GLYPH<CP> GLYPH<D1> GLYPH<CQ> GLYPH<D1> GLYPH<CG> GLYPH<C7> GLYPH<BG> GLYPH<B4>GLYPH<D9>GLYPH<D4> GLYPH<DB> GLYPH<CP>GLYPH<D6>GLYPH<CS>GLYPH<B5> GLYPH<CG> GLYPH<C7> GLYPH<BG> GLYPH<B4>GLYPH<CS>GLYPH<D3> GLYPH<DB>GLYPH<D2> GLYPH<DB> GLYPH<CP>GLYPH<D6>GLYPH<CS>GLYPH<B5> GLYPH<C5> GLYPH<D4>GLYPH<D6>GLYPH<D3>GLYPH<D8>GLYPH<D3>GLYPH<D2> GLYPH<D7>GLYPH<CX>GLYPH<D8>GLYPH<CT>GLYPH<D7> GLYPH<C5>GLYPH<BP>GLYPH<CA>GLYPH<CQ>GLYPH<B8> GLYPH<BV>GLYPH<D7> GLYPH<CG>GLYPH<BP>GLYPH<CB>GLYPH<B8> GLYPH<CB>GLYPH<CT> GLYPH<CY> GLYPH<C3>GLYPH<CP>GLYPH<CV>GLYPH<D3>GLYPH<D1> GLYPH<AJ> GLYPH<CT> GLYPH<D0>GLYPH<CP>GLYPH<D8>GLYPH<D8>GLYPH<CX> GLYPH<CT> FIG. 1: (Color online) Lattice structure of hydrogen-bonded crystals M 3 H(XO 4 ) 2 where the proton sites form the Kagom´e lattice (right figure). The left figure presents an example of protons order b elow the critical temperature. The solid (red) lines denote hydrogen bonds. arXiv:1001.0808v1[cond-mat.str-el]6 Jan 2010 An experimental candidate to realize this situation is hydrogen-bonded crystals of alkali-hydrosulfates or hydrose- lenates M$_{3}$H(XO$_{4}$)$_{2}$ (M=Cs,Rb,K,Tl, X=S,Se) [5]. These materials exhibit an abrupt change in the electrical conduc- tivity accompanied with a ferroelastic deformation around T$_{c}$ = 400 K: above T$_{c}$ the conductivity within the a - b plane is very high and it seems to be related to the hopping motion of protons, i.e., super-proton conductivity; below T$_{c}$ , the pro- tons appear to be localized in some ordering pattern which satisfies the condition that one tetrahedron of XO − 4 has only one hydrogen bond (see Fig. 1). In the regime where only proton ordering is taken into account, an effective model can provide a description of the protons forming the Kagom´e net- When we turn our attention to itinerant systems on the Kagom´e lattice, a greater variety of physical phenomena can be observed. Of particular interest is the competition of dis- tinct ordered states associated with the charge degrees of free- dom. From this point of view, an intriguing system is that of 1/3-filled Kagom´e lattice fermions. If long-range repul sive interactions are taken into account, there exists a huge num- ber of (nearly) degenerate charge-ordered (CO) states in the strong-coupling regime; a melting of the CO may take place as some ratio of the interaction and hopping. Introduction — For a long time, the exotic phenomena emergent in geometrical frustration have been fascinating but challenging subjects of research in condensed matter physics [1]. An essential difficulty of frustrated systems i s attributed to their highly-degenerate ground states in the clas- sical sense. It is common practice to determine how the degeneracy is removed or how the frustration is minimized by adding quantum fluctuations. On a related issue, one of the most intensively studied systems is quantum spins on the Kagom´e lattice, which consists of corner-sharing trian- gles. Very recently, so-called herbertsmithite has been re- vealed as a promising candidate for an experimental real- ization of an S = 1 / 2 Kagom´e antiferromagnet. Both ex- perimentally [2, 3] and theoretically [4], the low-temperature phase of this system is characterized by a spin liquid state with a small or possibly even no energy gap. work, as discussed later in the paper. Since the number of corner-sharing triangles is equivalent to the number of tetra- hedra, the critical behavior in these materials can be described by a metal-insulator transition (MIT) in the Kagom´e lattice at 1/3 filling. Another possible experimental realization may be given by recently developed laser-cooling techniques. It was re- ported [6] that a two-dimensional optical trimerized Kagom´e lattice was constructed and that the coupling constants could be controlled using a triple laser beam design. Furthermore, a scheme proposed this year would construct an optical Kagom´e lattice at 1/3 filling with the use of just two standing waves a nd more controllable interactions [7]. Motivated by the optical lattice systems, a model of hard- core bosons on the Kagom´e lattice was studied with large scale quantum Monte Carlo simulations and phenomenologi- cal dual vortex theory [8, 9]. At 1/3 and 2/3 fillings a weak first-order superfluid-solid transition induced by the near est- neighbor repulsion was found. Thus, in our work presented here it is natural to consider how this transition occurs in fermion systems. Although the effective model can be shown to be equivalent for hard core bosons and spinless fermions in the strong-coupling limit, features for each, in the weak to intermediate coupling regimes, may differ completely due to the absence of a band picture in boson systems; here the dis- We discuss the metal-insulator transition of the spinless fermion model on the Kagom´e lattice at 1/3-filling. The system is analyzed using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of the effective model with a plaquette order. We find that the qualitative properties of the metal- insulator transition are totally different depending on the sign of the hopping integrals, reflecting the difference of band structure at the Fermi level. PACS numbers: 71.10.Hf, 71.27.+a, 71.10.-w Satoshi Nishimoto, 1 Masaaki Nakamura, 2 Aroon O’Brien, 3 and Peter Fulde 3,4 $^{1}$Leibniz-Institut f¨ur Festk¨orper- und Werkstoffforschung Dresden, D-01171 Dresden, Germany 2 Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551, Japan 3 Max-Planck-Institut f¨ur Physik komplexer Systeme, N¨othnitzer Straße 38, D-01187 Dresden, Germany $^{4}$Asia Pacific Center for Theoretical Physics, Pohang, Korea (Dated: October 28, 2018) Metal-insulator transition of the Kagom´e lattice fermions at 1/3 filling