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The two-dimensional Jordan-Wigner transformation is used to investigate the zero temperature spin-Peierls transition for an anisotropic two-dimensional XY model in adiabatic limit. The phase diagram between the dimerized (D) state and uniform (U) state is shown in the parameter space of dimensionless interchain coupling $h$ $(=J_{perp}/J)$ and spin-lattice coupling $eta$. It is found that the spin-lattice coupling $eta$ must exceed some critical value $eta_c$ in order to reach the D phase for any finite $h$. The dependence of $eta_c$ on $h$ is given by $-1/ln h$ for $hto 0$ and the transition between U and D phase is of first-order for at least $h>10^{-3}$.
For broad nanoscale applications, it is crucial to implement more functional properties, especially those ferroic orders, into two-dimensional materials. Here GdI$_3$ is theoretically identified as a honeycomb antiferromagnet with large $4f$ magnetic
We consider the one-dimensional extended Hubbard model in the presence of an explicit dimerization $delta$. For a sufficiently strong nearest neighbour repulsion we establish the existence of a quantum phase transition between a mixed bond-order wave
Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change
The renormalization group flows of the one-dimensional anisotropic XY model and quantum Ising model under a transverse field are obtained by different multiscale entanglement renormalization ansatz schemes. It is shown that the optimized disentangler
Earlier Monte-Carlo calculations on the dissipative two-dimensional XY model are extended in several directions. We study the phase diagram and the correlation functions when dissipation is very small, where it has properties of the classical 3D-XY t