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Journal of Physics Conference Series

Quantum phases ofAB2fermionic chains

Luz Stefany Murcia-Correa, R Franco, Jereson Silva-Valencia

Published Feb 1, 2016• 2 citations
Publisher

Abstract

A fermionic chain is a one-dimensional system with fermions that interact locally and can jump between sites in the lattice, in particular an AB n chain type, where A and B are sites that exhibit a difference in energy level of Δ and site B is repeated n-times, such that the unit cell has n +1 sites. A limit case of this model, called the ionic Hubbard model (n = 1), has been widely studied due to its interesting physics and applications. In this paper, we study the ground state of an AB 2 chain, which describes the material R 4 [ Pt 2 ( P 2 O 5 H 2 ) 4 X] · nH 2 O . Specifically, we consider a filling with two electrons per unit cell, and using the density matrix renormalization group method we found that the system exhibits the band insulator and Mott correlated insulator phases, as well as an intermediate phase between them. For couplings of Δ = 2,10 and 20, we estimate the critical points that separate these phases through the structure factor and the energy gap in the sector of charge and spin, finding that the position of the critical point rises as a function of Δ.

DOI
10.1088/1742-6596/687/1/012066

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A fermionic chain is a one-dimensional system with fermions that interact locally and can jump between sites in the lattice, in particular an AB n chain type, where A and B are sites that exhibit a difference in energy level of Δ and site B is repeated n-times, such that the unit cell has n +1 sites. A limit case of this model, called the ionic Hubbard model (n = 1), has been widely studied due to its interesting physics and applications. In this paper, we study the ground state of an AB 2 chain, which describes the material R 4 [ Pt 2 ( P 2 O 5 H 2 ) 4 X] · nH 2 O . Specifically, we consider a filling with two electrons per unit cell, and using the density matrix renormalization group method we found that the system exhibits the band insulator and Mott correlated insulator phases, as well as an intermediate phase between them. For couplings of Δ = 2,10 and 20, we estimate the critical points that separate these phases through the structure factor and the energy gap in the sector of charge and spin, finding that the position of the critical point rises as a function of Δ.
We investigate the ground-state phase diagram of the Hubbard model for the ${\mathrm{AB}}_{N\ensuremath{-}1}$ chain with filling 1∕N1∕N1∕N, where NNN is the number of atoms per unit cell. In the strong-coupling limit, a charge transition takes place from a band insulator (BI) to a correlated insulator for increasing on-site repulsion UUU and positive on-site energy difference $\ensuremath{\Delta}$ (energy at A sites lower than at B sites). In the weak-coupling limit, a bosonization analysis suggests that for N>2N>2N>2 the physics is qualitatively similar to the case N=2N=2N=2 which has already been studied: an intermediate phase emerges, which corresponds to a bond-ordered ferroelectric insulator (FI) with spontaneously broken inversion symmetry. We have determined the quantum phase diagram for the cases N=3N=3N=3 and N=4N=4N=4 from the crossings of energy levels of appropriate excited states, which correspond to jumps in the charge and spin Berry phases, and from the change of sign of the localization parameter zLc{z}_{L}^{c}zLc​. From these techniques we find that, quantitatively, the BI and FI phases are broader for N>2N>2N>2 than when N=2N=2N=2, in agreement with the bosonization analysis. Calculations of the Drude weight and zLc{z}_{L}^{c}zLc​ indicate that the system is insulating for all parameters, with the possible exception of the boundary between the BI and FI phases.
We investigate three different types of quantum phase transition occurring in quasi one-dimensional systems theoretically and numerically. First, we study the band-insulator to Mott-insulator transition occurring in charge-transfer complexes, for which the half-filled one-dimensional ionic Hubbard model is considered to be the prototype model. The study is carried out by first deriving an effective spin-one model, and then studying the model numerically using the density matrix renormalization group. We perform a careful finite-size scaling analysis of the mass gaps, order-parameters, and relative susceptibility. We confirm the existence of two quantum critical points. Analysis of the critical exponents confirms that the band-insulator-to-spontaneously-dimerized phase transition belong to the 2D Ising class. The spontaneously dimerized phase undergoes a phase transition to the Mott-insulator which is an infinite-order. Second, we investigate the Mott metal-insulator transition for the half-filled Hubbard model with both nearest-neighbor t and next-nearest-neighbor t′ hopping terms. We study the model using the bosonization approach and density matrix renormalization group simulations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We present results of density matrix renormalization group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving the spin and the charge degrees of freedom. Finally, we investigate quantum phase transitions phases in low-dimensional fermionic and spin models that go from uniform to spatially inhomogeneous, i.e., dimerized, trimerized, or incommensurate, phases. We propose a new approach based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions and also provide significant information about certain relevant features of the excitation spectrum; in particular, they can identify the wave vector of soft modes in critical models.
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 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 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.
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