The pseudogap and strange metal states in the square-lattice Hubbard model: a comprehensive study

TL;DR

This study addresses the origin and mutual relationship of the pseudogap and strange metal states in cuprates by solving the square-lattice Hubbard model with a ladder dual-fermion approach augmented by a self-energy correction. It shows that both states emerge when the Van Hove singularity is pinned near the Fermi level around a characteristic hole concentration $p_{MS}$, with the pseudogap arising from renormalized classical AFM fluctuations and the strange metal from extended quantum critical AFM fluctuations that produce $ ext{Im}\, ext{Sigma}_{k}(\, ext{ω})$ scaling and a $T$-linear resistivity. The strange metal phase features nearly complete AFM nesting on the Fermi surface and $ ext{ω}/T$ scaling in the dynamical spin susceptibility with overdamped spin waves at the Planckian limit, while the pseudogap region exhibits a reduced spectral weight near the X point and Fermi arcs. The results provide a unified framework linking ARPES, transport, and neutron-scattering observations, and highlight the pivotal role of VHS pinning and AFM fluctuations in stabilizing these non-Fermi-liquid states.

Abstract

To clarify the origin of the pseudogap and strange metal states as well as their mutual relationship in cuprate superconductors, a comprehensive study on the spectral function, Fermi surface, resistivity and dynamical spin susceptivity of the Hubbard model on the square lattice has been conducted by means of the ladder dual-fermion approximation with an electron self-energy correction. It is found that the appearance of these two states requires that the characteristic hole concentration below which the Mott-Heisenberg and Slater mechanisms of electron localization occurs $p_{\rm MS}$ nearly coincides with the hole concentration where the Van Hove singularity (VHS) point is placed at the vicinity of the Fermi level. When this condition is met the VHS point is pined at which the nesting condition of the antiferromagnetic (AFM) fluctuation is fulfilled almost everywhere on the Fermi surface in wide range of the hole concentration in a metallic state, i.e., the strange metal state. The spin fluctuation of the strange metal state is nearly quantum critical and the dynamical spin susceptivity is well described by overdamped spin wave having the $ω/T$ scaling with the relaxation rate at the Planckian limit. Because of these distinctive features of the strange metal state, the $k$ dependence of scattering rate of electrons is small and electrons behave as the marginal Fermi liquid, resulting in $T$-linear resistivity. In contrast, the pseudogap state is magnetically in the renormalized classical regime and the pseudogap is formed near the X point where the nesting condition of the short-range AFM order is fulfilled.

Figures (22)

• Figure 1: $p$-$T$ phase diagrams for $U=8$ with $t'=0$ (a), $t'=-0.2$ (b) and $t'=-0.3$ (c) and for $U=6$ with $t'=-0.2$ (d). In each panel the temperatures of pseudogap formation $T^{*}$, the VHS point at the Fermi level $T_{\rm VHS}$, transition to the $d$-wave superconductor $T_{\rm SC}$, commensurate to incommensurate crossover of AFM fluctuation $T_{\rm C-IC}$ and metal-insulator phase separation $T_{\rm PS}$ are presented. The positions of the end point of the pseudogap phase $p^*$ and the AFM QCP $p_{\rm QCP}$ are indicated by the arrows. In (c), the crossover temperature between the AFM and ferromagnetic fluctuation $T_{\rm AFM-FM}$ is also depicted and the hole concentration where $T_{\rm VHS}=0$$p_{\rm VHS}$ is indicated by the arrow.
• Figure 2: $D/n^2$ versus $n$ plots. The results of LDFA with (diamonds) and without (triangles) the self-energy correction for $U=4$, $t'=0$ and $\beta=4$ are shown. For comparison the DCA data reproduced from Ref. JPFLeBlanc2015 are also depicted as crosses.
• Figure 3: Chemical potential $\mu$ versus hole concentration $p$ curves for various temperatures for $U=6$ with $t'=0$.
• Figure 4: (a) $T_{\rm CPMI}$ (triangles) as functions of $U$; (b) $U$ dependence of $p_{\rm MS}$ (diamonds), $p_{\rm CPMI}$ (triangles) and $p_{\rm C-IC}$ (circles) and the metal-insulator phase separation region (hatched red aria) on $U$--$p$ plane together with the AFM quantum critical points $p_{\rm QCP}$ for $U=3$, 4, 5, 6, 7 and 8 (crosses).
• Figure 5: $p$ dependence of DOS for $U=8$ with $t'=0$ (a), $t'=-0.2$ (b) and $t'=-0.3$ (c).