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Physical Review Letters

Phase transition in dissipative Fermi systems

J. M. Wheatley

Published Sep 2, 1991• 8 citations
Publisher

Abstract

A dissipative Fermi system is defined and the low-temperature thermodynamics is examined. Below a critical density the system behaves as a Boltzmann gas with Curie behavior of the susceptibility. Above the critical density, conventional Fermi behavior reappears, with Pauli behavior of the susceptibility. The diamagnetic susceptibility is smooth through the transition region which thus represents a type of metal-to-metal transition. In contrast, a dissipative ideal Bose system is Boltzmann-like for any density at low temperature.

DOI
10.1103/physrevlett.67.1181

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A dissipative Fermi system is defined and the low-temperature thermodynamics is examined. Below a critical density the system behaves as a Boltzmann gas with Curie behavior of the susceptibility. Above the critical density, conventional Fermi behavior reappears, with Pauli behavior of the susceptibility. The diamagnetic susceptibility is smooth through the transition region which thus represents a type of metal-to-metal transition. In contrast, a dissipative ideal Bose system is Boltzmann-like for any density at low temperature.
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The spin susceptibility χ(T)χ(T)χ(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 TTT, 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 χ(T)χ(T)χ(T) is shown to contain a Curie-Weiss component χCW(T)∼(T−ΘW)−1χ_{\rm CW}(T)\sim (T-Θ_{\rm W})^{-1}χCW​(T)∼(T−ΘW​)−1, with the Weiss temperature ΘWΘ_{\rm W}ΘW​ vanishing at the critical density for the transition.
We study an exactly-solvable model which shows a zero-temperature transition from a non-Fermi liquid to a Fermi liquid as a function of particle density. The quantum critical point separating these two states is not associated with the usual ordering transition of a bosonic degree of freedom. We analyze the properties of this critical point in terms of an effective density of states, and we use this concept to generalize this transition to a class of related quantum critical points. We study the superconducting instability of the low-density (non-Fermi liquid) regime and we show that it has an enhanced pair susceptibility relative to the Fermi liquid. We comment on the applicability of our results to low-carrier density superconductors.
Introduction In this chapter we study metal–insulator transitions which occur due to correlations between the charge carriers. This quantum phase transitions results from the competition between kinetic energy and Coulomb repulsion where the latter has the tendency to localise the electrons. The simplest model which describes this competition is the one-band Hubbard model with its two energy scales, the bandwidth W and the Coulomb repulsion U between electrons of opposite spins on the same site. For a fixed density of electrons, n = 1; as the ratio U/W increases, we expect to find a zero-temperature phase transition from a metallic state to an insulator where the electrons are frozen at the lattice sites. The method employed here to investigate this transition is the Gutzwiller approach (Gutzwiller, 1965). This is a variational method which played an important role in providing a framework for the ideas of Mott on the problem of the metal–insulator transition (Mott, 1974). On the metallic side of the transition, this approach describes a metal with renormalised Fermi liquid parameters, essentially with enhanced effective mass and uniform susceptibility. This is the so-called highly correlated electron gas (Brinkman and Rice, 1970) for which the metal oxide V 2 O 3 is the prototype system. In the insulating side, Gutzwiller's approximation yields a noninteracting system of localised electrons. This insulating phase is incompressible , i.e. has zero compressibility and infinite zero temperature susceptibility. The latter is not a consequence of interactions but simply due to the divergence of the Curie susceptibility, χ ∝ 1 /T , of non-interacting moments at T = 0. Then, in Gutzwiller's approach the transition is from a paramagnetic metal to a paramagnetic insulator. We will continue using the designation Mott transition to describe this type of phase transition where the insulating phase has no long-range magnetic order. In real systems, most frequently, localisation due to interactions is accompanied by the appearance of antiferromagnetic order.
The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study the quantum phase diagram, equation of state, and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behavior at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in a harmonic trap is also studied within the local-density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insight into understanding the universal features of many-body critical phenomena.