Abstract We investigate the influence of exchange interactions on quantum entanglement and magnon Nernst effect in the two-dimensional ferromagnet on honeycomb lattice. We analyze the effect of the variation induced on spin Nernst coefficient induced by the variation of the exchange parameters on entanglement. We use entanglement negativity as quantifier of entanglement and quantum correlations which is a useful measure to study entanglement in mixed state. Moreover, we studied the spin Nernst coefficient where we get that it tends to zero at T = 0, due to absence of thermally excited magnons at zero temperature. Simulations using Lanczos algorithm and exact diagonalization are performed for a finite size lattice and exhibit a behavior for entanglement negativity different from mean field theory.
Quantum Simulation
Strongly interacting fermions in a two-dimensional lattice form a checkerboard pattern, with spins of opposite directions occupying neighboring sites of the lattice. When an external magnetic field is applied, the situation becomes more complicated—should the spins align with the field, or try to preserve the checkerboard order? Brown et al. studied this problem using 6Li atoms in an optical lattice with unequal numbers of two spin components; the imbalance between the two played the role of an effective magnetic field. With the field applied, the checkerboard pattern correlations of the spin component perpendicular to the field became stronger than those of the spin component parallel to the field, indicating that the system was approaching the so-called canted antiferromagnetic state.
Science , this issue p. [1385][1]
[1]: /lookup/doi/10.1126/science.aam7838
We study the spin excitation spectra of the two-dimensional spin-
21 Heisenberg model with a checkerboard structure using stochastic analytic continuation of the imaginary-time correlation function obtained from a quantum Monte Carlo simulation. The checkerboard models have two different antiferromagnetic nearest-neighbor interactions
J1 and
J2, and the tuning parameter
g is defined as
J2/J1. The dynamic spin structure factors are systematically calculated in all phases of the models as well as at the critical points. To give a full understanding of the dynamic spectra, spin wave theory is employed to explain some features of numerical results, especially for the low-energy part. When
g is close to 1, the features of the spin excitation spectra of each checkerboard model are roughly the same as those of the original square lattice antiferromagnetic Heisenberg model, and the high-energy continuum among them is discussed. In contrast to the other checkerboard structures investigated in this paper, the $3\ifmmode\times\else\texttimes\fi{}3$ checkerboard model has distinctive excitation features, such as a gap between a low-energy gapless branch and a gapped high-energy part that exists when
g is small. The gapless branch in this case can be regarded as a spin wave in N\'eel order formed by a ``block spin'' in each $3\ifmmode\times\else\texttimes\fi{}3$ plaquette with an effective exchange interaction originating from renormalization. One unexpected finding is that the continuum also appears in this low-energy branch.