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arXiv:2502.14603 · Physical review. B./Physical review. B

Topological phase transition through tunable nearest-neighbor interactions in a one-dimensional lattice

Rajashri Parida, Diptiman Sen, Tapan Mishra

Published Jul 25, 2025• 3 citations
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Abstract

We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show that the system undergoes a transition from a bond-ordered (BO) phase to a charge-density wave-II (CDW-II) phase as the attractive interaction strength increases at a fixed repulsive interaction. For a specific interaction pattern, the BO phase exhibits topological properties, which vanish when the pattern is altered, leading to a transition from a topological BO phase to a trivial BO phase through a gap-closing point where both interactions vanish. We identify these phases using a combination of order parameters, topological invariants, edge-state analysis and Thouless charge pumping. By extending our analysis beyond half-filling, we explore the phase diagram across all densities and identify the superfluid (SF) and the pair-superfluid (PSF) phases, characterized by single-particle and bound-pair excitations at incommensurate densities. The proposed model is experimentally realizable in platforms such as Rydberg excited or ultracold atoms in optical lattices, offering a versatile framework to study such interplay between topology and interactions in low-dimensional systems.

DOI
10.1103/kxqp-57vj

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We investigate the phase diagram of a one-dimensional model of hardcore bosons or spinless fermions with tunable nearest-neighbor interactions. By introducing alternating repulsive and attractive interactions on consecutive bonds, we show that the system undergoes a transition from a bond-ordered (BO) phase to a charge-density wave-II (CDW-II) phase as the attractive interaction strength increases at a fixed repulsive interaction. For a specific interaction pattern, the BO phase exhibits topological properties, which vanish when the pattern is altered, leading to a transition from a topological BO phase to a trivial BO phase through a gap-closing point where both interactions vanish. We identify these phases using a combination of order parameters, topological invariants, edge-state analysis and Thouless charge pumping. By extending our analysis beyond half-filling, we explore the phase diagram across all densities and identify the superfluid (SF) and the pair-superfluid (PSF) phases, characterized by single-particle and bound-pair excitations at incommensurate densities. The proposed model is experimentally realizable in platforms such as Rydberg excited or ultracold atoms in optical lattices, offering a versatile framework to study such interplay between topology and interactions in low-dimensional systems.
We investigate the topological properties of hardcore bosons possessing nearest-neighbor repulsive interactions on a two-leg ladder. We show that by allowing nearest-neighbor dimerized interactions instead of hopping dimerization, the system exhibits topological phases and phase transitions under proper conditions. First, by assuming uniform hopping throughout the ladder, we show that when interaction along the legs are dimerized and the dimerization pattern is different in the legs, a trivial rung-Mott insulator to a topological bond order phase transition occurs as a function of the dimerization strength. However, for a fixed dimerization strength, the system exhibits a topological to trivial phase transition with increase in the rung hopping. A completely different scenario appears when the rung interaction is turned on. We obtain that for a ladder with uniform hopping, the repulsive interaction either turns the topological phase into a trivial rung-Mott insulator or a charge density wave phase. Such topological features are absent when the dimerization pattern in the nearest-neighbor interaction is considered to be identical in both the legs of the ladder. We numerically obtain the ground-state properties and also show the signatures of topological phase transitions through Thouless charge pumping.
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor interactions.Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations.The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles.In relation with recent studies, we show several emergent transition lines with a central charge c = 3/2 between the Luttinger liquid and the cluster Luttinger liquid phases.These results could be experimentally investigated using highly tunable quantum simulators.
We show that a one-dimensional lattice of spinless fermions can undergo a topological phase transition only due to the effect of interaction. By allowing a dimerized interaction among the particles we show that the system exhibits a symmetry protected topological phase which does not exist in the absence of interaction and the system is a gapless state. The nontrivial topological character appears due to the onset of two degenerate bond-order phases as a function of dimerized interaction which are found to be topologically distinct from each other. As a result a topological phase transition occurs between these bond-order phases through a gap closing point. However, in the limit of strong interaction, the topologically distinct bond-order phases are separated from each other through a gapped charge density wave phase possessing a local antiferromagnetic order. We characterize this emergent topological nature by the edge states, Berry phase, and a nonlocal string order parameter and provide possible experimental signatures in terms of Thouless charge pumping and density-density correlation.
We study the ground-state properties of the extended Bose-Hubbard model in a one-dimensional dimerized optical lattice. In the limit of strong on-site repulsion, i.e., hardcore bosons, and strong nearest-neighbor interaction, a stable density-wave (DW) phase is obtained at half-filling as a function of lattice dimerization. Interestingly, at quarter-filling we obtain the signatures of an insulating phase which has the character of both the bond order (BO) and the DW insulators, which we call a bond-order density-wave (BODW) phase. Moreover, we show that for a fixed hopping dimerization there occurs a BO-DW phase crossover as a function of the nearest-neighbor interaction and the BODW phase is more robust when the hopping dimerization is stronger. We further examine the stability of the BODW phase in the limit of finite on-site interactions.
We study a system of hard-core bosons at half-filling in a one-dimensional optical superlattice. The bosons are allowed to hop to nearest- and next-nearest-neighbor sites. We obtain the ground-state phase diagram as a function of microscopic parameters using the finite-size density-matrix renormalization-group method. Depending on the sign of the next-nearest-neighbor hopping and the strength of the superlattice potential the system exhibits three different phases, namely the bond-order (BO) solid, the superlattice induced Mott insulator (SLMI), and the superfluid (SF) phase. When the signs of both hopping amplitudes are the same (the unfrustratedase), the system undergoes a transition from the SF to the SLMI at a nonzero value of the superlattice potential. On the other hand, when the two amplitudes differ in sign (the frustrated case), the SF is unstable to switching on a superlattice potential and also exists only up to a finite value of the next-nearest-neighbor hopping. This part of the phase diagram is dominated by the BO phase which breaks translation symmetry spontaneously even in the absence of the superlattice potential and can thus be characterized by a bond-order parameter. The transition from BO to SLMI appears to be first order.
The interacting bosons in one-dimensional inversion-symmetric superlattices are investigated from the topological aspect. The complete phase diagram is obtained by an atomic-limit analysis and quantum Monte Carlo simulations and comprises three kinds of phases: superfluid, persisted charge-density-wave and Mott insulators, and emergent insulators in the presence of nearest-neighbor hoppings. We find that all emergent insulators are topological, which are characterized by the Berry phase $\ensuremath{\pi}$ and a pair of degenerate in-gap boundary states. The mechanism of the topological bosonic insulators is qualitatively discussed and the ones with higher fillings can be understood as a 13\frac{1}{3}31​-filling topological phase on a background of trivial charge-density-wave or Mott insulators.