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Spin liquids in quantum antiferromagnetic models on two dimensional frustrated lattices.

Yasir Dr. Iqbal 1 
1 FFC - Fermions Fortement Corrélés (LPT)
LPT - Laboratoire de Physique Théorique
Abstract : The journey in search of exotic magnetic phases of matter which melt even at T=0 solely under the strength of quantum fluctuations, has been long and arduous both on the theoretical and experimental fronts. The breakthrough came quite recently, with the discovery of Herbertsmithite, a geometrically perfect kagome lattice compound with spin-1/2 magnetic moments. Pioneering experiments using NMR, µSR, and neutron scattering showed a complete absence of frozen or ordered spin magnetic moments, thus providing strong signatures of a quantum paramagnetic phase. Theoretically, Herbertsmithite is extremely well modeled by the spin-1/2 quantum Heisenberg antiferromagnet on the kagome lattice, a solution of which remains till date a critically outstanding problem. Several approximate numerical and analytical approaches have vouched for different ground states, ranging from gapped topological Z2 spin liquids and an exotic algebraic U(1) Dirac spin liquid to chiral spin liquids and valence-bond crystals. In this thesis, the problem is attacked within the realm of a fermionic slave-particle approach, namely the SU(2) Schwinger fermion formalism. It is concluded that a gapless algebraic U(1) Dirac spin liquid has the lowest variational energy and can in fact occur as a real physical spin liquid ground state. A sophisticated implementation of state-of-the-art numerical techniques such as variational quantum Monte Carlo, Green's function Monte Carlo, and application of Lanczos steps within a variational scheme have been used. It is shown that contrary to conventional wisdom, the projected U(1) Dirac spin liquid in "2+1" dimensions is remarkably robust towards a wide class of perturbations that include topological Z2 spin liquids and valence-bond crystals. Furthermore, the application of a couple of Lanczos steps on the U(1) Dirac spin liquid wave function shows that its energy is competitive with previously proposed topological Z2 spin liquids. This fact combined with experimental insights which point towards a gapless spin liquid in Herbertsmithite, lend support to the claim that the true ground state of the model is in fact an algebraic U(1) Dirac spin liquid.
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Submitted on : Tuesday, November 19, 2013 - 5:40:36 PM
Last modification on : Monday, July 4, 2022 - 9:51:34 AM
Long-term archiving on: : Saturday, April 8, 2017 - 1:48:21 AM


  • HAL Id : tel-00752096, version 2



Yasir Dr. Iqbal. Spin liquids in quantum antiferromagnetic models on two dimensional frustrated lattices.. Strongly Correlated Electrons [cond-mat.str-el]. Université Paul Sabatier - Toulouse III, 2012. English. ⟨NNT : ⟩. ⟨tel-00752096v2⟩



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