Long-range interacting quantum systems

Defenu, Nicolò; Donner, Tobias; Macrì, Tommaso; Pagano, Guido; Ruffo, Stefano; Trombettoni, Andrea

doi:10.48550/arxiv.2109.01063

Cited by 47 publications

(118 citation statements)

References 590 publications

(861 reference statements)

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“…In the latter approach, the longrange XXZ model can be simulated in two steps: a set of radial normal modes can be used to induce an XY antiferromagnetic coupling by asymmetrically driving the spinmotion couplings 69 . This procedure creates an effective magnetic field along the z direction allowing to retain only the spin preserving parts of the Ising interactions 59 .…”

Section: Trapped-ion Implementationmentioning

confidence: 99%

Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model

Macrì,

Lepori,

Pagano

et al. 2021

Preprint

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Experimental platforms based on trapped ions, cold molecules, and Rydberg atoms have made possible the investigation of highly-nonlocal spin-1/2 Hamiltonians with long-range couplings. Here, we study the effects of such non-local couplings in the long-range spin-1/2 XXZ Heisenberg Hamiltonian. We calculate explicitly the two-spin energy spectrum, which describes all possible energetic configurations of two spins pointing in a specific direction embedded in a background of spins with opposite orientation. For fast decay of the spin-spin couplings, we find that the two-spin energy spectrum is characterized by well-defined discrete values, corresponding to bound states, separated by a set of continuum states describing the scattering region. In the deep long-range regime instead, the bound states disappear as they get incorporated by the scattering region. The presence of two-spin bound states results to be crucial to determine both two-and many-spin dynamics. On one hand, radically different two-spin spreadings can be observed by tuning the decay of the spin couplings. On the other hand, two-spin bound states enable the dynamical stabilization of effective antiferromagnetic states in the presence of ferromagnetic couplings. Finally, we propose a novel scheme based on a trapped-ion quantum simulator to experimentally realize the long-range XXZ model and to study its out-of-equilibrium properties.

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Section: Trapped-ion Implementationmentioning

confidence: 99%

Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model

Macrì,

Lepori,

Pagano

et al. 2021

Preprint

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“…In this work we investigate the non-Hermitian dynamics of a mesoscopic system of few particles coupled via long-range interactions among them [57]. We find that the interactions and geometric arrangement of coupled spins enrich the PT phase diagrams (Sec.…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian dynamics and $\mathcal{PT}$-symmetry breaking in interacting mesoscopic Rydberg platforms

Lourenço,

Higgins,

Zhang

et al. 2021

Preprint

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We simulate the dissipative dynamics of a mesoscopic system of long-range interacting particles which can be mapped into non-Hermitian spin models with a PT symmetry. We find rich PTphase diagrams with PT -symmetric and PT -broken phases. The dynamical regimes can be further enriched by modulating tunable parameters of the system. We outline how the PT symmetries of such systems may be probed by studying their dynamics. We note that systems of Rydberg atoms and systems of Rydberg ions with strong dipolar interactions are particularly well suited for such studies. We show that for realistic parameters, long-range interactions allow the emergence of new PT -symmetric regions, generating new PT -phase transitions. In addition, such PT -symmetry phase transitions are found by changing the Rydberg atoms configurations. We monitor the transitions by accessing the populations of the Rydberg states. Their dynamics display oscillatory or exponential dependence in each phase.

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“…To better understand the different aspects of MBL, several quantum information concepts [10][11][12][13][14][15][16] have been theoretically developed and several experiments on newly emerging quantum simulators have been performed [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Most of the MBL literature have been dedicated to 1D short-range interactions, however, several fundamental problems remain open for systems with long-range couplings [34,35]. These systems are very relevant as many interactions in nature are inherently long-ranged and certain quantum simulators, e.g.…”

mentioning

confidence: 99%

“…These long-range couplings can now be realized in ion trap [71,72] systems. Many types of long-range models [34,35] such as Coulomb, van der Waals and dipole-dipole interactions, are special cases of Hamiltonian H. We systematically investigate two different regimes: (i) uniform couplings in which a=b; and (ii) nonuniform couplings in which b is finite (power-law Ising interaction) and a→∞ (nearest-neighbor tunneling).…”

mentioning

confidence: 99%

Floquet-induced localization in long-range many-body systems

Yousefjani¹,

Bose²,

Bayat³

2022

Preprint

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The fate of many-body localization in long-range interacting systems is not fully settled and several open problems still exist. For instance, the phase boundary between ergodic and many-body localized regimes has yet to be fully determined. In addition, the dynamical growth of entanglement in the many-body localized phase of such systems is under debate. Here, we introduce a Floquet dynamics which can induce many-body localization in a disorder-free long-range interacting system through temporal random local rotations. The phase diagram has been determined for two types of long-range couplings. Interestingly, our Floquet mechanism shows more localizing power than conventional static disorder methods as it pushes the phase transition boundary in favor of the many-body localized phase. Moreover, our comprehensive long-time simulations reveal that in longrange many-body localized systems the entanglement grows as ∼ (ln t) γ (for some constant γ). This is in sharp contrast with the conjecture of algebraic growth, in previous perturbative studies, and can smoothly recover the well-known logarithmic entanglement growth in short-range interacting systems.

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Long-range interacting quantum systems

Cited by 47 publications

References 590 publications

Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model

Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model

Non-Hermitian dynamics and $\mathcal{PT}$-symmetry breaking in interacting mesoscopic Rydberg platforms

Floquet-induced localization in long-range many-body systems

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