Abstract
We investigate the finite-size scaling of the entanglement gap in the one-dimensional long-range quantum spherical model (QSM). We focus on the weak long-range QSM, for which the thermodynamic limit is well-defined. This model exhibits a continuous phase transition, separating a paramagnetic from a ferromagnet phase. The universality class of the transition depends on the long-range exponent α. We show that in the thermodynamic limit the entanglement gap is finite in the paramagnetic phase, and it vanishes in the ferromagnetic phase. In the ferromagnetic phase the entanglement gap is understood in terms of standard magnetic correlation functions. The half-system entanglement gap decays as δξ ≃ CαL−(1/2−α/4), where the constant Cα depends on the low-energy properties of the model and L is the system size. This reflects that the lower part of the dispersion is affected by the long range physics. Finally, multiplicative logarithmic corrections are absent in the scaling of the entanglement gap, in contrast with the higher-dimensional case.
| Original language | English |
|---|---|
| Article number | 245002 |
| Number of pages | 31 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 56 |
| Issue number | 24 |
| Early online date | 23 May 2023 |
| DOIs | |
| Publication status | Published - 16 Jun 2023 |
Bibliographical note
This is the Accepted Manuscript version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online athttps://dx.doi.org/10.1088/1751-8121/acd232
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Keywords
- entanglement
- entanglement gap
- quantum spherical model
- long-range interactions
- one dimensional systems