delta(p)$, which becomes well pronounced when this function has a pair of nodes lying on either side of the Fermi surface. We demonstrate that such a situation arises if the P-wave pairing interaction $V(p_1,p_2)$, evaluated at the Fermi surface, has a sign opposite to that anticipated in BCS theory. Taking account of the momentum structure of the gap function, we derive a closed relation between the two ratios that contains no adjustable parameters and agrees with the experimental data. Some important features of the effective pairing interaction are inferred from the analysis., Comment: 17 pages, 4 figures

The gap equation in the $^1S_0$-channel is solved for a nuclear slab with the separable form of the Paris potential. The gap equation is considered in the model space in terms of the effective pairing interaction which is found in the complementary subspace. The absolute value of the gap $\Delta$ turned out to be very sensitive to the cutoff $K_{max}$ in the momentum space in the equation for the effective interaction. It is necessary to take $K_{max}=160-180 fm^{-1}$ to guarantee 1% accuracy for $\Delta$. The gap equation itself is solved directly, without any additional approximations. The solution reveals the surface enhancement of the gap $\Delta$ which was earlier found with an approximate consideration. A strong surface-volume interplay was found also implying a kind of the proximity effect. The diagonal matrix elements of $\Delta$ turned out to be rather close to the empirical values for heavy atomic nuclei., Comment: 17 pages, 12 figures

Low-temperature thermodynamic properties of strongly interacting Fermi liquids with fermion condensate are investigated. We demonstrate that the spin susceptibility of these systems exhibits the Curie-Weiss law, and the entropy contains a temperature-independent term. The excessive entropy is released at the superconducting transition, enhancing the specific heat jump Delta C and rendering it proportional to the effective Curie constant. The theoretical results are favorably compared with the experimental data on the heavy fermion metal CeCoIn5, as well as He-3 films., Comment: 4 pages, 2 figures. V.2: a reference added; minor changes as in the published version

The behavior of strongly correlated Fermi systems is investigated beyond the onset of a phase transition where the single-particle spectrum $\xi({\bf p})$ becomes flat. The Landau-Migdal quasiparticle picture is shown to remain applicable on the ordered side of this transition. Nevertheless, low-temperature properties evaluated within this picture show profound changes relative to results of Landau theory, as a direct consequence of the flattening of $\xi({\bf p})$. Stability conditions for this class of systems are examined, and the nature of antiferromagnetic quantum phase transitions is elucidated., Comment: 5 pages, 5 figures

The damping of single-particle degrees of freedom in strongly correlated two-dimensional Fermi systems is analyzed. Suppression of the scattering amplitude due to the damping effects is shown to play a key role in preserving the validity of the Landau-Migdal quasiparticle picture in a region of a phase transition, associated with the divergence of the quasiparticle effective mass. The results of the analysis are applied to elucidate the behavior of the conductivity $\sigma(T)$ of the two-dimensional dilute electron gas in the density region where it undergoes a metal-insulator transition., Comment: 7 pages, 6 figures. Improved and slightly extended version: new paragraph about Hall effect + new Fig.6

Thermodynamic characteristics of Fermi systems are investigated in the vicinity of a phase transition where the effective mass diverges and the single-particle spectrum becomes flat. It is demonstrated that at extremely low temperatures $T$, the flattening of the spectrum is reflected in non-Fermi-liquid behavior of the inverse susceptibility $\chi^{-1}(T) \sim T^{\alpha}$ and the specific heat $C(T)/T\sim T^{-\alpha}$, with the critical index $\alpha=2/3$. In the presence of an external static magnetic field $H$, both these quantities are found to exhibit a scaling behavior, e.g. $\chi^{-1}(T,H)=\chi^{-1}(T,0)+ T^{2/3}F(H/T)$, in agreement with available experimental data., Comment: 4 pages, 2 figures

The spin susceptibility $\chi(T)$ of strongly correlated Fermi systems is investigated in the density region where Fermi-liquid theory fails. We attribute this failure to a specific quantum phase transition associated with a rearrangement of the Landau state at low temperatures $T$, retaining the assumption that the Landau quasiparticle picture survives in a generic sense. Taking into account the resulting modification of the quasiparticle istribution function, the spin susceptibility $\chi(T)$ is shown to contain a Curie-Weiss component $\chi_{\rm CW}(T)\sim (T-\Theta_{\rm W})^{-1}$, with the Weiss temperature $\Theta_{\rm W}$ vanishing at the critical density for the transition., Comment: 4 pages, 3 figures

A new scenario for neutron-star cooling is proposed, based on the correspondence between pion condensation, occurring in neutron matter due to critical spin-isospin fluctuations, and the metal-insulator phase transition in a two-dimensional electron gas. Beyond the threshold density for pion condensation, where neutron-star matter loses its spatial homogeneity, the neutron single-particle spectrum acquires an insulating gap that quenches neutron contributions to neutrino-production reactions and to the star's specific heat. In the liquid phase at densities below the transition point, spin-isospin fluctuations are found to play dual roles. On the one hand, they lead to a multi-sheeted neutron Fermi surface that extends to low momenta, thereby activating the normally forbidden direct-Urca cooling mechanism; on the other, they amplify the nodeless $P$-wave neutron superfluid gap while suppressing $S$-wave pairing. In this picture, lighter stars without a pion-condensed core experience slow cooling, while enhanced cooling occurs in heavier stars through direct-Urca emission from a narrow shell of the interior., Comment: 4 pages, 2 figures. Revised version. Accepted for publication in Phys.Rev.Lett

The rearrangement of the Fermi surface of a homogeneous Fermi system upon approach to a second-order phase transition is studied at zero temperature. The analysis begins with an investigation of solutions of the equation $\epsilon(p)=\mu$, a condition that ordinarily has the Fermi momentum $p_F$ as a single root. The emergence of a bifurcation point in this equation is found to trigger a qualitative alteration of the Landau state, well before the collapse of the collective degree of freedom that is responsible for the second-order transition. The competition between mechanisms that drive rearrangement of the Landau quasiparticle distribution is explored, taking into account the feedback of the rearrangement on the spectrum of critical fluctuations. It is demonstrated that the transformation of the Landau state to a new ground state may be viewed as a first-order phase transition., Comment: 16 pages, 10 figures

The impact of long-range spin-spin correlations on the structure of a flat portion in single-particle spectra $\xi(p)$, which emerges beyond the point, where the Landau state loses its stability, is studied. We supplement the well-known Nozieres model of a Fermi system with limited scalar long-range forces by a similar long-range spin-dependent term and calculate the spectra versus its strength $g$. It is found that Nozieres results hold as long as $g>0$. However, with $g$ changing its sign, the spontaneous magnetization is shown to arise at any nonzero $g$. The increase of the strength $|g|$ is demonstrated to result in shrinkage of the domain in momentum space, occupied by the flat portion of $\xi(p)$, and, eventually, in its vanishing., Comment: 7 pages, 15 figures