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arXiv:2503.20347

Fixed points and critical temperature near quantum critical points in $d$-wave cuprate superconductors

Qi-Qi Yue, Yi-sheng Fu, Jing Wang

Published Mar 26, 2025• 0 citations
arXivHTMLPDF

Abstract

We study the critical behavior driven by potential quantum critical points (QCPs) termed as $τ_{0,x,y,z}$-Type QCPs in the $d$-wave cuprate superconductors. Within the framework of the renormalization group approach, we construct the coupled flow equations of all interaction parameters and obtain several unique properties. On one hand, the interaction parameters flow toward several fixed points (FPs) at certain critical energy scales. We identify two different types of FPs designated at the clean limit. FP-I is characterized by the divergence of the quadratic parameter and exhibits robustness against variations in interaction parameters. In contrast, FP-II is dominated by the cubic and quartic interaction parameters, and it is sensitive to initial conditions, leading to five subclasses. Besides, we find that disorder scattering can influence fermion velocities and critical energy scales, and even destabilize certain FPs around the $τ_{x,z}$-QCPs, driving the system toward a preempted disorder-induced FP. On the other hand, we find that quantum fluctuations play a critical role in shaping the critical temperature ($T_c$) as the system approaches these QCPs. Near the $τ_x$-QCP, $T_c$ is considerably suppressed for both FP-I and FP-II. In contrast, near the $τ_0$-QCP, $T_c$ undergoes a substantial decrease for FP-I but only a slight decrease for FP-II. Conversely, $T_c$ exhibits an increasing trend near the $τ_y$-QCP, with a pronounced peak at $v_{Δ0}/v_{F0} \sim 0.25$. However, numerical analysis suggests that the $τ_z$-QCP is unlikely to be physically realizable. Additionally, we realize that $T_c$ can also be modified by the emergence of disorder-induced FPs in the vicinity of the $τ_x$-QCP. These findings would provide valuable insights into the critical low-energy properties of $d$-wave cuprate superconductors and related materials.

DOI
10.48550/arxiv.2503.20347

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Abstract We present a T = 0 K renormalization group (RG) phase diagram for the hole-doped 2D Hubbard model on the square lattice. The RG method employed is nonperturbative in treating quantum fluctuations of the single-particle occupation number via the unitarily decoupling of one electronic state at every RG step. As a result, the RG phase diagram possesses the quantum fluctuation energy scale (ω) as one of its axes. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flows, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point (QCP) possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. The QCP is characterised using both thermodynamic and quantum information-theoretic measures. d-wave superconducting order is shown to arise from this quantum critical state of matter. The pseudogap phase possesses a variety of fluctuations that lead to several symmetry-broken phases at low-energies. Benchmarking of the ground state energy per particle and the double-occupancy fraction obtained from a finite-size scaling analysis against existing numerical results yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (T PG), onset temperature for pairing (T ons), formation of the Mott liquid (T ML) and superconductivity (T C) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.
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