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arXiv:2002.07181 · Proceedings of the National Academy of Sciences

Linear resistivity and Sachdev-Ye-Kitaev (SYK) spin liquid behavior in a quantum critical metal with spin-1/2 fermions

Peter Cha, Nils Wentzell, Olivier Parcollet, Antoine Georges, Eun-Ah Kim

Published Jul 22, 2020• 72 citations
arXivHTMLPDF

Abstract

"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.

DOI
10.1073/pnas.2003179117

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"Strange metals" with resistivity depending linearly on temperature T down to low T have been a long-standing puzzle in condensed matter physics. Here, we consider a lattice model of itinerant spin-[Formula: see text] fermions interacting via onsite Hubbard interaction and random infinite-ranged spin-spin interaction. We show that the quantum critical point associated with the melting of the spin-glass phase by charge fluctuations displays non-Fermi liquid behavior, with local spin dynamics identical to that of the Sachdev-Ye-Kitaev family of models. This extends the quantum spin liquid dynamics previously established in the large-M limit of [Formula: see text] symmetric models to models with physical [Formula: see text] spin-[Formula: see text] electrons. Remarkably, the quantum critical regime also features a Planckian linear-T resistivity associated with a T-linear scattering rate and a frequency dependence of the electronic self-energy consistent with the marginal Fermi liquid phenomenology.
We numerically study a model of interacting spin-1/21/21/2 electrons with random exchange coupling on a fully connected lattice. This model hosts a quantum critical point separating two distinct metallic phases as a function of doping: a Fermi-liquid phase with a large Fermi-surface volume and a low-doping phase with local moments ordering into a spin glass. We show that this quantum critical point has non-Fermi-liquid properties characterized by TTT-linear Planckian behavior, $\ensuremath{\omega}/T$ scaling, and slow spin dynamics of the Sachdev-Ye-Kitaev type. The $\ensuremath{\omega}/T$ scaling function associated with the electronic self-energy is found to have an intrinsic particle-hole asymmetry, a hallmark of a ``skewed'' non-Fermi liquid.
Despite considerable theoretical effort, there has been no consensus on the description of the strange metal state seen in high temperature superconductors and its linear in T resistivity. Here, we construct a simple solvable model of itinerant electrons interacting through random couplings on a honeycomb lattice composed of Sachdev-Ye-Kitaev quantum dots which describes electrons without quasiparticle excitations. This model is solvable in the large-N limit and displays a temperature dependant crossover between two regimes. By tuning the strength of this interaction relative to the bandwidth of the itinerant electrons, we can additionally obtain a finite T crossover to a fully incoherent regime that also has a linear in T resistivity. In the non-Fermi liquid regime, the dc resistivityincreases linearly with temperature over a broad range of temperatures. The self energy has a singular frequency dependence but lacks momentum dependence which is reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞ . In the low-temperature and strong-coupling limit, the behaviour parallels that of Dirac fermions. We discuss the implications of theseresults and further possibilities in such studies.
We investigate a model of electrons with random and all-to-all hopping and spin exchange interactions, with a constraint of no double occupancy. The model is studied in a Sachdev–Ye–Kitaev-like large- M limit with SU( M ) spin symmetry. The saddle-point equations of this model are similar to approximate dynamic mean-field equations of realistic, nonrandom, t - J models. We use numerical studies on both real and imaginary frequency axes, along with asymptotic analyses, to establish the existence of a critical non–Fermi-liquid metallic ground state at large doping, with the spin correlation exponent varying with doping. This critical solution possesses a time-reparameterization symmetry, akin to Sachdev–Ye–Kitaev (SYK) models, which contributes a linear-in-temperature resistivity over the full range of doping where the solution is present. It is therefore an attractive mean-field description of the overdoped region of cuprates, where experiments have observed a linear- T resistivity in a broad region. The critical metal also displays a strong particle–hole asymmetry, which is relevant to Seebeck coefficient measurements. We show that the critical metal has an instability to a low-doping spin-glass phase and compute a critical doping value. We also describe the properties of this metallic spin-glass phase.
We construct examples of translationally invariant solvable models of strongly correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi-liquid behavior. In the marginal-Fermi-liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi surfaces. The self-energy has a singular frequency dependence but lacks momentum dependence, reminiscent of a dynamical mean-field-theory-like behavior but in dimensions d < ∞. In the low-temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi surface in the non-Fermi-liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse-grained descriptions of a class of intermediate-scale non-Fermi-liquid behavior in generic correlated metals.
A central question in frustrated quantum magnets is how quantum fluctuations destabilize spin-glass order and promote quantum spin-liquid behavior. We study the equilibrium dynamics of an infinite-range quantum Heisenberg model with random couplings, in which local magnetic moments arise from N_{f} flavors of spinful fermions. We employ an expansion in N_{f}, which controls the strength of quantum fluctuations, and self-consistently include 1/N_{f} corrections to the Luttinger-Ward functional. In the large-N_{f} limit, where quantum fluctuations are weak, the high- and low-temperature phases are respectively paramagnetic and spin glass ordered, with a transition temperature independent of N_{f}. For small numbers of fermionic flavors, however, quantum fluctuations substantially suppress the ordering temperature. We show that this behavior reflects the proximity of the system to a Sachdev-Ye-Kitaev (SYK) regime, realizing quantum spin-liquid dynamics over a broad range of finite frequencies, where both fermionic and spin spectral densities display critical behavior over a broad range of finite frequencies, with the latter exhibiting the scale-invariant form χ^{''}(ω)∼sgn(ω). At the lowest energies and temperatures, spin glass dynamics ultimately take over, producing a universal sub-Ohmic dynamical spin susceptibility χ^{''}(ω)∼sgn(ω)sqrt[|ω|]. Our results highlight a direct connection between the suppression of spin-glass order and the emergence of SYK criticality in a frustrated quantum magnet.
Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of high temperature superconducting materials [extended Sachdev-Ye-Kitaev (SYK) models]. We identify the low energy collective excitations as neutral energy excitations, diffusing in the lattice of the thermalized non-Fermi liquid phase. However, the diffusion is heavily hindered by coupling to the pseudo-Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. The imaginary time evolution of the extended model in the strong interaction and 1/N1/N1/N expansion limit is presented in the incoherent nonchaotic regime. On the other hand, a Fermi electronic liquid at low energy becomes marginal when perturbed by the SYK dots. A critical temperature for superconductivity is derived, which is not BCS-like, in case the collective excitations are assumed to mediate an attractive Cooper pairing.