Study of the Leggett-Garg Inequality on the Sachdev-Ye-Kitaev model

Reza, Tasnum (2019) Study of the Leggett-Garg Inequality on the Sachdev-Ye-Kitaev model. Masters thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

The Sachdev-Ye-Kitaev (SYK) model is a 0 + 1 dimensional model of majorana fermions with four body all-to-all random interactions, which has gained a lot of prominence in recent years due to its significance in quantum chaos and resemblance with quantum holography. In this thesis, we use some universal features of random matrix ensembles to understand the Nmod8 classifications of our model which is a variant of the SYK model. We then aim to investigate any emergent classical behaviour of the model at large N limit. This is done by using the Leggett-Garg Inequality (LGI) which is the temporal analog for Bell’s Inequality that sets a temporal correlation bound for classical systems based on two assumptions of Macrorealism (MR) and Non-Invasive Measurability (NIM). Additionally, we also perform LGI on some modifications of the SYK model by tuning the effective coupling constant J and make interesting observations under certain parametric conditions.

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