Multipartite Entanglement in Topological Quantum Phases

Pezzé, Luca; Gabbrielli, Marco; Lepori, Luca; Smerzi, Augusto

doi:10.1103/physrevlett.119.250401

Cited by 109 publications

(106 citation statements)

References 51 publications

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“…Notably, even there, β remains smaller than 2, implying that multipartite entanglement cannot be detected using local operators involving (linear combinations of) c i and c † i . This results enlarges the picture achieved for the LR Kitaev chain [47,53].…”

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confidence: 62%

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Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

2018

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We study the zero-temperature phase diagram of a two dimensional square lattice loaded by spinless fermions, with nearest-neighbor hopping and algebraically decaying pairing. We find that for sufficiently long-range pairing, new phases occur, not continuously connected with any short-range phase and not belonging to the standard families of topological insulators/superconductors. These phases are signaled by the violation of the area law for the Von Neumann entropy, by semi-integer Chern numbers, and by edge modes with nonzero mass. The latter feature results in the absence of single-fermion edge conductivity, present instead in the short-range limit. The definition of a bulk-topology and the presence of a bulk-boundary correspondence is suggested also for the long-range phases. Recent experimental proposals and advances open the possibility to probe the described long-range effects in near-future realistic set-ups. PACS numbers:Introduction -In recent years, the topological phases of matter have become a central focus for physical investigation. A groundbreaking result is the classification of the symmetry-protected topologically inequivalent classes for non interacting fermionic systems (topological insulators/superconductors) [1][2][3][4][5][6]. This theoretical breakthrough has been probed on particular solid-state compounds [7][8][9][10].Notwithstanding the presence of a nonvanishing bulk energy gap, the most relevant feature displayed by nontrivial topological insulators/superconductors is a conductivity localized on the edges, due to massless edge mode with a dynamics well distinguished from the bulk excitations. Moreover, continuous transitions with a vanishing mass gap generally divide phases with different topology (even if also first order transitions seem possible if perturbative interactions between fermions are added [11]). Regarding the entanglement content, topological insulators/superconductors display exponentially saturating entanglement and correlations, giving rise to the area-law for the Von Neumann entropy between the two elements of a real-space bipartition.These features characterize quantum systems governed by Hamiltonians with short-range (SR) terms. However, in recent years, long-range (LR) classical and quantum systems [12], obtained renewed attention. Independent theoretical works have concluded that LR systems can exhibit many interesting and unusual properties, essentially due to the violation of locality (see e.g. [13][14][15][16][17][18][19][20]). In particular, one-dimensional LR models can host new phases, manifesting striking properties, not present in the SR limit. [15][16][17][21][22][23][24][25][26][27][28][29][30].In spite of these relevant achievements, full comprehension and classification phases emerging from Hamiltonians with LR terms are still not available.In [29] a partial solution to these problems has been discussed, exploiting one-dimensional topological superconductive chains as playgrounds, but inferring nontrivial properties also for LR topological insulators...

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supporting

confidence: 62%

“…Role of the SST at α ≤ 1 -Further insight on the QPT at α = 1 is achieved analyzing the fidelity susceptibility [45][46][47], defined by…”

mentioning

confidence: 99%

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

2018

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“…Some discontinuities, suggesting phase transitions, around a = 1 have been observed, e.g., in the von Neumann entropy at half chain and in the related mutual information, in the Berry phase [39], in the fidelity susceptibility and in the finite-size scaling behaviour of the multipartite entanglement [52].…”

Section: The Phase Diagramsmentioning

confidence: 99%

Long-range topological insulators and weakened bulk-boundary correspondence

Lepori

Dell’Anna

2017

New J. Phys.

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We investigate the appearance of new types of insulators and superconductors in long-range (LR) fermionic quantum systems. These phases are not included in the famous 'ten-fold way classification' (TWC), valid in the short-range (SR) limit. This conclusion is obtained analysing at first specific onedimensional models, in particular their phase diagrams and entanglement properties. The LR phases are signalled, for instance, by the violation of the area-law for the von Neumann entropy and by a corresponding peculiar entanglement spectrum (ES). Later on, the origin of the deviations from the TWC is investigated from a more general point of view and in any dimension, showing that it is related with the presence of divergences occurring in the spectrum, due to the LR couplings. A satisfying characterization for the LR phases can be achieved, at least for one-dimensional quantum systems, as well as the definition of a nontrivial topology for them, resulting in the presence of massive edge states, provided a careful evaluation of the LR contributions. Our results allows to infer, at least for onedimensional models, the weakening of the bulk-boundary correspondence, due to the important correlations between bulk and edges, and consequently to clarify the nature of the massive edge states. The emergence of this peculiar edge structure is signalled again by the bulk ES. The stability of the LR phases against local disorder is also discussed, showing notably that this ingredient can even strengthen the effect of the LR couplings. Finally, we analyse the entanglement content of the paradigmatic LR Ising chain, inferring again important deviations from the SR regime, as well as the limitations of bulk-boundary (tensor-network based) approaches to classify LR spin models.

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“…The interesting physics associated to LR interaction concerns also fermionic lattice systems, characterized by nontrivial topological invariants [36-38, 69, 72-77]. Notably, for these systems, BE is known to characterize only partially the LR regimes, not being able to distinguish in general the different LR phases [38,74], while ME appears to be more indicative [50][51][52].…”

Section: The Modelmentioning

confidence: 99%

“…In particular, ME is able to capture the richness of multiparticle correlations of many-body states beyond BE. The QFI of a quantum states calculated with respect to different operators Ô provides a 'multipartite-entanglement tomography' that gives information not only about ME, but also about global properties of the correlation functions [47][48][49][50][51]. The QFI is thus able to recognize different phases and QPTs of a many-body model.…”

Section: Introductionmentioning

confidence: 99%

Multipartite-entanglement tomography of a quantum simulator

2019

Self Cite

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Multipartite-entanglement tomography, namely the quantum Fisher information (QFI) calculated with respect to different collective operators, allows to fully characterize the phase diagram of the quantum Ising chain in a transverse field with variable-range interaction. In particular, it recognizes the phase stemming from long-range (LR) antiferromagnetic interaction, a capability also shared by the spin squeezing. Furthermore, the QFI locates the quantum critical points, both with vanishing and nonvanishing mass gap. In this case, we also relate the finite-size power-law exponent of the QFI to the critical exponents of the model, finding a signal for the breakdown of conformal invariance in the deep LR regime. Finally, the effect of a finite temperature on the multipartite entanglement, and ultimately on the phase stability, is considered. In light of the current realizations of the model with trapped ions and of the potential measurability of the QFI, our approach yields a promising strategy to probe LR physics in controllable quantum systems.

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Multipartite Entanglement in Topological Quantum Phases

Cited by 109 publications

References 51 publications

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

Edge insulating topological phases in a two-dimensional superconductor with long-range pairing

Long-range topological insulators and weakened bulk-boundary correspondence

Multipartite-entanglement tomography of a quantum simulator

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