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

Switzer, Eric D. [Donostia International Physics Center (DIPC), San Sebastian (Spain); National Institute of Standards and Technology, Gaithersburg, MD (United States); University of Central Florida, Orlando, FL (United States)] (ORCID:0000000168245360)·Robertson, Niall F. [IBM Research Europe - Dublin (Ireland)] (ORCID:0000000194315203)·Keenan, Nathan [IBM Research Europe - Dublin (Ireland); Trinity College Dublin (Ireland); Trinity Quantum Alliance, Dublin (Ireland)]·Rodríguez-Alcaraz, Ángel [Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Euskadi (Spain); University of the Basque Country, Donostia-San Sebastián (Spain)] (ORCID:0009000647781520)·D’Urbano, Andrea [IBM Research Europe - Dublin (Ireland)] (ORCID:0009000783762674)·Pokharel, Bibek [IBM T.J. Watson Research Center, New York, NY (United States)] (ORCID:0000000342841353)·Rahman, Talat S. [Donostia International Physics Center (DIPC), San Sebastian (Spain); University of Central Florida, Orlando, FL (United States)] (ORCID:0000000338897776)·Shtanko, Oles [IBM Research – Almaden, San Jose, CA (United States)]·Zhuk, Sergiy [IBM Research Europe - Dublin (Ireland)]·Lorente, Nicolás [Donostia International Physics Center (DIPC), San Sebastian (Spain); Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Euskadi (Spain)] (ORCID:0000000309528031)
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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.

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Switzer, Eric D. [Donostia International Physics Center (DIPC), San Sebastian (Spain); National Institute of Standards and Technology, Gaithersburg, MD (United States); University of Central Florida, Orlando, FL (United States)] (ORCID:0000000168245360), Robertson, Niall F. [IBM Research Europe - Dublin (Ireland)] (ORCID:0000000194315203), Keenan, Nathan [IBM Research Europe - Dublin (Ireland); Trinity College Dublin (Ireland); Trinity Quantum Alliance, Dublin (Ireland)], Rodríguez-Alcaraz, Ángel [Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Euskadi (Spain); University of the Basque Country, Donostia-San Sebastián (Spain)] (ORCID:0009000647781520), D’Urbano, Andrea [IBM Research Europe - Dublin (Ireland)] (ORCID:0009000783762674), Pokharel, Bibek [IBM T.J. Watson Research Center, New York, NY (United States)] (ORCID:0000000342841353), Rahman, Talat S. [Donostia International Physics Center (DIPC), San Sebastian (Spain); University of Central Florida, Orlando, FL (United States)] (ORCID:0000000338897776), Shtanko, Oles [IBM Research – Almaden, San Jose, CA (United States)], Zhuk, Sergiy [IBM Research Europe - Dublin (Ireland)], Lorente, Nicolás [Donostia International Physics Center (DIPC), San Sebastian (Spain); Centro de Física de Materiales CFM/MPC (CSIC-UPV/EHU), Euskadi (Spain)] (ORCID:0000000309528031). 2026-01-28. Realization of two-dimensional discrete time crystals with anisotropic Heisenberg coupling. https://doi.org/10.1038/s41467-025-67787-1

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