Quantum Time Crystals from Hamiltonians with Long-Range Interactions

Kozin, V. K.; Kyriienko, Oleksandr

doi:10.1103/physrevlett.123.210602

Cited by 118 publications

(65 citation statements)

References 58 publications

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“…The first class comprises quantum scarred models [10][11][12][13] that avoid relaxation for special but physically relevant initial conditions. The second class of systems that defy relaxation to equilibrium are quantum time crystals [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], where time-translation symmetry breaking occurs for typical states, or equivalently, on the level of dynamical response functions [30,33].…”

Section: Introductionmentioning

confidence: 99%

Rigorous bounds on dynamical response functions and time-translation symmetry breaking

Medenjak¹,

Prosen

Zadnik

2020

SciPost Phys.

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Dynamical response functions are standard tools for probing local physics near the equilibrium. They provide information about relaxation properties after the equilibrium state is weakly perturbed. In this paper we focus on systems which break the assumption of thermalization by exhibiting persistent temporal oscillations. We provide rigorous bounds on the Fourier components of dynamical response functions in terms of extensive or local dynamical symmetries, i.e., extensive or local operators with periodic time dependence. Additionally, we discuss the effects of spatially inhomogeneous dynamical symmetries. The bounds are explicitly implemented on the example of an interacting Floquet system, specifically in the integrable Trotterization of the Heisenberg XXZ model.

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Section: Introductionmentioning

confidence: 99%

Rigorous bounds on dynamical response functions and time-translation symmetry breaking

Medenjak¹,

Prosen

Zadnik

2020

SciPost Phys.

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“…Usually, random white noise fluctuations are expected by the thermal equilibrium movement. Such regular oscillation also constitutes a natural occurrence of Floquet states with its electronic structure, and Hamiltonian exhibiting periodicity 16 . Dynamics of electron and atoms is simulated for 1200 fs by rt-TDDFT.…”

Section: Resultsmentioning

confidence: 99%

Electron-phonon coupling induced intrinsic Floquet electronic structure

Song

Wang

2020

npj Quantum Mater.

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Floquet states are a topic of intense contemporary interest, which is often induced by coherent external oscillating perturbation (e.g., laser, or microwave) which breaks the continuous time translational symmetry of the systems. Usually, electron–phonon coupling modifies the electronic structure of a crystal as a non-coherent perturbation and seems difficult to form Floquet states. Surprisingly, we found that the thermal equilibrium electron–phonon coupling in M(MoS)3 and M(MoSe)3 (where M is a metallic element) exhibits a coherent behavior, and the electronic structure can be described by the Floquet theorem. Such a coherent Floquet state is caused by a selective giant electron–phonon coupling, with thermodynamic phonon oscillation serving as a driving force on the electronic part of the system. The quasi-1D Dirac cone at the Fermi energy has its band gap open and close regularly. Similarly, the electric current will oscillate even under a constant voltage.

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“…The concept of a time crystal, that is, a state which spontaneously breaks time translation symmetry, has been hotly debated [23,[34][35][36] following its initial proposal [37]. The difficulties arising in its formulation were sidestepped by considering periodically driven systems, for which a precise definition of a DTC was put forward in Ref.…”

Section: Discrete Time Crystalmentioning

confidence: 99%

Discrete time crystal in the gradient-field Heisenberg model

Dyke

Warren

et al. 2020

Phys. Rev. B

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We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients. Specifically, we study a finite Heisenberg spin chain in the presence of a gradient field, which can be realized experimentally in quantum dot systems using micromagnets or nuclear spin polarization. Our numerical simulations reveal time crystalline order over a broad range of realistic quantum dot parameters, as evidenced by the long-time preservation of spin expectation values and the asymptotic form of the mutual information. We also consider the undriven system and present several diagnostics for many-body localization that are complementary to those recently studied. Our results show that these non-ergodic phases should be realizable in modest-sized quantum dot spin arrays using only demonstrated experimental capabilities. arXiv:1912.05130v1 [quant-ph]

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Quantum Time Crystals from Hamiltonians with Long-Range Interactions

Cited by 118 publications

References 58 publications

Rigorous bounds on dynamical response functions and time-translation symmetry breaking

Rigorous bounds on dynamical response functions and time-translation symmetry breaking

Electron-phonon coupling induced intrinsic Floquet electronic structure

Discrete time crystal in the gradient-field Heisenberg model

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