Novel quantum criticality due to emergent topological conservation law in high-$T_c$ cuprates

TL;DR

This paper proposes a new type of quantum criticality in high-temperature cuprates, driven by topological conservation laws and collective instanton excitations, challenging traditional symmetry-breaking paradigms.

Contribution

It introduces a topological framework for understanding quantum criticality in strongly correlated electrons, emphasizing gauge flux stability and instanton effects near the Mott transition.

Findings

Identification of stable instanton excitations governed by gauge flux changes.

Discovery of a hidden quantum critical point related to topological charge conservation.

Explanation of divergent charge compressibility at zero temperature near Mott transition.

Abstract

We argue that in strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of $2\pi$. By unraveling consequences of the non-trivial topology of the charge gauge U(1) group, we found that the pinning of $\mu$ and the zero-temperature divergence of charge compressibility $\kappa\sim\partial n_e/\partial\mu$ defines novel "hidden" quantum criticality on verge of the Mott transition governed by the protectorate of stable topological numbers rather than Landau paradigm of the symmetry breaking.