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A bipartite variant of the Sachdev-Ye-Kitaev model from a strained Kitaev honeycomb model

Mikael Fremling, Lars Fritz

Published May 13, 2021• 1 citation
OpenAlex

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

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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 $\ensuremath{\gamma}$ 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.

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Here we revisit the thermodynamics of the Kitaev quantum spin liquid realized on the honeycomb lattice. We address two main questions: First, we investigate whether there are observable thermodynamic signatures of the topological Majorana boundary modes of the Kitaev honeycomb model. We argue that for the time-reversal invariant case the residual low-temperature entropy is the primary thermodynamic signature of these Majorana edge modes, and verify using large-scale Monte Carlo simulations that this residual entropy is present in the full Kitaev model. When time-reversal symmetry is broken, the Majorana edge modes are potentially observable in more direct thermodynamic measurements such as the specific heat, though only at temperatures well below the bulk gap. % Second, we study the energetics, and the corresponding thermodynamic signatures, of the flux excitations in the Kitaev model. Specifically, we study the flux interactions on both cylinder and torus geometries numerically, and quantify their impact on the thermodynamics of the Kitaev spin liquid by using a polynomial fit for the average flux energy as a function of flux density and extrapolating it to the thermodynamic limit. By comparing this model to Monte Carlo simulations, we find that flux interactions have a significant quantitative impact on the shape and the position of the low-temperature peak in the specific heat.

•Aug 4, 2020•0 citations
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.
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.
The authors study in detail the quantum mechanical model of NNN Majorana fermions with random interactions of a few fermions at a time (Sachdev-Ye-Kitaev model) in the large NNN limit. At low energies, the system is strongly interacting and an emergent conformal symmetry develops. Performing technical calculations, the authors elucidate a number of properties of the model near the conformal point.
Through a mixture of analytic and numerical techniques, we explore the optimal approximation by a free Majorana state to individual disorder realizations of the Sachdev-Ye-Kitaev model, along with a generalization of it. We elucidate the properties of the known time-reversal symmetry breaking phase in the generalized model, finding strong evidence of "spin glass" order. For the Sachdev-Ye-Kitaev model itself, our results are inconclusive but suggest a similar order may be present at zero temperature.
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 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 NNN 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.
Here we revisit the thermodynamics of the Kitaev quantum spin liquid realized on the honeycomb lattice. We address two main questions: First, we investigate whether there are observable thermodynamic signatures of the topological Majorana boundary modes of the Kitaev honeycomb model. We argue that for the time-reversal invariant case the residual low-temperature entropy is the primary thermodynamic signature of these Majorana edge modes, and verify using large-scale Monte Carlo simulations that this residual entropy is present in the full Kitaev model. When time-reversal symmetry is broken, the Majorana edge modes are potentially observable in more direct thermodynamic measurements such as the specific heat, though only at temperatures well below the bulk gap. % Second, we study the energetics, and the corresponding thermodynamic signatures, of the flux excitations in the Kitaev model. Specifically, we study the flux interactions on both cylinder and torus geometries numerically, and quantify their impact on the thermodynamics of the Kitaev spin liquid by using a polynomial fit for the average flux energy as a function of flux density and extrapolating it to the thermodynamic limit. By comparing this model to Monte Carlo simulations, we find that flux interactions have a significant quantitative impact on the shape and the position of the low-temperature peak in the specific heat.