Strongly correlated Fermi systems as a new state of matter

TL;DR

This review introduces a new state of matter in strongly correlated Fermi systems, characterized by fermion condensation quantum phase transition (FCQPT), which explains the universal non-Fermi liquid behavior across various heavy-fermion systems.

Contribution

It presents the concept of FCQPT as a universal mechanism underlying the new state of matter in strongly correlated Fermi systems, supported by experimental data and scaling analysis.

Findings

FCQPT leads to flat bands and fermion condensates in HF systems.

Universal scaling behavior observed in thermodynamic and transport properties.

Fermion condensation explains non-Fermi liquid behavior across diverse materials.

Abstract

The aim of this review paper is to expose a new state of matter exhibited by strongly correlated Fermi systems represented by various heavy-fermion (HF) metals, two-dimensional liquids like $\rm ^3He$, compounds with quantum spin liquids, quasicrystals, and systems with one-dimensional quantum spin liquid. We name these various systems HF compounds, since they exhibit the behavior typical of HF metals. In HF compounds at zero temperature the unique phase transition, dubbed throughout as the fermion condensation quantum phase transition (FCQPT) can occur; this FCQPT creates flat bands which in turn lead to the specific state, known as the fermion condensate. Unlimited increase of the effective mass of quasiparticles signifies FCQPT; these quasiparticles determine the thermodynamic, transport and relaxation properties of HF compounds. Our discussion of numerous salient experimental data within the framework of FCQPT resolves the mystery of the new state of matter. Thus, FCQPT and the fermion condensation can be considered as the universal reason for the non-Fermi liquid behavior observed in various HF compounds. We show analytically and using arguments based completely on the experimental grounds that these systems exhibit universal scaling behavior of their thermodynamic, transport and relaxation properties. Therefore, the quantum physics of different HF compounds is universal, and emerges regardless of the microscopic structure of the compounds. This uniform behavior allows us to view it as the main characteristic of a new state of matter exhibited by HF compounds.