To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.To the conventional Peierls-Hubbard model, involving both on-site (U) and nearest-neighbor (V) Coulomb repulsions, we add ``off-diagonal'' terms, not expressible purely in terms of site densities, representing bond-bond (W) and mixed bond-site (X) electron-electron repulsive interactions involving nearest neighbors. We review earlier analyses of these interactions and discuss relative magnitudes of the parameters in applications to real materials. As a specific illustration, we investigate the effects of the off-diagonal W and X terms on dimerization in the one-dimensional, half-filled-band Peierls-Hubbard models, which have been widely applied to conjugated polymers (such as trans-polyacetylene) and to related quasi-one-dimensional charge-density wave (CDW) systems. Using both weak- and strong-coupling perturbation theory for large systems and exact diagonalizations of small systems, we investigate thoroughly the nature of the ground state of the model. For a broad range of the site-diagonal Hubbard parameters (U,V), including the values believed to be relevant to trans-polyacetylene, we find that the off-diagonal terms (W,X) initially enhance dimerization, thereby stabilizing the dimerized [or bond-order-wave (BOW)] ground state. For (unphysically) large values of W relative to U and V, dimerization is destroyed, and the BOW ground state goes over to a ferromagnetic ground state or a CDW ground state, depending on the relative sizes of U, V, and W. We conclude with a general discussion of the applicability of the Peierls-Hubbard models to quasi-one-dimensional materials, including the potential importance of the breaking of charge conjugation (``particle-hole'') symmetry by the X term.

Physical review. B, Condensed matterJul 1, 1990132 citations

Bond spin-density-wave phase in the staggered magnetic field

Hiromi Otsuka

Physica B Condensed MatterFeb 17, 20030 citations

Revealing the topological nature of the bond order wave in a strongly correlated quantum system

Sergi Julià-Farré, Daniel González-Cuadra, A. Patscheider +5 more

polyacetylene.There, a bond order wave (BOW) arises spontaneously from the coupling between electrons and phonons through a Peierls mechanism [19], which can also occur in spin-boson models [20][21][22].Interestingly, similar BOW phases also appear in interacting single-species systems, induced by frustration between competing orders , including strongly correlated electrons, quantum magnets, or ultracold atomic systems.Although the insulating nature and effective dimerization of these systems have been very carefully characterized, their topological nature still needs to be unveiled.The latter requires an accurate analysis of such many-body interacting systems, as the sole presence of a spontaneous dimerization, i.e., a local order parameter, does not directly translate into a nontrivial topology.In this Letter, we reveal and characterize the SPT nature of such BOW phases arising from frustration in the presence of chiral symmetry [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].Moreover, we propose a realistic implementation and detection scheme for the realization of the frustration-induced topological BOW phase with dipolar gases in optical lattices.Our proposal allows us to go beyond the experimental simulation of noninteracting SPT phases, promising to access both bulk and edge physics of a strongly correlated topological phase with richer phenomenology.More specifically, we focus our analysis on the onedimensional (1D) extended Fermi-Hubbard (EFH) model.We demonstrate that, in the case of an infinite chain, two exactly degenerate BOW ground states occur.These states are 2643-1564/2022/4(3)/L032005(7) L032005-1polyacetylene.There, a bond order wave (BOW) arises spontaneously from the coupling between electrons and phonons through a Peierls mechanism [19], which can also occur in spin-boson models [20][21][22].Interestingly, similar BOW phases also appear in interacting single-species systems, induced by frustration between competing orders , including strongly correlated electrons, quantum magnets, or ultracold atomic systems.Although the insulating nature and effective dimerization of these systems have been very carefully characterized, their topological nature still needs to be unveiled.The latter requires an accurate analysis of such many-body interacting systems, as the sole presence of a spontaneous dimerization, i.e., a local order parameter, does not directly translate into a nontrivial topology.In this Letter, we reveal and characterize the SPT nature of such BOW phases arising from frustration in the presence of chiral symmetry [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].Moreover, we propose a realistic implementation and detection scheme for the realization of the frustration-induced topological BOW phase with dipolar gases in optical lattices.Our proposal allows us to go beyond the experimental simulation of noninteracting SPT phases, promising to access both bulk and edge physics of a strongly correlated topological phase with richer phenomenology.More specifically, we focus our analysis on the onedimensional (1D) extended Fermi-Hubbard (EFH) model.We demonstrate that, in the case of an infinite chain, two exactly degenerate BOW ground states occur.These states are 2643-1564/2022/4(3)/L032005(7) L032005-1

arXiv:2112.08785Physical Review ResearchJul 8, 20222 citations

Coupled dimer and bond-order-wave order in the quarter-filled one-dimensional Kondo lattice model

Yixuan Huang, D. N. Sheng, C. S. Ting

Motivated by experiments on the organic compound ${(\text{Per})}_{2}[\text{Pt}{(\text{mnt})}_{2}]$ , we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak-coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter ${J}_{c}$ , with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such a phase transition. We also show that the localized spins in this insulating state have quasi-long-ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.Motivated by experiments on the organic compound ${(\text{Per})}_{2}[\text{Pt}{(\text{mnt})}_{2}]$, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak-coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter ${J}_{c}$, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such a phase transition. We also show that the localized spins in this insulating state have quasi-long-ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.

arXiv:2009.13089Physical review. B./Physical review. BDec 24, 20205 citations

Statistical mechanics of polyacetylene (CH)x

Harald Grosse, Keiichi R. Ito, Yong Moon Park

Nuclear Physics BJan 1, 19865 citations

Motivated by experiments on the organic compound

{(\text{Per})}_{2}[\text{Pt}{(\text{mnt})}_{2}]

, we study the ground state of the one-dimensional Kondo lattice model at quarter filling with the density matrix renormalization group method. We show a coupled dimer and bond-order-wave (BOW) state in the weak-coupling regime for the localized spins and itinerant electrons, respectively. The quantum phase transitions for the dimer and the BOW orders occur at the same critical coupling parameter

{J}_{c}

, with the opening of a charge gap. The emergence of the combination of dimer and BOW order agrees with the experimental findings of the simultaneous Peierls and spin-Peierls transitions at low temperatures, which provides a theoretical understanding of such a phase transition. We also show that the localized spins in this insulating state have quasi-long-ranged spin correlations with collinear configurations, which resemble the classical dimer order in the absence of a magnetic order.