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arXiv:2404.06532 · Physical review. B./Physical review. B

Solvable models of two-level systems coupled to itinerant electrons: Robust non-Fermi liquid and quantum critical pairing

Evyatar Tulipman, Noga Bashan, Jörg Schmalian, Erez Berg

Published Oct 9, 2024• 15 citations
arXivHTMLPDF

Abstract

Strange metal behavior is traditionally associated with an underlying putative quantum critical point at zero temperature. However, in many correlated metals, e.g., high-${T}_{c}$ cuprate superconductors, strange metallicity persists at low temperatures over an extended range of microscopic parameters, suggesting the existence of an underlying quantum critical phase, whose possible physical origins remain poorly understood. Systematic investigations of physical scenarios giving rise to such a critical, non-Fermi liquid (NFL) phase are therefore crucial to better understand this puzzling behavior. In a previous study [Bashan et al., Phys. Rev. Lett. 132, 236501 (2024)], we considered a solvable large-$N$ model consisting of itinerant electrons coupled to local two-level systems (TLSs) via spatially random interactions, inspired by the possibility of emergent metallic glassiness due to frustrated competing orders, and found that the system hosts an NFL phase with tunable exponents at intermediate couplings. In this paper, we expand our investigation to the following: (i) We study the extent to which this NFL phase is generic by considering various deformations of our theory, including coupling of electrons to multiple operators of the TLSs and arbitrarily directed TLS fields. We find that the physical picture obtained in Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)] qualitatively persist in a wide region of parameter space, showcasing the robustness of the NFL phase. (ii) We analyze the superconducting instability caused by the coupling of TLSs to electrons, and find a rich structure, including quantum critical pairing associated with the NFL phase and conventional BCS-like pairing in the weak and strong coupling limits. (iii) We elaborate on the analysis of Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)], including single-particle, transport, and thermodynamic properties.

