Critical behavior of the extended Hubbard model with bond dimerization

Abstract

Exploiting the matrix-product-state based density-matrix renormalization group (DMRG) technique we study the one-dimensional extended ($U$-$V$) Hubbard model with explicit bond dimerization in the half-filled band sector. In particular we investigate the nature of the quantum phase transition, taking place with growing ratio $V/U$ between the symmetry-protected-topological and charge-density-wave insulating states. The (weak-coupling) critical line of continuous Ising transitions with central charge $c=1/2$ terminates at a tricritical point belonging to the universality class of the dilute Ising model with $c=7/10$. We demonstrate that our DMRG data perfectly match with (tricritical) Ising exponents, e.g., for the order parameter $\beta =1/8$ (1/24) and correlation length $\nu =1$ (5/9). Beyond the tricritical Ising point, in the strong-coupling regime, the quantum phase transition becomes first order.

6 pages, 7 figures, contributions to SCES 2017

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Cited by in corpus (5)

• Quantum phase transitions in the dimerized extended Bose-Hubbard model
• Exotic criticality in the dimerized spin-1 $XXZ$ chain with single-ion anisotropy
• Quantum simulation of the tricritical Ising model in tunable Josephson junction ladders
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Emergent tri-criticality in magnetic metamaterials