We describe the phases of a solvable $t\text{\ensuremath{-}}J$ model of electrons with infinite-range, and random, hopping, and exchange interactions, similar to those in the Sachdev-Ye-Kitaev models. The electron fractionalizes, as in an ``orthogonal metal,'' into a fermion
f, which carries both the electron spin and charge, and a boson $\ensuremath{\phi}$. Both
f and $\ensuremath{\phi}$ carry emergent
Z2 gauge charges. The model has a phase in which the $\ensuremath{\phi}$ bosons are gapped, and the
f fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates, without spatial structure. The model also has an extended, critical, ``quasi-Higgs'' phase where both $\ensuremath{\phi}$ and
f are gapless, and the electron operator $\ensuremath{\sim}f\ensuremath{\phi}$ has a Fermi liquid-like $1/\ensuremath{\tau}$ propagator in imaginary time, $\ensuremath{\tau}$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by
Z2 fractionalization and the anomalous exponents of the
f and $\ensuremath{\phi}$ excitations. This quasi-Higgs phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.
Prominent systems like the high-T_{c} cuprates and heavy fermions display intriguing features going beyond the quasiparticle description. The Sachdev-Ye-Kitaev (SYK) model describes a (0+1)D quantum cluster with random all-to-all four-fermion interactions among N fermion modes which becomes exactly solvable as N→∞, exhibiting a zero-dimensional non-Fermi-liquid with emergent conformal symmetry and complete absence of quasiparticles. Here we study a lattice of complex-fermion SYK dots with random intersite quadratic hopping. Combining the imaginary time path integral with real time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio L≡(κρ/T) varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.
"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 propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle-point solutions at a large number
N of fermions are obtained and show a characteristic scale-invariant ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/2}$ behavior of the spectral function below the transition which is replaced by a ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$ singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle-point equations and discussed in the broader context of the field.
The Sachdev-Ye-Kitaev (SYK) model is a concrete model for a non-Fermi liquid with maximally chaotic behavior in
(0+1) dimensions. In order to gain some insights into real materials in higher dimensions where fermions could hop between different sites, here we consider coupling a SYK lattice by constant hopping. We call this the dispersive SYK model. Focusing on
(1+1)-dimensional homogeneous hopping, by either tuning the temperature or the relative strength of the random interaction (hopping) and constant hopping, we find a crossover between a dispersive metal to an incoherent metal, where the dynamic exponent
z changes from 1 to $\ensuremath{\infty}$. We study the crossover by calculating the spectral function, charge density correlator, and the Lyapunov exponent. We further find the Lyapunov exponent becomes larger when the chemical potential is tuned to approach a van Hove singularity because of the large density of states near the Fermi surface. The effect of the topological nontrivial bands is also discussed.
A variety of exotic non-Fermi liquid (NFL) states have been observed in many condensed matter systems, with different scaling relations between transport coefficients and temperature. The ``standard'' approach to studying these NFLs is by coupling a Fermi liquid to quantum critical fluctuations, which potentially can drive the system into a NFL. In this work we seek for an alternative understanding of these various NFLs in a unified framework. We first construct two ``elementary'' randomness-free models with four-fermion interactions only, whose many properties can be analyzed exactly in certain limit just like the Sachdev-Ye-Kitaev model. The most important new feature of our models is that, the fermion scaling dimension in the conformal invariant solution in the infrared limit is tunable by charge density. Then based on these elementary models, we propose two versions of lattice models with four-fermion interactions which give us non-Fermi liquid behaviors with dc resistivity scaling $\ensuremath{\varrho}\ensuremath{\sim}{T}^{\ensuremath{\alpha}}$ in a finite-temperature window, and $\ensuremath{\alpha}\ensuremath{\in}[1,2)$ depends on the fermion density in the model, which is a rather universal feature observed in many experimental systems.