Optical conductivity of the Hubbard chain away from half filling

Abstract

We consider the optical conductivity σ 1 (ω) in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, σ 1 (ω) is computed for a range of interaction strengths and dopings. We identify an energy scale E opt above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of σ 1 (ω) for frequencies just above E opt which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.

Mobile impurity approach to the optical conductivity in the Hubbard chain

“…Our main result is to show that the MIM approach predicts a smooth, slow increase in σ 1 (ω) for frequencies above E opt . This is in contrast to the half-filled case 40 and previous predictions 50 , but consistent with recent dynamical DMRG computations 59 . The results presented in this work are by construction specific to the Hubbard model.…”

“…We have studied the optical conductivity σ 1 (ω) in the one dimensional Hubbard at zero temperature and close to half filling. Recent DMRG computations 59 have shown that in this regime σ 1 (ω) is very small within a "pseudo-gap" and exhibits a rapid increase above an energy scale E opt that depends on doping as well as the interaction strength U . Using the Bethe Ansatz we have identified the relevant excitations that contribute to σ 1 (ω) for ω > E opt .…”

Excitonic optical spectra and energy structures in a one-dimensional Mott insulator demonstrated by applying a many-body Wannier functions method to a charge model

“…Applying the definitions in Eqs. ( 17) and ( 19) 37), (38), (39), and (41), the optical spectra with and without a modulated electric field for the HD model are calculated with |J ex in Eq. ( 40) of In this section, exemplifying the case of (i) in Sect.III (V 1 = V = 2.8T and V α≥2 = 0), we perform finite-size exact diagonalization calculations of optical conductivity spectra of a charge model with and without H (C) φ term (see Eqs.…”

“…Here, to theoretically analyze such excited states in general, non-perturbative schemes such as exact diagonalization method and DMRG method [32,33] are only permitted because of strong correlations arising from strong Coulomb interactions between electrons. At present, several reliable σ(ω) in a 1D extended Hubbard model at halffilling with huge size have already been calculated by DDMRG scheme [30,[34][35][36][37][38][39]. However, in that scheme, because the highly renormalized wavefunctions of both the ground state and photoexcited states are obtained as numerical data, to convert the data into corresponding wavefunctions of the real system size is far difficult.…”

The fate of pairing and spin-charge separation in the presence of long-range antiferromagnetism

“…Most of the research in this area has been focused on the study of paradigmatic, simple model Hamiltonians that are supposed to capture all the basic ingredients for high temperature superconductivity such as the Hubbard and t − J models and variations of them [1][2][3][4][5][6]. In this context, much effort has been devoted to their low-dimensional versions [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. Particularly, in one dimension the physics of these systems can be universally described in the framework of Luttinger liquid (LL) theory [25][26][27][28][29][30]: the natural excitations in 1D are described in terms of spin and charge excitations that propagate coherently with different velocities and characterized by distinct energy scales, leading to the concept of spin-charge separation.…”