Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2004.07267 · Physical review. B./Physical review. B

Quantum time crystals with programmable disorder in higher dimensions

Augustine Kshetrimayum, M. Goihl, Dante Marvin Kennes, Jens Eisert

Published Jun 10, 2021• 36 citations
arXivHTMLPDF

Abstract

We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems undergoing nonequilibrium dynamics. They are stabilized by many-body localization arising from disorder. We directly target the thermodynamic limit using instances of infinite tensor network states, and we implement disorder in a translationally invariant setting by introducing auxiliary systems at each site. We discuss how such disorder can be realized in programmable quantum simulators: This gives rise to the interesting situation in which a classical tensor network simulation can contribute to devising a blueprint of a quantum simulator featuring prethermal time crystalline dynamics, one that will ultimately have to be built in order to explore the stability of this phase of matter for long times.

DOI
10.1103/physrevb.103.224205

Related papers

Many-body–localized discrete time crystal with a programmable spin-based quantum simulator

J. Randall, C. E. Bradley, Floris V. Van Der Gronden +7 more

The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.

arXiv:2107.00736•Science•Nov 4, 2021•199 citations

Observation of a Prethermal U(1) Discrete Time Crystal

Andrew Stasiuk, Paola Cappellaro

A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry.Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium.These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization.This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems.Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature.In this work, we conclusively observe the emergence of a prethermal Uð1Þ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature.In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent Uð1Þ conservation law.Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.

arXiv:2303.10238•Physical Review X•Oct 26, 2023•20 citations

Simulation of Higher-Dimensional Discrete Time Crystals on a Quantum Computer

Christopher Sims

The study of topologically ordered states has given rise to a growing interest in symmetry-protected states in quantum matter. Recently, this theory has been extended to quantum many-body systems, which demonstrate ordered states at low temperatures. An example of this is the discrete time crystal (DTC), which has been demonstrated in a real quantum computer and in driven systems. These states are periodic in time and are protected from disorder to a certain extent. In general, DTCs can be classified into two phases: the stable many-body localization (MBL) state and the disordered thermal state. This work demonstrates the by generalizing DTCs to two dimensions, where there was an decrease in the thermal noise and an increase in the operating range of the MBL range in the presence of disorder.

arXiv:2303.02727•Crystals•Jul 30, 2023•3 citations

Classical approaches to prethermal discrete time crystals in one, two, and three dimensions

Andrea Pizzi, Andreas Nunnenkamp, Johannes Knolle

Prethermal discrete time crystals (pDTC) are new collective nonequilibrium phases of matter that break, up to exponentially long times, the discrete time translational symmetry of a periodic drive. Previously studied as a quantum phenomenon, this paper establishes that pDTCs also emerge for classical Hamiltonian dynamics even in their `higher-order and fractional' version. This enables efficient simulations of such phenomena in experimentally relevant settings, including a study of the interplay between dimensionality and interaction range.

arXiv:2108.07272•Physical review. B./Physical review. B•Sep 27, 2021•44 citations

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

Eric D. Switzer, Niall Robertson, Nathan Keenan +7 more

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.

arXiv:2501.18036•Nature Communications•Jan 28, 2026•1 citation

Colloquium : Quantum and classical discrete time crystals

Michael P. Zaletel, Mikhail D. Lukin, Christopher R. Monroe +3 more

The spontaneous breaking of time-translation symmetry has led to the discovery of a new phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations that result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. The breaking of ergodicity is focused upon as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the ac Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there is a diverse array of strategies to stabilize time-crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time-crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits are reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

arXiv:2305.08904•Reviews of Modern Physics•Jul 7, 2023•193 citations
We present fresh evidence for the presence of discrete quantum time crystals in two spatial dimensions. Discrete time crystals are intricate quantum systems that break discrete time translation symmetry in driven quantum many-body systems undergoing nonequilibrium dynamics. They are stabilized by many-body localization arising from disorder. We directly target the thermodynamic limit using instances of infinite tensor network states, and we implement disorder in a translationally invariant setting by introducing auxiliary systems at each site. We discuss how such disorder can be realized in programmable quantum simulators: This gives rise to the interesting situation in which a classical tensor network simulation can contribute to devising a blueprint of a quantum simulator featuring prethermal time crystalline dynamics, one that will ultimately have to be built in order to explore the stability of this phase of matter for long times.
The discrete time crystal (DTC) is a nonequilibrium phase of matter that spontaneously breaks time-translation symmetry. Disorder-induced many-body localization can stabilize the DTC phase by breaking ergodicity and preventing thermalization. Here, we observe the hallmark signatures of the many-body–localized DTC using a quantum simulation platform based on individually controllable carbon-13 nuclear spins in diamond. We demonstrate long-lived period-doubled oscillations and confirm that they are robust for generic initial states, thus showing the characteristic time-crystalline order across the many-body spectrum. Our results are consistent with the realization of an out-of-equilibrium Floquet phase of matter and introduce a programmable quantum simulator based on solid-state spins for exploring many-body physics.
A time crystal is a state of periodically driven matter that breaks discrete time-translation symmetry.Time crystals have been demonstrated experimentally in various programmable quantum simulators, and they exemplify how nonequilibrium, driven quantum systems can exhibit intriguing and robust properties absent in systems at equilibrium.These robust driven states need to be stabilized by some mechanism, with the preeminent candidates being many-body localization and prethermalization.This introduces additional constraints that make it challenging to experimentally observe time crystallinity in naturally occurring systems.Recent theoretical work has developed the notion of prethermalization without temperature, expanding the class of time-crystal systems to explain time-crystalline observations at (or near) infinite temperature.In this work, we conclusively observe the emergence of a prethermal Uð1Þ time-crystalline state at quasi-infinite temperature in a solid-state NMR quantum emulator by verifying the requisites of prethermalization without temperature.In addition to observing the signature period-doubling behavior, we show the existence of a long-lived prethermal regime whose lifetime is significantly enhanced by strengthening an emergent Uð1Þ conservation law.Not only do we measure this enhancement through the global magnetization, but we also exploit on-site disorder to measure local observables, ruling out the possibility of many-body localization and confirming the emergence of long-range correlations.
The study of topologically ordered states has given rise to a growing interest in symmetry-protected states in quantum matter. Recently, this theory has been extended to quantum many-body systems, which demonstrate ordered states at low temperatures. An example of this is the discrete time crystal (DTC), which has been demonstrated in a real quantum computer and in driven systems. These states are periodic in time and are protected from disorder to a certain extent. In general, DTCs can be classified into two phases: the stable many-body localization (MBL) state and the disordered thermal state. This work demonstrates the by generalizing DTCs to two dimensions, where there was an decrease in the thermal noise and an increase in the operating range of the MBL range in the presence of disorder.
Prethermal discrete time crystals (pDTC) are new collective nonequilibrium phases of matter that break, up to exponentially long times, the discrete time translational symmetry of a periodic drive. Previously studied as a quantum phenomenon, this paper establishes that pDTCs also emerge for classical Hamiltonian dynamics even in their `higher-order and fractional' version. This enables efficient simulations of such phenomena in experimentally relevant settings, including a study of the interplay between dimensionality and interaction range.
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.
The spontaneous breaking of time-translation symmetry has led to the discovery of a new phase of matter: the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations that result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. The breaking of ergodicity is focused upon as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the ac Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there is a diverse array of strategies to stabilize time-crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time-crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits are reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.