Discrete Time Crystal in Quantum Sherrington-Kirkpatrick Model

Bothra, Aarya (2025) Discrete Time Crystal in Quantum Sherrington-Kirkpatrick Model. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Aarya Bothra (20MS187)) 20MS187_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

Spontaneous time-translation symmetry breaking in periodically driven quantum systems has led to the discovery of discrete time crystals (DTCs). They have emerged as a fascinating non-equilibrium phase of matter characterized by long-lived subharmonic oscillations. While most established realizations rely on short-range interactions stabilized by many-body localization, the role of long-range interactions in supporting stable DTC behavior remains an open question. In this work, we confront this challenge by focusing on the periodically driven quantum Sherrington- Kirkpatrick (SK) model of an Ising spin glass model with all-to-all random interactions between spins. Based on three different protocols for invoking quantum dynamics, we identify that the SK model invariably sustains a robust DTC phase with the characteristic feature of spatiotemporal order created by long-lived period-doubling oscillations and minimal state-to-state variability. To understand the role of disorder and interaction structure more profoundly, we compared these results with those from other long-range interacting models where couplings are uniform and disorder is introduced only through a random local field. In contrast to the SK model, these systems exhibit strong initial state dependence with many even decaying rapidly. The results in this work have also been reported in the preprint: arXiv:2504.19378.

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