Interaction-induced phases in the half-filled Bernevig-Hughes-Zhang model in one dimension

Abstract

We explore the ground-state properties of a one-dimensional model with two orbitals per site, where, in addition to atomic energies $\pm M$, intra- and inter-orbital hoppings, the intra-orbital Hubbard ($U$) and nearest-neighbor density-density ($V$) repulsions are included. Our results are primarily based on a Jastrow-Slater wave function and variational Monte Carlo methods, but also corroborated by density-matrix renormalization group calculations. In the non-interacting limit, when varying $M>0$, a gapless point separates a trivial phase from a topological one. The inclusion of a finite Hubbard-$U$ repulsion does not give rise to any phase transition within the topological region, inducing a smooth crossover into a Haldane (spin gapped) insulator; notably, the string-order parameter, which characterizes the latter phase, is already finite in the non-interacting limit. Most importantly, at finite values of $U$, the transition between the trivial and topological states is not direct, since an emergent insulator, which shows evidence of sustaining gapless spin excitations, intrudes between them. A small $V$ interaction further stabilizes the intermediate insulator, while a sufficiently large value of this nearest-neighbor repulsion gives rise to two different charge-density wave insulators, one fully gapped and another still supporting gapless spin excitations. Our results demonstrate the richness of multi-orbital Hubbard models, in the presence of a topologically non-trivial band structure, and serve as a basis for future investigations on similar two-dimensional models.

arXiv comment11 pages, 11 figures

References in corpus (35)

• Topological Insulators
• Magic-angle graphene superlattices: a new platform for unconventional superconductivity
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
• Theory of Intertwined Orders in High Temperature Superconductors
• The ITensor Software Library for Tensor Network Calculations
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Electron Localization in the Insulating State
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Wave function optimization in the variational Monte Carlo method
• Correlation Effects in Quantum Spin-Hall Insulators: A Quantum Monte Carlo Study
• Variational description of Mott insulators
• Mott Physics and Topological Phase Transition in Correlated Dirac Fermions
• Quantum phase transitions in the Kane-Mele-Hubbard model
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Topological invariants and interacting one-dimensional fermionic systems
• First order character and observable signatures of topological quantum phase transitions
• Fluctuation driven topological Hund insulators
• Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators
• A study on correlation effects in two dimensional topological insulators
• String order and adiabatic continuity of Haldane chains and band insulators
• Mott Physics on Helical Edges of 2D Topological Insulators
• Phase diagram of the Kane-Mele-Coulomb model
• Topological phase in one-dimensional interacting fermion system
• Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model
• Quenched dynamics and spin-charge separation in an interacting topological lattice
• First order topological phase transition of the Haldane--Hubbard model
• How Hidden Orders Generate Gaps in 1D Fermionic Systems
• Non-local order parameters for the 1D Hubbard model
• First-Order Topological Quantum Phase Transition in a Strongly Correlated Ladder
• From Luttinger liquid to Mott insulator: the correct low-energy description of the one-dimensional Hubbard model by an unbiased variational approach
• A real-space many-body marker for correlated ${\mathbb{Z}}_2$ topological insulators
• A Jastrow wave function for the spin-1 Heisenberg chain: the string order revealed by the mapping to the classical Coulomb gas

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