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arXiv:2105.06119 · Physical review. B./Physical review. B

Sachdev-Ye-Kitaev type physics in the strained Kitaev honeycomb model

Mikael Fremling, Lars Fritz

Published Feb 25, 2022• 6 citations
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Abstract

In this work, we investigate whether the Kitaev honeycomb model can serve as a starting point to realize the intriguing physics of the Sachdev-Ye-Kitaev (SYK) model. The starting point is to strain the system, which leads to flat bands reminiscent of Landau levels, thereby quenching the kinetic energy. The presence of weak residual perturbations, such as Heisenberg interactions and the $\ensuremath{\gamma}$ term, creates effective interactions between the Majorana modes when projected into the flux-free sector. We assume the resulting interactions to be effectively random. This leads to a bipartite Sachdev-Ye-Kitaev model (b-SYK) with very similar properties as the SYK model. We also hypothesize under which conditions one would expect the standard SYK model in such a setup.

DOI
10.1103/physrevb.105.085147

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In this work we investigate whether the Kitaev honeycomb model can serve as a starting point to realize the intriguing physics of the Sachdev-Ye-Kitaev model. The starting point is to strain the system which leads to flat bands reminiscent of Landau levels, thereby quenching the kinetic energy. The presence of weak residual perturbations, such as Heisenberg interactions and the $\gamma$-term, creates effective interactions between the Majorana modes when projected into the flux-free sector. Taking into account a disordered boundary results in an interaction that is effectively random. While we find that in a strained nearest-neighbor Kitaev honeycomb model it is unlikely to find the Sachdev-Ye-Kitaev model, it appears possible to realize a bipartite variant with similar properties. We furthermore argue that next-nearest-neighbor terms can lead to actual Sachdev-Ye-Kitaev physics, if large enough.

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In this work, we investigate whether the Kitaev honeycomb model can serve as a starting point to realize the intriguing physics of the Sachdev-Ye-Kitaev (SYK) model. The starting point is to strain the system, which leads to flat bands reminiscent of Landau levels, thereby quenching the kinetic energy. The presence of weak residual perturbations, such as Heisenberg interactions and the \ensuremathγ\ensuremath{\gamma}\ensuremathγ term, creates effective interactions between the Majorana modes when projected into the flux-free sector. We assume the resulting interactions to be effectively random. This leads to a bipartite Sachdev-Ye-Kitaev model (b-SYK) with very similar properties as the SYK model. We also hypothesize under which conditions one would expect the standard SYK model in such a setup.
In this work we investigate whether the Kitaev honeycomb model can serve as a starting point to realize the intriguing physics of the Sachdev-Ye-Kitaev model. The starting point is to strain the system which leads to flat bands reminiscent of Landau levels, thereby quenching the kinetic energy. The presence of weak residual perturbations, such as Heisenberg interactions and the γ\gammaγ-term, creates effective interactions between the Majorana modes when projected into the flux-free sector. Taking into account a disordered boundary results in an interaction that is effectively random. While we find that in a strained nearest-neighbor Kitaev honeycomb model it is unlikely to find the Sachdev-Ye-Kitaev model, it appears possible to realize a bipartite variant with similar properties. We furthermore argue that next-nearest-neighbor terms can lead to actual Sachdev-Ye-Kitaev physics, if large enough.
The Sachdev-Ye-Kitaev (SYK) model is zero-dimensional model simulating quantum chaos using interacting Majorana fermions.Previously proposals have been made to realize the SYK model in fermionic systems that can support majorana zero modes. In this work, we simulate the SYK model in a Kitaev spin chain, where zero modes also exist in the ground state from the fermionic representation of spins. By adding other interactions as perturbations, we lift the degenerate majorana zero modes and obatin an effective SYK interactions. Although the majorana fermions are nonlocal in forms of spin operators, we show that the out-of-time-ordered correlator (OTOC) of the majorana fermions can be approximately simulated in forms of spin operators. Our proposal sheds light in simulating the fermonic SKY model and the related physics in purely bosonic systems.
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 ttt-JJJ 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 NNN 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.
The SYK model of Sachdev, Ye and Kitaev is a recent model of N Majorana fermions coupled via quartic random interaction. It has the extraordinary properties of being exactly solvable at large N , having emergent conformal symmetry in the IR, and exhibiting maximal quantum chaos. The confluence of these properties make SYK a highly attractive candidate for a solvable AdS/CFT correspondence. What’s more, it was found to capture elements of non-Fermi-liquid behavior in strange metals. This thesis introduces the SYK model and discusses a recent variant, the SYK∗ model of Marcus and Vandoren. In the latter, the effective action is derived and branches of conformal solutions are discussed. The parameter space of SYK∗ is investigated for large and small M . The former reveals a phase separation and a N critical point in the T−M plane is claimed to exist.
We point out that a classical analog of the Sachdev-Ye-Kitaev (SYK) model, a solvable model of quantum many-body chaos, was studied long ago in the turbulence literature. Motivated by the Navier-Stokes equation in the turbulent regime and the nonlinear Schrödinger equation describing plasma turbulence, in which there is mixing between many different modes, the random coupling model has a Gaussian-random coupling between any four of a large number N of modes. The model was solved in the 1960s, before the introduction of large-N path-integral techniques, using a method referred to as the direct interaction approximation. We use the path integral to derive the effective action for the model. The large-N saddle gives an integral equation for the two-point function, which is very similar to the corresponding equation in the SYK model. The connection between the SYK model and the random coupling model may, on the one hand, provide new physical contexts in which to realize the SYK model and, on the other hand, suggest new models of turbulence and techniques for studying them.
The Sachdev-Ye-Kitaev (SYK) model is a model of qqq interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large NNN expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in NNN. We then derive the form of the effective action to all orders.