Emergent locality in systems with power-law interactions

Luitz, David J.; Lev, Yevgeny Bar

doi:10.1103/physreva.99.010105

Cited by 51 publications

(51 citation statements)

References 56 publications

(113 reference statements)

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“…In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large α. This result parametrically improves previous bounds [4][5][6][7], compares favorably with recent numerical simulations [8,9], and can be realized in quantum simulators with dipolar interactions [10,11]. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems [6,12], and improve bounds on environmental decoherence in experimental quantum information processors.Almost five decades ago, Lieb and Robinson proved that spatial locality implies the ballistic propagation of quantum information [1].…”

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confidence: 75%

“…Our results are very similar to the numerical simulations of [8], where it was argued that a finite speed of scrambling arises for α 1.8 in a model with timedependent random Hamiltonian. However, in another model with fixed Hamiltonian [9], it was found that α 1 marked the onset of the finite scrambling speed. We expect that (6) holds with α = α for all models, including those which are not (by our definition) frustrated.…”

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confidence: 97%

“…If such bounds were tight, then insulating a quantum processor from its environment would be absolutely crucial. Yet numerical simulations cast into doubt the tightness of these formal bounds: two groups have recently shown that t s r in one dimensional models with α 1.8 [8] or even α > 1 [9], depending on microscopic details.…”

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confidence: 99%

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Finite Speed of Quantum Scrambling with Long Range Interactions

2019

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In a locally interacting many-body system, two isolated qubits, separated by a large distance r, become correlated and entangled with each other at a time t ≥ r/v [1]. This finite speed v of quantum information scrambling limits quantum information processing [2], thermalization [3] and even equilibrium correlations [4]. Yet most experimental systems contain long range power law interactions -qubits separated by r have potential energy V (r) ∝ r −α . Examples include the long range Coulomb interactions in plasma (α = 1) and dipolar interactions between spins (α = 3). In one spatial dimension, we prove that the speed of quantum scrambling remains finite for sufficiently large α. This result parametrically improves previous bounds [4][5][6][7], compares favorably with recent numerical simulations [8,9], and can be realized in quantum simulators with dipolar interactions [10,11]. Our new mathematical methods lead to improved algorithms for classically simulating quantum systems [6,12], and improve bounds on environmental decoherence in experimental quantum information processors.Almost five decades ago, Lieb and Robinson proved that spatial locality implies the ballistic propagation of quantum information [1]. Intuitively defining a "scrambling time" t s (r) by the time at which an initially isolated qubit can significantly entangle with another a distance r away, locality implies that t s (r)r. This result has deep implications in theoretical physics: emergent spacetime locality arising from microscopic quantum mechanics without manifest relativistic invariance may play a crucial role in understanding quantum gravity through the holographic correspondence [13]. Moreover, if quantum information can only propagate with a finite speed, a classical computer can efficiently approximate early time quantum dynamics [12], and a quantum information processor with short-range interactions cannot become entangled with an infinite environment arbitrarily quickly [14,15], despite the exponentially large Hilbert space in many-body quantum systems.While the Lieb-Robinson theorem is quite elegant, it is not useful for a typical quantum information processor. A qubit in an experimental device is usually a spin or atomic degree of freedom, or Josephson junction. Such objects generically interact with long range interactions, and until now, whether locality of quantum scrambling necessarily persists in the presence of long range interactions has remained unclear. In 2005, Hastings and Koma used the canonical Lieb-Robinson theorem to prove that when α > d, t s (r) log r [4]; more recently, this bound has been improved for α > 2d to t s (r) r (α−2d)/(α−d) [6]. If such bounds were tight, then insulating a quantum processor from its environment would be absolutely crucial. Yet numerical simulations cast into doubt the tightness of these formal bounds: two groups have recently shown that t s r in one dimensional models with α 1.8 [8] or even α > 1 [9], depending on microscopic details.In this letter, we prove that t s (r) r whenever α > 3...

