Topological Quantum Liquids with Long-Range Couplings

Patrick, Kristian; Neupert, Titus; Pachos, Jiannis K.

doi:10.1103/physrevlett.118.267002

Cited by 46 publications

(32 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This implies that the entanglement entropy may violate the area law while the system is non critical. This happens in the so-called Long-Range Kitaev chain [8,9], which has been the object of an intense study in the last years [10][11][12][13][14]. Apart from the theoretical interest, as a model to analyse the role of conformal symmetry in critical points, there has been recently a spectacular development of experimental devices where these long range interactions can be simulated [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy in the long-range Kitaev chain

et al. 2018

View full text Add to dashboard Cite

In this paper we complete the study on the asymptotic behaviour of the entanglement entropy for Kitaev chains with long range pairing. We discover that when the couplings decay with the distance with a critical exponent new properties for the asymptotic growth of the entropy appear. The coefficient of the leading term is not universal any more and the connection with conformal field theories is lost.We perform a numerical and analytical approach to the problem showing a perfect agreement. In order to carry out the analytical study, a new technique for computing the asymptotic behaviour of block Toeplitz determinants with discontinuous symbols has been developed.

show abstract

Section: Introductionmentioning

confidence: 99%

Entanglement entropy in the long-range Kitaev chain

et al. 2018

View full text Add to dashboard Cite

show abstract

“…Even more interestingly, very recent works [26,28,29,[35][36][37][38][39][40][41][42][43] have suggested that LR systems can host new phases at sufficiently small values of the decay exponents α for the Hamiltonian terms. These phases often manifest interesting features not owned by the SR ones, including continuous quantum phase transitions without mass gap closure, violation of the area-law for the von Neumann entropy and of the Mermin-Wagner theorem, emergence of massive edge states.…”

Section: Introductionmentioning

confidence: 99%

Long-range topological insulators and weakened bulk-boundary correspondence

Lepori

Dell’Anna

2017

New J. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…Generalization to long-range Kitaev chain and higher dimensions.-We further give an example of a Kitaev chain with long-range pairing [54][55][56][57]:…”

mentioning

confidence: 99%