Variational study of the interacting, spinless Su–Schrieffer–Heeger model

Abstract

We study the phase diagram and the total polarization distribution of the Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane-Mele-Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution 'walks across' smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as it happens when a Rice-Mele onsite potential is turned on.

Interacting Rice-Mele model: Bulk and boundaries

“…with R(κ ) and κ bc defined in Eqs. (19) and (20). The pole contribution coincides with the negative edge state density at μ = 0.…”

“…However, in many respects this understanding relies on ideas which make explicit use of the concept of independent particles. Insights on the relation between topology and the physics of interacting many-body systems are based either on case studies for specific models or on general considerations of how to extend the concept of topological invariants to the realm of correlated systems [13][14][15][16][17][18][19][20][21][22][23][24].…”

Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings

“…Moreover, Yoshida et al 32 showed a correlations-driven edge-Mott state with gapful charge and gapless spin excitations, which corresponds to the degeneracy of the entanglement spectrum of bulk. For the spinless SSH model, the correlation represented by the nearest neighbor Hubbard interaction was supposed to induce the charge density wave state (CDW) in the whole domain of the nearest neighbor hoppings 33 . However, the effects of correlations on the two-dimensional SSH model have not yet been investigated.…”

Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model

“…In this work we apply a variational Monte Carlo [27] for strongly correlated bosonic models based on the Baeriswyl wavefunction [28][29][30][31][32][33][34] (BWF) and exact diagonalization (ED) to study the superfluid response and the polarization amplitude [35][36][37][38][39][40][41][42][43][44] of the one-dimensional BHM. Central to our study is the derivation of the expression for the superfluid weight valid in variational calculations, and emphasis of the role of interference between Peierls phases of particle paths in calculating the superfluid weight.…”