Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study
Although the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field theories, however it typically requires numerical calculation to...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2013-01-01
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| Series: | New Journal of Physics |
| Online Access: | https://doi.org/10.1088/1367-2630/15/7/073048 |
| _version_ | 1797751384534155264 |
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| author | Stephen Inglis Roger G Melko |
| author_facet | Stephen Inglis Roger G Melko |
| author_sort | Stephen Inglis |
| collection | DOAJ |
| description | Although the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field theories, however it typically requires numerical calculation to access them in interacting theories. In this paper, we use large-scale T = 0 quantum Monte Carlo simulations to examine in detail the second Rényi entropy of entangled regions at the QCP in the transverse-field Ising model in 2 + 1 space–time dimensions—a fixed point for which there is no exact result for the scaling of entanglement entropy. We calculate a universal coefficient of a vertex-induced logarithmic scaling for a polygonal entangled subregion, and compare the result to interacting and non-interacting theories. We also examine the shape-dependence of the Rényi entropy for finite-size toroidal lattices divided into two entangled cylinders by smooth boundaries. Remarkably, we find that the dependence on cylinder length follows a shape-dependent function calculated previously by Stephan et al (2013 New J. Phys. 15 015004) at the QCP corresponding to the 2 + 1 dimensional quantum Lifshitz free scalar field theory. The quality of the fit of our data to this scaling function, as well as the apparent cutoff-independent coefficient that results, presents tantalizing evidence that this function may reflect universal behaviour across these and other very disparate QCPs in 2 + 1 dimensional systems. |
| first_indexed | 2024-03-12T16:48:44Z |
| format | Article |
| id | doaj.art-8846749b68bb45dcaf1104856eb74e98 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:48:44Z |
| publishDate | 2013-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-8846749b68bb45dcaf1104856eb74e982023-08-08T11:28:16ZengIOP PublishingNew Journal of Physics1367-26302013-01-0115707304810.1088/1367-2630/15/7/073048Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo studyStephen Inglis0Roger G Melko1Department of Physics and Astronomy, University of Waterloo , Ontario N2L 3G1, CanadaDepartment of Physics and Astronomy, University of Waterloo , Ontario N2L 3G1, Canada; Perimeter Institute for Theoretical Physics , Waterloo, Ontario N2L 2Y5, CanadaAlthough the leading-order scaling of entanglement entropy is non-universal at a quantum critical point (QCP), sub-leading scaling can contain universal behaviour. Such universal quantities are commonly studied in non-interacting field theories, however it typically requires numerical calculation to access them in interacting theories. In this paper, we use large-scale T = 0 quantum Monte Carlo simulations to examine in detail the second Rényi entropy of entangled regions at the QCP in the transverse-field Ising model in 2 + 1 space–time dimensions—a fixed point for which there is no exact result for the scaling of entanglement entropy. We calculate a universal coefficient of a vertex-induced logarithmic scaling for a polygonal entangled subregion, and compare the result to interacting and non-interacting theories. We also examine the shape-dependence of the Rényi entropy for finite-size toroidal lattices divided into two entangled cylinders by smooth boundaries. Remarkably, we find that the dependence on cylinder length follows a shape-dependent function calculated previously by Stephan et al (2013 New J. Phys. 15 015004) at the QCP corresponding to the 2 + 1 dimensional quantum Lifshitz free scalar field theory. The quality of the fit of our data to this scaling function, as well as the apparent cutoff-independent coefficient that results, presents tantalizing evidence that this function may reflect universal behaviour across these and other very disparate QCPs in 2 + 1 dimensional systems.https://doi.org/10.1088/1367-2630/15/7/073048 |
| spellingShingle | Stephen Inglis Roger G Melko Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study New Journal of Physics |
| title | Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study |
| title_full | Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study |
| title_fullStr | Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study |
| title_full_unstemmed | Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study |
| title_short | Entanglement at a two-dimensional quantum critical point: a T = 0 projector quantum Monte Carlo study |
| title_sort | entanglement at a two dimensional quantum critical point a t 0 projector quantum monte carlo study |
| url | https://doi.org/10.1088/1367-2630/15/7/073048 |
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