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Solomon A. Owerre

Publications and source records attributed to Solomon A. Owerre.

4 recordsLinked to original sources
arXiv2023

Frustration, solitons, and entanglement in spin chains

Defects in frustrated antiferromagnetic spin chains are universally present in geometrically frustrated systems. We consider the defects of the one-dimensional, spin-$s$ XXZ chain with single-ion anisotropy on a periodic chain with $N$ sites that was famously studied by Haldane. For $N$ odd the antiferromagnetic model is frustrated, and the ground state must include a soliton defect. We consider the Heisenberg interaction perturbatively and determine the corresponding perturbative solitonic ground state. Then we compute the entanglement spectrum, entanglement entropy (EE), capacity of entanglement (CE), and spin correlations in the solitonic ground state. For weak frustration, we find an algebraic violation of the area law for the EE consistent with recent results on weakly frustrated chains. Our analysis then moves beyond the weak frustration regime, and we obtain a novel extensive scaling law for the EE when strong frustration prevails, signalling large entanglement, and failure of the quasiparticle interpretation in this regime. Enhanced frustration results in less total correlations, but relatively more nonlocal correlations.

cond-mat.str-el↗
arXiv2014

Macroscopic quantum spin tunnelling with two interacting spins

We study the simple Hamiltonian, $H=-K(S_{1z}^2 +S_{2z}^2)+ λ\vec S_1\cdot\vec S_2$, of two, large, coupled spins which are taken equal, each of total spin $s$ with $λ$ the exchange coupling constant. The exact ground state of this simple Hamiltonian is not known for an antiferromagnetic coupling corresponding to the $λ>0$. In the absence of the exchange interaction, the ground state is four fold degenerate, corresponding to the states where the individual spins are in their highest weight or lowest weight states, $|\hskip-1 mm\uparrow, \uparrow\rangle, |\hskip-1 mm\downarrow, \downarrow\rangle, |\hskip-1 mm\uparrow, \downarrow\rangle, |\hskip-1 mm\downarrow, \uparrow\rangle$, in obvious notation. The first two remain exact eigenstates of the full Hamiltonian. However, we show the that the two states $ |\hskip-1 mm\uparrow, \downarrow\rangle, |\hskip-1 mm\downarrow, \uparrow\rangle$ organize themselves into the combinations $|\pm\rangle=\frac{1}{\sqrt 2} (|\hskip-1 mm\uparrow, \downarrow\rangle \pm |\hskip-1 mm\downarrow \uparrow\rangle)$, up to perturbative corrections. For the anti-ferromagnetic case, we show that the ground state is non-degenerate, and we find the interesting result that for integer spins the ground state is $|+\rangle$, and the first excited state is the anti-symmetric combination $|-\rangle$ while for half odd integer spin, these roles are exactly reversed. The energy splitting however, is proportional to $λ^{2s}$, as expected by perturbation theory to the $2s^{\rm th}$ order. We obtain these results through the spin coherent state path integral.

cond-mat.str-el↗
arXiv2013

Spin Wave Theory of Spin 1/2 XY Model with Ring Exchange on a Triangular Lattice

We present the linear spin wave theory calculation of the superfluid phase of a hard-core boson $J$-$K$ model with nearest neighbour exchange $J$ and four-particle ring-exchange $K$ at half filling on the triangular lattice, as well as the phase diagrams of the system at zero and finite temperatures. We find that the pure $J$ model (XY model) which has a well known uniform superfluid phase with an ordered parameter $M_x= \neq 0$ at zero temperature is quickly destroyed by the inclusion of a negative-$K$ ring-exchange interactions, favouring a state with a $(\frac{4π}{3}, 0)$ ordering wavevector. We further study the behaviour of the finite-temperature Kosterlitz-Thouless phase transition ($T_{KT}$) in the uniform superfluid phase, by forcing the universal quantum jump condition on the finite-temperature spin wave superfluid density. We find that for $K \textless 0$, the phase boundary monotonically decreases to T=0 at $K/J = -4/3$, where a phase transition is expected and $T_{KT}$ decreases rapidly while for positive $K$, $T_{KT}$ reaches a maximum at some $K\neq 0$. It has been shown on a square lattice using quantum Monte Carlo(QMC) simulations that for small $K\textgreater 0$ away from the XY point, the zero-temperature spin stiffness value of the XY model is decreased\cite{F}. Our result seems to agree with this trend found in QMC simulations.

cond-mat.str-el↗