Quantum criticality in the two-dimensional Hubbard model

TL;DR

This study uses advanced numerical methods to analyze the two-dimensional Hubbard model, revealing a quantum phase transition at a critical doping that separates a pseudogap metal from a Fermi liquid, with implications for understanding cuprate superconductors.

Contribution

It provides the first direct evidence of a continuous quantum phase transition in the Hubbard model using real-frequency dynamics at zero temperature.

Findings

Identifies a critical doping $p^{ ext{*}}$ for the transition.

Shows collapse of Fermi-liquid scale at $p^{ ext{*}}$.

Describes the evolution of spectral weight and Fermi arcs across the transition.

Abstract

We study the normal-state, doping-driven phase diagram of the square-lattice Hubbard model using the dynamical cluster approximation combined with the numerical renormalization group as a cluster solver, which gives direct access to real-frequency dynamics at essentially zero temperature. In a parameter regime relevant for cuprates, $U=7t$ and $t'=-0.3t$, we find a critical doping $p^{\ast}$ that marks a continuous quantum phase transition between a pseudogap metal and a normal Fermi liquid. The transition is identified by a continuous collapse, from both sides, of the Fermi-liquid scale extracted from charge, spin, and $d_{x^2-y^2}$-wave pairing susceptibilities. This collapse produces a non-Fermi-liquid regime at intermediate energy scales, which appears to extend to arbitrarily low scales at $p^{\ast}$. As $p^{\ast}$ is crossed from the normal Fermi liquid at $p>p^{\ast}$ into the pseudogap metal at $p<p^{\ast}$, the coherent low-energy spectral weight in the antinodal region is lost and replaced by a narrow, metallic pseudogap, while the nodal region evolves smoothly and remains comparatively coherent. This gives rise to Fermi arcs in the pseudogap metal at $p<p^{\ast}$, since the zero-frequency spectral weight remains large in the nodal region but is strongly suppressed in the antinodal region.