From gapped excitons to gapless triplons in one dimension

Abstract

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.

Interaction-driven topological phase transitions in fermionic SU($3$) systems

“…The effect of interaction on a band insulator (BI) and emergence of Mott physics in the strong coupling regime has been an interesting problem for a long time [8], initially motivated by the observation of neutral-ionic phase transition in organic compounds [9]. A spontaneously dimerized phase [10][11][12][13] stabilized by condensation of a singlet exciton [14][15][16][17] separates the NI from Mott insulator (MI) as is studied via the 1D ionic Hubbard model. The ground state phase diagram of the model on the square lattice is controversial [18][19][20], and on the honeycomb lattice an intermediate (semi-)metallic phase is expected [21][22][23].…”

Probing the Bond Order Wave Phase Transitions of the Ionic Hubbard Model by Superlattice Modulation Spectroscopy

“…In one dimension, this model has been the subject of a large number of studies using a variety of techniques including bozonization, density renormalization group, exact diagonalization and quantum Monte Carlo methods [8][9][10][11][12][13][14][15][16][17][18][19]. A smaller number of studies have also focused on the excitations of the ionic Hubbard model [20][21][22][23][24]. Despite initial controversy, theoretical investigations point to the existence, at half filling, of a bond order wave phase occuring around U ∼ ∆ characterized by the spontaneous dimerization of the hopping, i.e.…”

Orientational bond and Néel order in the two-dimensional ionic Hubbard model

“…In the absence of any electron-electron bound state, ∆ c , being twice the minimum of the fermion dispersion, equals the charge gap. We use the term charge gap because it has been used in previous papers on the IHM [4][5][6][7] . Fig.…”

“…In 1D, it is well understood that the BI at small Hubbard interaction U is separated from quasi-long-range ordered MI at large U by an intermediate phase with alternating bond order (BO) 3 . The position of the two transition points (U c1 from BI to BO and U c2 from BO to MI) 4,5 and the excitation spectrum 6,7 of the model are determined quantitatively. We highlight that the transition to the BO phase is signaled by the softening of an exciton [3][4][5] located at momentum π (setting the lattice constant to unity) 6,7 .…”

“…The position of the two transition points (U c1 from BI to BO and U c2 from BO to MI) 4,5 and the excitation spectrum 6,7 of the model are determined quantitatively. We highlight that the transition to the BO phase is signaled by the softening of an exciton [3][4][5] located at momentum π (setting the lattice constant to unity) 6,7 .…”