Quantum critical behavior of the one-dimensional ionic Hubbard model

TL;DR

This study uses density-matrix renormalization group methods to analyze the phase diagram of the one-dimensional ionic Hubbard model, revealing two quantum critical points and an intermediate dimerized phase with continuous transitions.

Contribution

It provides a comprehensive finite-size scaling analysis of the ionic Hubbard model, identifying two quantum critical points and characterizing the nature of phase transitions and critical exponents.

Findings

Evidence for two quantum critical points.

Identification of an intermediate spontaneously dimerized phase.

Critical exponents differ from Ising universality class.

Abstract

We study the zero-temperature phase diagram of the half-filled one-dimensional ionic Hubbard model. This model is governed by the interplay of the on-site Coulomb repulsion and an alternating one-particle potential. Various many-body energy gaps, the charge-density-wave and bond-order parameters, the electric as well as the bond-order susceptibilities, and the density-density correlation function are calculated using the density-matrix renormalization group method. In order to obtain a comprehensive picture, we investigate systems with open as well as periodic boundary conditions and study the physical properties in different sectors of the phase diagram. A careful finite-size scaling analysis leads to results which give strong evidence in favor of a scenario with two quantum critical points and an intermediate spontaneously dimerized phase. Our results indicate that the phase transitions are continuous. Using a scaling ansatz we are able to read off critical exponents at the first critical point. In contrast to a bosonization approach, we do not find Ising critical exponents. We show that the low-energy physics of the strong coupling phase can only partly be understood in terms of the strong coupling behavior of the ordinary Hubbard model.