# Realization of two-dimensional discrete time crystals with anisotropic Heisenberg coupling

## TL;DR

The paper demonstrates a 2D discrete time crystal using anisotropic Heisenberg coupling on a quantum simulator, revealing new non-equilibrium phases.

## Contribution

First realization of a 2D DTC with anisotropic Heisenberg coupling using quantum processors.

## Key findings

- A 2D DTC phase is stabilized with anisotropic Heisenberg interactions.
- The phase diagram includes spin-glass, ergodic, and time-crystalline phases.
- Initialization and driving protocols influence the DTC stability.

## Abstract

A discrete time crystal (DTC) is an out-of-equilibrium phase of matter that spontaneously breaks discrete time-translation symmetry. Previous studies have been limited to a set of models with Ising-like couplings - and mostly only in one dimension - thus precluding our understanding of the existence (or not) of DTCs in models with more realistic interactions. In this work, by combining the latest generation of IBM quantum processors with state-of-the-art tensor network methods, we demonstrate the existence of a DTC in a two-dimensional system governed by anisotropic Heisenberg interactions. We uncover a rich phase diagram encompassing spin-glass, ergodic, and time-crystalline phases, and identify the interplay of initialization, interaction anisotropy, and driving protocols in stabilizing the DTC phase. By extending the study of Floquet matter beyond simplified models, we lay the groundwork for exploring how driven systems bridge the gap between quantum coherence and emergent non-equilibrium thermodynamics.

Experimental realizations of discrete time crystals have mainly involved 1D models with Ising-like couplings. Here, the authors realize a 2D discrete time crystal with anisotropic Heisenberg coupling on a quantum simulator based on superconducting qubits, uncovering a rich phase diagram.