Discrete time crystals represent a paradigmatic nonequilibrium phase of periodically driven matter. Protecting its emergent spatiotemporal order necessitates a mechanism that hinders the spreading of defects, such as localization of domain walls in disordered quantum spin chains. In this work, we establish the effectiveness of a different mechanism arising in clean spin chains: the confinement of domain walls into "mesonic " bound states. We consider translationally invariant quantum Ising chains periodically kicked at arbitrary frequency, and we discuss two possible routes to domain-wall confinement: longitudinal fields and interactions beyond nearest neighbors. We study the impact of confinement on the order-parameter evolution by constructing domain-wall-conserving effective Hamiltonians and analyzing the resulting dynamics of domain walls. On the one hand, we show that for arbitrary driving frequency, the symmetry-breaking-induced confining potential gets effectively averaged out by the drive, leading to deconfined dynamics. On the other hand, we rigorously prove that increasing the range R of spin-spin interactions J(i,j) beyond nearest neighbors enhances the order-parameter lifetime exponentially in R. Our theory predictions are corroborated by a combination of exact and matrix-product-state simulations for finite and infinite chains, respectively. The long-lived stability of spatiotemporal order identified in this work does not rely on Floquet prethermalization nor on eigenstate order, but rather on the nonperturbative origin of vacuum-decay processes. We point out the experimental relevance of this new mechanism for stabilizing a long-lived time-crystalline response in Rydberg-dressed spin chains.

Discrete Time-Crystalline Response Stabilized by Domain-Wall Confinement / Collura, Mario; De Luca, Andrea; Rossini, Davide; Lerose, Alessio. - In: PHYSICAL REVIEW. X. - ISSN 2160-3308. - 12:3(2022), pp. 1-34. [10.1103/physrevx.12.031037]

Discrete Time-Crystalline Response Stabilized by Domain-Wall Confinement

Collura, Mario;De Luca, Andrea;Rossini, Davide;Lerose, Alessio
2022-01-01

Abstract

Discrete time crystals represent a paradigmatic nonequilibrium phase of periodically driven matter. Protecting its emergent spatiotemporal order necessitates a mechanism that hinders the spreading of defects, such as localization of domain walls in disordered quantum spin chains. In this work, we establish the effectiveness of a different mechanism arising in clean spin chains: the confinement of domain walls into "mesonic " bound states. We consider translationally invariant quantum Ising chains periodically kicked at arbitrary frequency, and we discuss two possible routes to domain-wall confinement: longitudinal fields and interactions beyond nearest neighbors. We study the impact of confinement on the order-parameter evolution by constructing domain-wall-conserving effective Hamiltonians and analyzing the resulting dynamics of domain walls. On the one hand, we show that for arbitrary driving frequency, the symmetry-breaking-induced confining potential gets effectively averaged out by the drive, leading to deconfined dynamics. On the other hand, we rigorously prove that increasing the range R of spin-spin interactions J(i,j) beyond nearest neighbors enhances the order-parameter lifetime exponentially in R. Our theory predictions are corroborated by a combination of exact and matrix-product-state simulations for finite and infinite chains, respectively. The long-lived stability of spatiotemporal order identified in this work does not rely on Floquet prethermalization nor on eigenstate order, but rather on the nonperturbative origin of vacuum-decay processes. We point out the experimental relevance of this new mechanism for stabilizing a long-lived time-crystalline response in Rydberg-dressed spin chains.
2022
12
3
1
34
031037
https://doi.org/10.1103/PhysRevX.12.031037
https://arxiv.org/abs/2110.14705
Collura, Mario; De Luca, Andrea; Rossini, Davide; Lerose, Alessio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/135892
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