arXiv:1806.11211 · Physical Review Letters

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid

A. V. Lunkin, Konstantin S. Tikhonov, M. V. Feigel’man

Published Dec 3, 2018• 30 citations

Abstract

We study stability of the Sachdev-Ye-Kitaev (SYK_{4}) model with a large but finite number of fermions N with respect to a perturbation, quadratic in fermionic operators. We develop analytic perturbation theory in the amplitude of the SYK_{2} perturbation and demonstrate stability of the SYK_{4} infrared asymptotic behavior characterized by a Green function G(τ)∝1/τ^{3/2}, with respect to weak perturbation. This result is supported by exact numerical diagonalization. Our results open the way to build a theory of non-Fermi-liquid states of strongly interacting fermions.

DOI: 10.1103/physrevlett.121.236601

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arXiv:1806.11211 · Physical Review Letters

Sachdev-Ye-Kitaev Model with Quadratic Perturbations: The Route to a Non-Fermi Liquid

A. V. Lunkin, Konstantin S. Tikhonov, M. V. Feigel’man

Published Dec 3, 2018• 30 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.121.236601

Related papers

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arXiv:1803.07197Physical review. B./Physical review. BJun 14, 201826 citations

N

, where

N

is the number of Majorana fermion operators, and also in the limit of large

N

and

M

, where

M

is the number of jump operators, the SYK Lindbladians are analytically tractable, and we obtain their stationary Green's functions, from which we can read off the decay rate. For finite

N

, we also study the distribution of the eigenvalues of the SYK Lindbladians.

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.

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 $\ensuremath{\rho}\ensuremath{\propto}{T}^{2/5}$ 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.

We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the maximal chaotic non-Fermi-liquid phase described by the ordinary

q=4

SYK model has marginally relevant or irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the

{\mathrm{SYK}}_{q}

model with a

q

-fermion interaction, similar perturbations can lead to a series of new fixed points with continuously varying exponents.

\mathrm{SYK}

model. It exhibits two distinct phases separated by a quantum phase transition characterized by a power-law, ${\ensuremath{\sim}|\ensuremath{\omega}|}^{\ensuremath{-}1/3}$, scaling of the low-energy spectral density, despite being a noninteracting model. By relaxing (ii), we obtain close relatives of the

\mathrm{SYK}

model which exhibit interesting behaviors, including a chaotic non-Fermi liquid phase with continuously varying fermion scaling dimension, and a phase transition to a disordered Fermi liquid as a function of interaction range and disorder length scale.