First-principles phase diagram of an interacting ionic chain

DFT is one of the most popular methods used for simulating the properties of real materials, primarily due to its balance between accuracy and computational efficiency. Though it is exact in principle, the Kohn-Sham implementation is mean-field-like, which hinders its reliability when studying strongly correlated materials with complex phase diagrams. In this work, we attempt to provide a concrete benchmark for DFT by systematically studying a simple 1D system: an evenly bonded ionic chain with two single-orbital atoms A and B. The atoms are allowed to have non-integer nuclear charges Z_A and Z_B, respectively, and we enforce that Z_A + Z_B = +2e so that the unit cell is neutral [1]. In real materials, the nuclear charge is always an integer. Removing this restriction is equivalent to allowing the staggered potential between the two sites to be continuous rather than discrete. In fact, the chain has a rich phase diagram owing to this continuity, which can be understood via the so-called ionic Hubbard model (IHM). The phase diagram of the IHM is already exactly known according to bosonization [2]. We provide a direct comparison of DFT to the IHM by mapping the model parameters to the bond length and charge ratio Z_A/Z_B of the "real" chain. We compare the phase diagrams at two levels of theory in the IHM: an analytical mean field solution and a numerical solution using density matrix renormalization group (DMRG). We find that DFT reproduces the signature spontaneously dimerized phase of the IHM when Peierls distortion is included, indicating that explicit symmetry breaking could be used as a tool to predict interaction-dependent order parameters from DFT.



[1] J. Furness, R. Zhang, J. Kidd, and J. Sun, Comm. Phys. 6, 246 (2023).

[2] M. Fabrizio, A. Gogolin, and A. Nersesyan, Phys. Rev. Lett. 83, 2014 (1999).