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.
We analyze the phase diagram of the spin-
21 Yukawa--Sachdev-Ye-Kitaev model, which describes complex spin-
21 fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. A recent work [Wang and Chubukov, Phys. Rev. Res. 2, 033084 (2020).] showed that, upon varying the filling or chemical potential, a first-order quantum phase transition exists between a non-Fermi-liquid (NFL) phase and an insulating phase. Here we show that in such a model with time-reversal symmetry this quantum phase transition is preempted by a pairing phase that develops as a low-temperature instability. As a remnant of the would-be NFL-insulator transition, the superconducting critical temperature rapidly decreases beyond a certain chemical potential. On the other hand, depending on the parameters, the first-order quantum phase transition extends to finite temperatures and terminates at a thermal critical point, beyond which the NFL and the insulator become the same phase, similar to that of the liquid-gas and metal-insulator transition in real materials. We determine the pairing phase boundary and the location of the thermal critical point via combined analytic and quantum Monte Carlo numeric efforts. Our results provide a model realization of the transition of NFLs towards superconductivity and insulating states and therefore offer a controlled platform for future investigations of the generic phase diagram that hosts a NFL, insulator, and superconductor and their phase transitions.
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.
We investigate models of electrons in the Sachdev-Ye-Kitaev class with random and all-to-all electron hopping, electron spin exchange, and Cooper-pair hopping. An attractive on-site interaction between electrons leads to superconductivity at low temperatures. Depending on the relative strengths of the hopping and spin exchange, the normal state at the critical temperature is either a Fermi-liquid or a non-Fermi liquid. We present a large-
M [where spin symmetry is enlarged to
SU(M)] study of the normal state to superconductor phase transition. We describe the transition temperature, the superconducting order parameter, and the electron spectral functions. We contrast between Fermi liquid and non-Fermi liquid normal states: we find that for weaker attractive on-site interaction there is a relative enhancement of
Tc when the normal state is a non-Fermi liquid, and correspondingly a strong deviation from BCS limit. Also, the phase transition in this case becomes a first-order transition for strong non-Fermi liquids. On the other hand, for stronger on-site interaction, there is no appreciable difference in
Tc between whether the superconductivity emerges from a Fermi liquid or a non-Fermi liquid. Notable features of superconductivity emerging from a non-Fermi liquid are that the superconducting electron spectral function is different from the Fermi-liquid case, with additional peaks at higher energies, and there is no Hebel-Slichter peak in the NMR relaxation rate in the non-Fermi liquid case.
We present and analyze an exactly solvable interacting fermionic pairing model, which features interactions that entangle states at momenta
k and
−k. These interactions give rise to novel correlated ground states, leading to a rich phase diagram that includes superconducting, multiple metallic, and Mott-insulating phases. At finite interaction strengths, we observe the emergence of multiple many-body Fermi surfaces, which violate Luttinger's theorem and challenge the conventional Landau-Fermi liquid paradigm. A distinguishing feature of our model is that it remains quantum integrable, even with the addition of pairing interactions of various symmetries, setting it apart from the Hatsugai-Kohmoto model. Our results provide an analytically tractable framework for studying strong correlation effects that give rise to fractionalized excitations and unconventional superconductivity, offering valuable insights into a broad class of integrable many-body systems.
We study an exactly-solvable model which shows a zero-temperature transition from a non-Fermi liquid to a Fermi liquid as a function of particle density. The quantum critical point separating these two states is not associated with the usual ordering transition of a bosonic degree of freedom. We analyze the properties of this critical point in terms of an effective density of states, and we use this concept to generalize this transition to a class of related quantum critical points. We study the superconducting instability of the low-density (non-Fermi liquid) regime and we show that it has an enhanced pair susceptibility relative to the Fermi liquid. We comment on the applicability of our results to low-carrier density superconductors.