We report large-scale first-principles simulations of melting of four different phases of Li at pressures ranging from 0 to 50 GPa. We find excellent agreement with existing experimental data at low pressures, and confirm that above 10 GPa the melting line develops a negative slope, in parallel to what occurs for Na at 30 GPa. Surprisingly, our results indicate that the melting temperature of the bcc phase is always higher than that of fcc Li, suggesting the intriguing possibility of the existence of a narrow field of bcc stability separating the fcc and liquid phases, as predicted by Alexander and McTague [Phys. Rev. Lett. 41, 702 (1978)]. DOI: 10.1103/PhysRevLett.104.185701 PACS numbers: 64.70.dj, 62.50.Àp, 65.20.Àw, 65.40.Àb The alkali elements Li and Na have long been described as simple metals, due to their prototypical atomic and electronic structure. At ambient conditions they adopt the bcc lattice arrangement, transforming into the fcc at higher pressure (at $7:5 GPa and room temperature in the case of Li, at 65 GPa in the case of Na), while their electronic structure is nearly free electronlike. However, recent theoretical and experimental studies have shown that these materials display unexpectedly complex behavior at high pressures. Neaton and Ashcroft [1,2] reported ab initio calculations predicting that pressure induces phase transitions to less symmetric, lower coordinated structures, associated to electronic localization [3,4], a rather counterintuitive prediction. Shortly after, Hanfland et al.[5] reported an experimental study of Li at high pressures, and although the actual sequence of high-pressure phases found by these authors was different than that predicted theoretically [1], they nevertheless confirmed the tendency to adopt low symmetry phases at high pressures. Other experimental efforts have shown that these high-pressure structural transformations are accompanied by changes in the electronic structure. Indeed, Struzhkin et al. [6] and Shimizu and coworkers [7] have reported the observation of superconductivity in Li at pressures above 20 GPa (at ambient pressure T c ¼ 0:4 mK [8]), with transition temperatures varying with pressure, but ranging between 9 and up to 20 K, one of the highest measured for any element. Matsuoka and Shimizu [9] have reported a metal-tosemiconductor transition in Li near 80 GPa of pressure. Similar results have been reported for Na at 118 GPa, where Na is found to transform to an orthorhombic phase behaving as a poor metal [10]. At even higher pressures (c.a. 200 GPa) Ma and coworkers [11] have reported the observation of a sixfold coordinated hexagonal structure of Na which happens to be transparent, implying an insulator band gap in the electronic structure.In an effort to further characterize the thermodynamic behavior of alkali metals at high pressures, Gregoryanz et al. [12] have measured the melting temperature of Na up to pressures of 130 GPa. It was found that its melting curve reaches a maximum at $31 GPa, and decreases at higher pressures. The n...