Here we introduce some of our works on kagome lattice.

The ground state of the S=1/2 kagome lattice antiferromagnet is considered to be a possible spin liquid. [see Han et al, 2012, Mendels, 2007 for experiments] In theories, [ for early studies Poilblanc, Misguish, Read-Sachdev, etc.], there are several measure for spin liquids. One is the topological term in the entanglement entropy, which is actually calculated for kagome lattice and its analogues by Jiang et al. and Depenbrock et al. in 2012. However, notice that this quantity has a nonnegligible size effect. There are other ways, such as examining the topological degeneracy by making use of the cylinder construction, or by plotting the entanglement spctrum [for chiral spin liquid in decorated kagome, Gong-Zhu-Sheng 2014].

There is a long discussion on whether the ground state of the kagome lattice antiferromagnet is spin gapped or not, and if yes, how large it should be. The old ED paper by Waldtmann, et al.1998 gives the size of the gap~J/20 based on the even and odd size scaling. The DMRG calculation keeping the aspect ratio to 1 is made by Jiang-Weng-Sheng 2008 which also gives J/20. The papers by Yan-Huse-White, Depenbrock-McCulloch-Schollwock [cylinder DMRG] concludes from their analysis that the value is at around J/10. He-Zaletel-Oshikawa-Pollmann[cylinder DMRG + boundary shift] says that it is gapless (Dirac). In our paper [Nishimoto-Shibata-Hotta 2013] we consider that the cylinderical construction overestimates the gap (it is actually demonstrated in the supplementary) and we expect the gap to be as small as J/20 (or smaller) by the small step in the magnetization curve at around zero field.

Recently, by evaluating the finite temperature susceptibility [Hotta-Asano, PRB

In [Nishimoto-Shibata-Hotta Nature Comm.

The phase just below the 5/9 plateau can be a supersolid [Plat-Momoi-Hotta PRB

We have recently developed a numerical method to exactly obtain the response functions against the weak to strong external field, [χ(q,ω)]. [Endoh-Hotta-Shimizu PRL

By applying this method to the kagome lattice antiferromagnet, we obtained an excitation spectrum [Im chi(q,omega)] in both the linear and nonlinear response regimes. The exotic features of the kagome lattice is observed: There is a broad peak at low energy part of the spectrum whose shape does not show any significant k(wave number)-dependence. This may indicate that there is a spinon excitation from the ground state, and it does not depend on k (nearly localized?).

This is the old work [Pollmann-Roychowdhury-Hotta-Penc, PRB