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arXiv:cond-mat/9807302 · Physical review. B, Condensed matter

Metal-insulator transition in one-dimensional Hubbard superlattices

Thereza Paiva, Raimundo R. dos Santos

Published Oct 15, 1998• 30 citations
arXivHTMLPDF

Abstract

We study the metal-insulator transition in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (i.e., positive on-site coupling) and free sites. The evolution of the local moment and of the charge gap (calculated from Lanczos diagonalization of chains up to 18 sites), together with a strong-coupling analysis, show that the electron density at which the system is insulating increases with the size of the free layer, relative to the repulsive one. In the insulating state, the mechanism of interaction between fermions separated by a free layer is the analog of superexchange, and the charge gap display universal features.

DOI
10.1103/physrevb.58.9607

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We study the metal-insulator transition in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (i.e., positive on-site coupling) and free sites. The evolution of the local moment and of the charge gap (calculated from Lanczos diagonalization of chains up to 18 sites), together with a strong-coupling analysis, show that the electron density at which the system is insulating increases with the size of the free layer, relative to the repulsive one. In the insulating state, the mechanism of interaction between fermions separated by a free layer is the analog of superexchange, and the charge gap display universal features.
We discuss how entanglement of strongly correlated fermions is influenced by a superlattice structure by considering a one-dimensional Hubbard superlattice, made up of a repeated pattern of LU{L}_{U}LU​ repulsive sites followed by L0{L}_{0}L0​ free sites. Lanczos diagonalization of lattices up to 24 sites is used to calculate the von Neumann entropy and the negativity. The breakdown of particle-hole symmetry broadens the maxima of the entropy in the underdoped region, while the entanglement in the overdoped region is crucially influenced by the nature of the magnetic state, with dips at densities corresponding to repulsive-layer singlets and to $q=\ensuremath{\pi}$ (in units of inverse unit cell length, LU+L0{L}_{U}+{L}_{0}LU​+L0​) spin-density waves. At these special densities, the system is either a Mott insulator or a ``compressible insulator.'' We have also found that sites within the same repulsive layer (for ${L}_{U}\ensuremath{\ge}2$) are monogamically entangled with each other, which may provide a route to control entanglement simultaneously in different length scales.
We investigate the charge and spin gaps, and the spin structure in half-filled one-dimensional Hubbard superlattices with one repulsive site and L0 free sites per unit cell. For odd L0, it is correlated metal at the particle–hole symmetric point, and then turns into band insulator beyond this point. For even L0, the system has a Mott insulator phase around the particle–hole symmetric point and undergoes a metal–insulator transition with on-site repulsion U increasing. For large U, there exists a multiperiodic spin structure, which results from the ferromagnetic (antiferromagnetic) correlation between the nearest neighboring repulsive sites for odd (even) L0.
We consider fermions on a one-dimensional superlattice, represented by a repeated pattern of repulsive (i.e., positive Hubbard UUU) and free (i.e., U=0U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0U=0) sites. Lanczos diagonalization of chains up to 12 sites at half filling shows that some patterns give rise to a weak form of frustration, sufficient to wipe out the spin-density-wave (SDW) correlations present in the otherwise homogeneous system. On the other hand, SDW correlations appear for some patterns above half filling, a feature absent in the homogeneous case. Below half filling, the local-moment maxima are displaced from the repulsive to the free sites. The peak in the magnetic structure factor is also shifted from $q\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{\pi}$, for the alternating configuration when $\ensuremath{\rho}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3$ and 5/3.
We study the formation of charge density waves (CDW's) in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive (U>0)(U>0)(U>0) and free (U=0)(U=0)(U=0) sites. By means of Lanczos diagonalizations for the ground state, we calculate the charge structure factor. Our results show that while the superlattice structure affects the modulation of the charge density waves, the periodicity can still be predicted through an effective density. We also show that, for a fixed repulsive layer thickness, the periodicity of the CDW is an oscillatory function of the free layer thickness.
We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-UUU couplings arranged in a repeated pattern of repulsive (i.e., U>0)U>0)U>0) and free (U=0)(U=0)(U=0) sites. Density matrix renormalization group diagonalization of finite systems is used to calculate the local moment and the magnetic structure factor in the ground state. We have found four regimes for magnetic behavior: uniform local moments forming a spin-density wave (SDW), ``floppy'' local moments with short-ranged correlations, local moments on repulsive sites forming long-period SDW's superimposed with short-ranged correlations, and local moments on repulsive sites solely with long-period SDW's; the boundaries between these regimes depend on the range of electronic densities $\ensuremath{\rho}$ and on the SL aspect ratio. Above a critical electronic density, ${\ensuremath{\rho}}_{\ensuremath{\uparrow}\ensuremath{\downarrow}},$ the SDW period oscillates both with $\ensuremath{\rho}$ and with the spacer thickness. The former oscillation allows one to reproduce all SDW wave vectors within a small range of electronic densities, unlike the homogeneous system. The latter oscillation is related to the exchange oscillation observed in magnetic multilayers. A crossover between regimes of ``thin'' to ``thick'' layers has also been observed.
Exact-diagonalization and quantum Monte Carlo methods are used to study the occurrence of a metal-insulator transition and the distribution of charges and magnetic moments in the ground state of a one- and two-dimensional half-filled system of correlated electrons, described by a one-band simplified Hubbard model extended with bond-charge--site-charge interactions. Numerical results for the electrical conductivity, the density of states, and the spin- and charge-density correlation functions strongly suggest that the bond-charge--site-charge interaction plays a fundamental role in the occurrence of a metal-insulator transition and of ferromagnetic order.