Critical charge instability on verge of the Mott transition and the origin of quantum protection in high-$T_c$ cuprates

TL;DR

This paper develops a topological effective theory for high-Tc cuprates, linking quantum criticality, charge instability, and the Mott transition through topological invariants and instanton configurations, explaining the stability of the superconducting state.

Contribution

It introduces a topological framework using instanton events and gauge flux attachment to describe the quantum criticality and stability of high-Tc cuprates near the Mott transition.

Findings

Identification of a topological quantum critical point in cuprates.

Link between topological charge and electronic filling.

Explanation of the quantum protectorate in strongly correlated systems.

Abstract

The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-Tc cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time," labeled by topological winding numbers, are essential configurations of the phase field dual to the charge. In analogy to the usual phase transition that is characterized by a sudden change of the symmetry, the topological phase transitions are governed by a discontinuous change of the topological numbers signaled by the divergence of the zero-temperature topological susceptibility. This defines a quantum criticality ruled by topologically conserved numbers rather than the Landau principle of the symmetry breaking. We show that in the limit of strong correlations topological charge is linked to the average electronic filling number and the topological susceptibility to the electronic compressibility of the system. We exploit the impact of these nontrivial U(1) instanton phase field configurations for the cuprate phase diagram which displays the "hidden" quantum critical point covered by the superconducting lobe in addition to a sharp crossover between a compressible normal "strange metal" state and a region characterized by a vanishing compressibility, which marks the Mott insulator. Finally, we argue that the existence of robust quantum numbers explains the stability against small perturbation of the system and attributes to the topological "quantum protectorate" as observed in strongly correlated systems.