Study of classical and quantum models on the stuffed honeycomb lattice

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2021-12
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Sahoo, Jyotisman
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Flint, Rebecca
Orth, Peter P
McQueeney, Robert J
Tuchin, Kirill
Miller, Gordon J
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Physics and Astronomy
Abstract
We study the stuffed honeycomb lattice, which consists of a honeycomb lattice with a superimposed triangular lattice formed by sites at the center of each hexagon. This lattice encompasses and interpolates between the honeycomb, triangular and dice lattices, preserving the hexagonal symmetry unlike the previously studied anisotropic lattices. We looked at its classical phase diagram through a mix of analytical and numerical techniques and argued the existence of an expanded spin liquid region around the triangular lattice limit. A finite field study mainly motivated by the S = 7/2 candidate, GdInO_3, revealed its connection to the triangular lattice phases in a magnetic field and more interestingly the effect of inversion breaking interactions and its competition with quantum fluctuations. In chapter 2, we use a combination of iterative minimization, classical Monte Carlo and analytical techniques to determine the complete ground state phase diagram. In particular, our analysis reveals the triangular lattice critical point to be a multicritical point with two new phases vanishing via second order transitions at the critical point. We analyze these phases within linear spin wave theory and discuss consequences for the S = 1/2 spin liquid. In chapter 3, we use a projective symmetry group analysis to determine all symmetric spin liquids on the stuffed honeycomb lattice Heisenberg model and additionally gain valuable insight into potential spin liquids on the honeycomb and triangular lattices, as well as how they might be connected. In particular, we find three stuffed honeycomb descendants of the U(1) Dirac spin liquid widely believed to be found on the J_1-J_2 triangular lattice. In chapter 4, we perform a semi-classical analysis to further strengthen the evidence of an expanded spin liquid region in the S=1/2 stuffed honeycomb Heisenberg model predicted by exact diagonalization. In chapter 5, apart from the effect of field in the generic stuffed honeycomb, we also argue the existence of Dzyaloshinskii-Moriya interactions in the stuffed honeycomb candidate, GdInO_3, to explain an anomalous 2/3 magnetization jump. We show how the competition between DM interactions and quantum fluctuations generates additional first order phase transitions that can explain the 2/3 magnetization jump. Chapter 6 ties up the key results from the separate projects discussed in this thesis into a general conclusion where I also motivate future directions of research.
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