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Exploring signatures of magnetic order in entanglement properties of finite-size two-dimensional quantum XXZ antiferromagnets at zero temperature - asymptotic behaviour and crossover phenomena

Fossheim, Andreas Götestam
Master thesis
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URI
https://hdl.handle.net/11250/2785515
Date
2020
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Abstract
I denne oppgaven ble entanglement-entropien, og dens generalisering Rényi-entropien, til den magnetisk ordnede grunntilstanden i to-dimensjonale endelige antiferromagneter studert ved hjelp av modifisert lineær spin-bølge-teori. En utvidelse av rammeverket utviklet i Ref. \citenum{DVJO} til en XXZ-model ble forsøkt. I easy plane-tilfellet ble det demonstrert analytisk for et gitt subsystem at det første subdominante leddet var universelt med en prefaktor $N_G/2$ i samsvar med predikasjonen i Ref. \citenum{MG}, hvor $N_G$ er antallet Goldstone-moder. En scaleringsfunskjon som viser hvordan systemet effektivt går fra å ha tre Goldstone-moder i Heisenberg-modellen til å ha kun én når anisotropien økte ble også funnet. I easy axis-tilfellet mislyktes modifiseringen av spin-bølge-teorien for modeller med kollineær orden ettersom de ikke ville bryte noen kontinuerlige symmetrier. For ikke-kollineær orden kan prosedyren fortsatt fungere, men dens beskrivelse vil ikke bli dekket av rammeverket utviklet her.
 
In this thesis, the entanglement entropy and its generalization, the Rényi entropy, of the magnetically ordered ground state of two-dimensional finite-size antiferromagnets is studied by means of modified linear spin wave theory. An extension of the framework developed in Ref. \citenum{DVJO} to an XXZ-model was attempted. In the easy plane-case, the first subleading term was for a particular choice of subsystem analytically demonstrated to be universal with a prefactor $N_G/2$ in accordance with the prediction of Ref. \citenum{MG}, where $N_G$ is the number of Goldstone modes. Furthermore, a scaling function was found showing how the system crosses over from effectively having two or three Goldstone modes near the pure Heisenberg model, to having only one as the anisotropy parameter is increased. In the easy axis-case, the modification of the spin wave theory fails for collinear types of order as they will have no broken continuous symmetries. For non-collinear order the procedure may still work, but its description will no longer fit into the framework developed here.
 
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NTNU

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