Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
- URL: http://arxiv.org/abs/2109.05037v6
- Date: Sat, 3 Dec 2022 23:03:36 GMT
- Title: Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
- Authors: Debanjan Chowdhury, Antoine Georges, Olivier Parcollet, Subir Sachdev
- Abstract summary: We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations.
The review is placed in the context of numerous experimental observations on correlated electron materials.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible
quantum many-body systems without quasiparticle excitations, and its
connections to various theoretical studies of non-Fermi liquids in condensed
matter physics. The review is placed in the context of numerous experimental
observations on correlated electron materials. Strong correlations in metals
are often associated with their proximity to a Mott transition to an insulator
created by the local Coulomb repulsion between the electrons. We explore the
phase diagrams of a number of models of such local electronic correlation,
employing a dynamical mean field theory in the presence of random spin exchange
interactions. Numerical analyses and analytical solutions, using
renormalization group methods and expansions in large spin degeneracy, lead to
critical regions which display SYK physics. The models studied include the
single-band Hubbard model, the $t$-$J$ model and the two-band Kondo-Heisenberg
model in the presence of random spin exchange interactions. We also examine
non-Fermi liquids obtained by considering each SYK model with random
four-fermion interactions to be a multi-orbital atom, with the SYK-atoms
arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces
without any low-energy quasiparticles in the absence of spatial disorder,
obtained by coupling a Fermi liquid to a gapless boson; a systematic large $N$
theory of such a critical Fermi surface, with SYK characteristics, is obtained
by averaging over an ensemble of theories with random boson-fermion couplings.
Finally, we present an overview of the links between the SYK model and quantum
gravity and end with an outlook on open questions.
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