Unveiling Novel Insights in Quantum Dynamics through Extended Sachdev-Ye-Kitaev Model

TL;DR

This paper re-evaluates the SYK model inspired by DSSYK insights, providing exact solutions, extending it to tensor field theory, and discovering phase transitions and cutoff dependencies that deepen understanding of quantum dynamics.

Contribution

It introduces a tensor field extension of the SYK model with a cutoff, revealing new phase transitions and precise solutions not previously reported.

Findings

Exact two-point function solutions

Discovery of first-order phase transitions

Linear relationship between coupling and cutoff

Abstract

Inspired by recent developments in the study of the model of double scaled SYK (DSSYK), as elucidated in a recent paper, we embark on a re-evaluation of the Sachdev-Ye-Kitaev (SYK) model. Our motivation stems from the insights gained from the DSSYK model, particularly its ability to capture essential features of quantum dynamics and gravitational effects. In this work, we delve into the SYK model, uncovering precise solutions for the two-point function and self-energy that have not been previously reported. Building upon the advancements made in particle physics phenomenology, we extend the SYK model to encompass tensor field theory. Through the incorporation of a cutoff term to ensure convergence, we substantially advance our understanding of quantum many-body physics. Our investigation extends to experimental parameter estimation and the exploration of cutoff dependency in random couplings, providing invaluable insights into system dynamics. The introduction of a novel tensor field theory replaces conventional fermionic degrees of freedom with tensorial counterparts, leading to the discovery of intriguing phase transition phenomena characterized by a first-order transition. Furthermore, we elucidate a direct linear relationship between the coupling parameter and the cutoff scale. These findings not only shed light on emergent behavior across both high-energy physics and condensed matter systems but also pave the way for further theoretical and experimental exploration, inspired by the recent advancements in the SYK model.