# Critical behavior of the extended Hubbard model with bond dimerization

## TL;DR

This study uses DMRG to analyze the quantum phase transition in a one-dimensional extended Hubbard model with bond dimerization, revealing a transition from continuous Ising to first-order behavior at a tricritical point.

## Contribution

It provides a detailed characterization of the phase transition and identifies the universality classes and critical exponents involved.

## Key findings

- Critical line of Ising transitions with c=1/2
- Tricritical point with c=7/10
- Transition becomes first order in strong coupling

## 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.