DOI
10.1103/physrevb.110.155118

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Strange metal behavior is traditionally associated with an underlying putative quantum critical point at zero temperature. However, in many correlated metals, e.g., high-Tc{T}_{c}Tc​ cuprate superconductors, strange metallicity persists at low temperatures over an extended range of microscopic parameters, suggesting the existence of an underlying quantum critical phase, whose possible physical origins remain poorly understood. Systematic investigations of physical scenarios giving rise to such a critical, non-Fermi liquid (NFL) phase are therefore crucial to better understand this puzzling behavior. In a previous study [Bashan et al., Phys. Rev. Lett. 132, 236501 (2024)], we considered a solvable large-NNN model consisting of itinerant electrons coupled to local two-level systems (TLSs) via spatially random interactions, inspired by the possibility of emergent metallic glassiness due to frustrated competing orders, and found that the system hosts an NFL phase with tunable exponents at intermediate couplings. In this paper, we expand our investigation to the following: (i) We study the extent to which this NFL phase is generic by considering various deformations of our theory, including coupling of electrons to multiple operators of the TLSs and arbitrarily directed TLS fields. We find that the physical picture obtained in Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)] qualitatively persist in a wide region of parameter space, showcasing the robustness of the NFL phase. (ii) We analyze the superconducting instability caused by the coupling of TLSs to electrons, and find a rich structure, including quantum critical pairing associated with the NFL phase and conventional BCS-like pairing in the weak and strong coupling limits. (iii) We elaborate on the analysis of Bashan et al. [Phys. Rev. Lett. 132, 236501 (2024)], including single-particle, transport, and thermodynamic properties.
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The discovery of high-temperature superconductors has raises questions that extend beyond the scope of quasiparticles, a foundational concept in condensed matter theory. This dissertation explores new theoretical approaches to quantum matter without quasiparticle excitations, with a particular focus on quantum criticality and the associated superconductivity in correlated electron compounds. The soluble Sachdev-Ye-Kitaev (SYK) model has recently emerged as a fascinating platform to address the unusual metallic states with T-linear resistivity. We first consider differ- ent variants of random Hubbard models, which share many similarities to key aspects of the original SYK model. Using a large M analysis and a renormalization group method, we propose the existence of quantum critical points with fractionalized excitations separating two distinct phases, which provides insights into the quantum phase transitions and non-Fermi liquid behaviors observed in cuprate superconductors. In the second part of this dissertation, we examine the interplay between non-Fermi liquids and superconductivity with two different pairing mechanisms. Under the framework of random Hubbard model, we demonstrate that superconductivity emerging from non-Fermi liquids strongly deviates from the BCS theory by tuning the relative strength of hopping and exchange interactions. Furthermore, we investigate a two-dimensional Yukawa-SYK model with spatially randomn interactions coupling a Fermi surface to a scalar field associated with a quantum phase transition. Our theory agrees well with transport properties analysed in cuprates, such as a T-linear resistivity and Planckian dissipation.
Non-Fermi liquid (NFL) behavior and strange metallicity, often marked by resistivity linear in temperature and the breakdown of Fermi liquid quasiparticles, are recurring themes in strongly correlated quantum materials, ranging from high-temperature cuprates to twisted van der Waals heterostructures. Enormous efforts are being made to uncover the origin of NFL underlying strange metallicity, yet progress remains slow. Here, we report appearance of an NFL phase in a discontinuous metal-NFL-insulator transition of the Holstein model away from half-filling. The NFL appears as a distinct ground state of finite regime in addition to the metal and insulator states in a phase diagram, not as a consequence of quantum criticality of a continuous transition. Also, the discontinuity of the metal-NFL transition produces a mixture between the two phases along the phase boundary to exhibit a two-fluid kind strange metallicity. The dynamical mean-field theory was employed with Wilson’s numerical renormalization group in infinite dimensions. We trace the NFL phase to a spin gap opening in the absence of a charge gap. This offers an intriguing route to understanding the NFL and intertwined superconductivity in correlated quantum materials.
Hybrid metal-semiconductor quantum circuits offer a controlled setting for realizing and probing strongly correlated quantum matter. A largely open question that may be addressed by such simulators is whether coupled critical states can combine into new non-Fermi liquid (NFL) phases. Inspired by the recent realization of a two-site charge-Kondo circuit [W. Pouse \textit{et al.}, \href{https://www.nature.com/articles/s41567-022-01905-4}{Nat. Phys. \textbf{19}, 492 (2023)}], we uncover the fate of coupled Kondo anyons emerging from the two-channel-Kondo critical point at each site. Bosonization and quantum Brownian motion methods yield the full quasiballistic phase diagram and low-temperature transport properties, while numerical renormalization group calculations resolve the complementary weak-coupling limit. Together, these provide a unified description, and reveal robust NFL phases with continuously tunable transport and susceptibility exponents. Stronger inter-site coupling ultimately produces a screened Fermi liquid.
In this paper we continue the analysis of the interplay between non-Fermi liquid and superconductivity for quantum-critical systems, the low-energy physics of which is described by an effective model with dynamical electron-electron interaction $V({\mathrm{\ensuremath{\Omega}}}_{m})\ensuremath{\propto}1/{|{\mathrm{\ensuremath{\Omega}}}_{m}|}^{\ensuremath{\gamma}}$ (the $\ensuremath{\gamma}$ model). In paper I [A. Abanov and A. V. Chubukov, Phys. Rev. B 102, 024524 (2020)], two of us analyzed the $\ensuremath{\gamma}$ model at T=0T=0T=0 for $0<\ensuremath{\gamma}<1$ and argued that there exists a discrete, infinite set of topologically distinct solutions for the superconducting gap, all with the same spatial symmetry. The gap function ${\mathrm{\ensuremath{\Delta}}}_{n}({\ensuremath{\omega}}_{m})$ for the nthn\mathrm{th}nth solution changes sign nnn times as the function of Matsubara frequency. In this paper we analyze the linearized gap equation at a finite TTT. We show that there exists an infinite set of pairing instability temperatures, Tp,n{T}_{p,n}Tp,n​, and the eigenfunction ${\mathrm{\ensuremath{\Delta}}}_{n}({\ensuremath{\omega}}_{m})$ changes sign nnn times as a function of a Matsubara number mmm. We argue that ${\mathrm{\ensuremath{\Delta}}}_{n}({\ensuremath{\omega}}_{m})$ retains its functional form below Tp,n{T}_{p,n}Tp,n​ and at T=0T=0T=0 coincides with the nthn\mathrm{th}nth solution of the nonlinear gap equation. Like in paper I, we extend the model to the case when the interaction in the pairing channel has an additional factor 1/N1/N1/N compared to that in the particle-hole channel. We show that Tp,0{T}_{p,0}Tp,0​ remains finite at large NNN due to special properties of fermions with Matsubara frequencies $\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}T$, but all other Tp,n{T}_{p,n}Tp,n​ terminate at Ncr=O(1){N}_{\text{cr}}=O(1)Ncr​=O(1). The gap function vanishes at $T\ensuremath{\rightarrow}0$ for N>NcrN>{N}_{\text{cr}}N>Ncr​ and remains finite for N<NcrN<{N}_{\text{cr}}N<Ncr​. This is consistent with the T=0T=0T=0 analysis.
A variety of low-temperature, normal-state properties of optimally and overdoped cuprate superconductors, including the DC and optical transport responses, are sufficiently anomalous that they might seem to be inconsistent with any quasiparticle description. However, we show by explicit construction that the most salient phenomena can be accounted for in a system with localized "strange scatterers" embedded into a Fermi liquid with a conventional quasiparticle description. Such scatterers could originate from "two-level systems" associated with an electronic glassy state with short-range charge-order correlations.