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Finite Speed of Quantum Scrambling with Long Range Interactions

2019

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“…Discussion.-In this work, using a numerically exact method, we studied transport in a disordered spin-chain with interactions between the spins decaying as x −α with distance. For clean systems and α > d/2 the long-range interaction appears to be a perturbative effect which is manifested by power-law tails of the relevant excitation profile, while the dynamics of the bulk of the excitation is governed by the local interactions [59,80]. Carrying over this analysis to long-range disordered systems suggests localization, since local interacting systems exhibit MBL at sufficiently strong disorder.…”

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confidence: 95%

Spin transport in a long-range-interacting spin chain

Kloss

Lev

2019

Phys. Rev. A

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Using a numerically exact technique we study spin transport and the evolution of spin-density excitation profiles in a disordered spin-chain with long-range interactions, decaying as a power-law, r −α with distance and α < 2. Our study confirms the prediction of recent theories that the system is delocalized in this parameters regime. Moreover we find that for α > 3/2 the underlying transport is diffusive with a transient super-diffusive tail, similarly to the situation in clean long-range systems. We generalize the Griffiths picture to long-range systems and show that it captures the essential properties of the exact dynamics.Introduction.-Many-body localization (MBL) extends the notion of Anderson localization to interacting systems [1]. For local interactions, its existence is well established theoretically [2, 3] and experimentally in one-dimensional systems [4-6] (see [7] for a recent review), but there is evidence of localization also in twodimensional systems [8][9][10][11][12][13]. For long-range interactions the fate of MBL is less clear. Some studies suggest that the many-body localization is stable for α > 2d [14-17], and some claim that the system is delocalized for all α in the thermodynamic limit [17][18][19]. Finite size systems of size L are claimed to exhibit an effective many-body-like localization transition at a critical disorder which scales with the system size (as a power-law for α < 2d), and diverges in the thermodynamic limit [14,16,17,19,20]. Understanding the dynamics of disordered systems with long-range interactions is of great importance to a number of physical systems, such as nuclear spins [21], dipoledipole interactions of vibrational modes [22][23][24], Frenkel excitons [25], nitrogen vacancy centers in diamond [26][27][28][29][30] and polarons [31]. Long range interactions are also common in atomic and molecular systems, where interactions can be dipolar [32][33][34][35][36][37], van der Waals like [32,38], or even of variable range [39][40][41][42]. Some aspects of the dynamics in such systems were studied numerically in Ref. [43], analytically in Ref. [44] and experimentally in Ref. 45, however spin transport in such systems was not considered.The delocalized phase of one-dimensional systems with local interactions, shows subdiffusive transport [46][47][48][49][50], accompanied by sublinear growth of the entanglement entropy [51][52][53] and intermediate statistics of eigenvalue spacing [54]. Anomalous transport is commonly explained by rare insulating regions, which effectively suppress transport in one-dimensional systems. This mechanism is known as the Griffith's picture [48,55,56] (see Ref.[57] for a recent review and also Ref.[58] were rare regions were introduced externally). In dimensions higher than one the Griffiths picture predicts diffusion, since rare regions can be circumvented [56], however approximate numerical studies [8] as also recent experiments [10,11] suggest that at least for short to inter-arXiv:1911.07857v1 [cond-mat.dis-nn]

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“…Another intriguing question is how the interplay between partial correlations in hopping and interaction amplitudes could affect localization properties in many-body systems with either or both hopping and interaction terms being longranged in the coordinate space. Specifically, the limiting fullycorrelated case of the interacting version of Burin-Maksimov model was recently analyzed in [60,[72][73][74][75][76], and the opposite situation without any constraints was considered in details in [77][78][79][80][81][82]. However, the intermediate regime represented by both finite means and dispersion in distribution functions of matrix elements needs deep consideration.…”

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confidence: 99%

Robustness of delocalization to the inclusion of soft constraints in long-range random models

Nosov

Khaymovich

2019

Phys. Rev. B

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Motivated by the constrained many-body dynamics, the stability of the localization-delocalization properties to the inclusion of the soft constraints is addressed in random matrix models. These constraints are modeled by correlations in long-ranged hopping with Pearson correlation coefficient different from zero or unity. Counterintuitive robustness of delocalized phases, both ergodic and (multi)fractal, in these models is numerically observed and confirmed by the analytical calculations. First, matrix inversion trick is used to uncover the origin of such robustness. Next, to characterize delocalized phases a method of eigenstate calculation, sensitive to correlations in long-ranged hopping terms, is developed for random matrix models and approved by numerical calculations and previous analytical ansatz. The effect of the robustness of states in the bulk of the spectrum the inclusion of to soft constraints is generally discussed for single-particle and many-body systems.

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Emergent locality in systems with power-law interactions

Cited by 51 publications

References 56 publications

Finite Speed of Quantum Scrambling with Long Range Interactions

Finite Speed of Quantum Scrambling with Long Range Interactions

Spin transport in a long-range-interacting spin chain

Robustness of delocalization to the inclusion of soft constraints in long-range random models

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