Reply to Comment on "Discrete Time Crystals: Rigidity Criticality and Realizations"

TL;DR

This paper defends the existence of many-body localized discrete time crystals against recent criticism, using finite-size scaling analysis, larger-scale simulations, and analytic arguments to reaffirm the original findings.

Contribution

The authors provide a robust rebuttal to claims against MBL DTC phases, clarifying analysis methods and extending simulations to support their original conclusions.

Findings

Finite-size scaling supports MBL DTC existence

Larger-scale simulations confirm original results

Boundary effects diminish with system size

Abstract

This is a reply to the comment from Khemani, Moessner and Sondhi (KMS) [arXiv:2109.00551] on our manuscript [Phys. Rev. Lett. 118, 030401 (2017)]. The main new claim in KMS is that the short-ranged model does not support an MBL DTC phase. We show that, even for the parameter values they consider and the system sizes they study, the claim is an artifact of an unusual choice of range for the crucial plots. Conducting a standard finite-size scaling analysis on the same data strongly suggests that the system is in fact a many-body localized (MBL) discrete time crystal (DTC). Furthermore, we have carried out additional simulations at larger scales, and provide an analytic argument, which fully support the conclusions of our original paper. We also show that the effect of boundary conditions, described as essential by KMS, is exactly what one would expect, with boundary effects decreasing with increasing system size. The other points in KMS are either a rehashing of points already in the literature (for the long-ranged model) or are refuted by a proper finite-size scaling analysis.