Abstract
Abstract We study a two-band dispersive Sachdev-Ye-Kitaev (SYK) model in 1 + 1 dimension. We suggest a model that describes a semimetal with quadratic dispersion at half-filling. We compute the Green's function at the saddle point using a combination of analytical and numerical methods. Employing a scaling symmetry of the Schwinger-Dyson equations that becomes transparent in the strongly dispersive limit, we show that the exact solution of the problem yields a distinct type of non-Fermi liquid with sublinear $\rho\propto T^{2/5}$ temperature dependence of the resistivity. A scaling analysis indicates that this state corresponds to the fixed point of the dispersive SYK model for a quadratic band touching semimetal.
Highlights
The 0 + 1 dimensional SYKq dot model [1,2] exhibits an approximate conformal symmetry in the infrared, is exactly solvable in the limit of a large number of fermion flavors, saturates the bound on quantum chaos, and is dual to gravitational theories in 1 + 1 dimensions [3–5]
We find through a scaling argument that when the system starts from the SYK fixed point at high temperature, it flows toward a distinct non-Fermi liquid (NFL) fixed point at zero temperature
In the case of a 1D half-filled semimetal with parabolic touching, we showed that the lowtemperature regime does not lead to a semimetal but to another type of incoherent NFL, whose transport properties will be addressed
Summary
Sachdev-Ye-Kitaev (SYKq) models describe strongly interacting fermions with infinite range, q-body, random all-toall interactions. Dispersive versions of the SYK model were used to describe incoherent or “Planckian” metals which lack well-defined quasiparticles [12,19,20] These incoherent metals typically have a crossover between the incoherent high-temperature regime and a low-temperature Fermi liquid behavior [15,16]. The hopping amplitudes between lattice sites is finely tuned such that this system describes a half-filled semimetal with quadratic dispersion and local SYK couplings. In the strongly dispersive regime, T t2/J, the scaling symmetry of the problem becomes transparent, albeit the absence of conformal symmetry In this limit, the incoherent regime extends down to zero frequency and temperature, unlike in the more conventional metallic case. In the strongly dispersive regime (T t2/J), where conformal symmetry is not present, we numerically extract the finite-temperature scaling functions of the Green’s function and of the self-energy.
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