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arXiv:cond-mat/0004162 · Physical review. B, Condensed matter

Transition from band insulator to Mott insulator in one dimension: Critical behavior and phase diagram

Jizhong Lou, Shaojin Qin, Tao Xiang, Changfeng Chen, Guang-Shan Tian, Zhao-Bin Su

Published Jul 25, 2003• 26 citations
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Abstract

We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at ${U=U}_{c}$ and ${U=U}_{s}$ that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase $(U<{U}_{c})$ and drops below the band gap when U exceeds a special point ${U}_{e}.$ The exciton gap closes at the first critical point ${U}_{c}$ while the charge and spin gaps persist and coincide between ${U}_{c}<U<{U}_{s}$ where the system is dimerized. Both the charge and spin gaps collapse at ${U=U}_{s}$ when the transition to the MI phase occurs. In the MI phase $(U>{U}_{s})$ the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.

DOI
10.1103/physrevb.68.045110

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We report a systematic study of the transition from a band insulator (BI) to a Mott insulator (MI) in a one-dimensional Hubbard model at half-filling with an on-site Coulomb interaction U and an alternating periodic site potential V. We employ both the zero-temperature density matrix renormalization group (DMRG) method to determine the gap and critical behavior of the system and the finite-temperature transfer matrix renormalization group method to evaluate the thermodynamic properties. We find two critical points at U=Uc{U=U}_{c}U=Uc​ and U=Us{U=U}_{s}U=Us​ that separate the BI and MI phases for a given V. A charge-neutral spin-singlet exciton band develops in the BI phase (U<Uc)(U<{U}_{c})(U<Uc​) and drops below the band gap when U exceeds a special point Ue.{U}_{e}.Ue​. The exciton gap closes at the first critical point Uc{U}_{c}Uc​ while the charge and spin gaps persist and coincide between Uc<U<Us{U}_{c}<U<{U}_{s}Uc​<U<Us​ where the system is dimerized. Both the charge and spin gaps collapse at U=Us{U=U}_{s}U=Us​ when the transition to the MI phase occurs. In the MI phase (U>Us)(U>{U}_{s})(U>Us​) the charge gap increases almost linearly with U while the spin gap remains zero. These findings clarify earlier published results on the same model, and offer insights into several important issues regarding an appropriate scaling analysis of DMRG data and a full physical picture of the delicate nature of the phase transitions driven by electron correlation. The present work provides a comprehensive understanding for the critical behavior and phase diagram for the transition from BI to MI in one-dimensional correlated electron systems with a periodic alternating site potential.
We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.
We have investigated the ground-state phase diagram of the one-dimensional Hubbard model with alternating chemical potentials at half-filling by bosonization technique and the Gaussian wave functional method. We calculate variations of the charge density wave (CDW) and the spin density wave (SDW) gaps, ad well as their classical trajectory c,s with increasing on-site Coulomb repoulsion potential. For the fixed potential, it is found that the transition from the band insulator (BI) to the spontaneously dimerized insulator (SDI) is of the Ising type, at which charge gap vanishes, while the transition from SDI to the Mott insulator (MI) is of the KT type.
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 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.
We investigate the neutral-to-ionic insulator-insulator transition in one-dimensional materials by treating a strong-coupling effective model based on the ionic Hubbard model using the density-matrix renormalization group and finite-size scaling. The effective model, formulated in a spin-one representation, contains a single parameter. We carry out an extensive finite-size scaling analysis of the relevant gaps and susceptibilities to characterize the two zero-temperature transitions. We find that the transition from the ionic band-insulating phase to an intermediate spontaneously dimerized phase is Ising, and the transition from the dimerized phase to the Mott-insulating phase is Kosterlitz-Thouless, in agreement with the field-theory-based predictions.
We use the density matrix renormalization group to study the quantum transitions that occur in the half-filled one-dimensional fermionic Hubbard model with onsite potential disorder. We find a transition from the gapped Mott phase with algebraic spin correlations to a gapless spin-disordered phase beyond a critical strength of the disorder Δc≈U/2Δ_c \approx U/2Δc​≈U/2. Both the transitions in the charge and spin sectors are shown to be coincident. We also establish the finite-size corrections to the charge gap and the spin-spin correlation length in the presence of disorder and using a finite-size-scaling analysis we obtain the zero temperature phase diagram of the various quantum phase transitions that occur in the disorder-interaction plane.
We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential---a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidence to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.