Physical Review Letters

Electronic Correlations in One-Dimensional Superlattices

Thereza Paiva, Raimundo R. dos Santos

Published Feb 12, 1996• 31 citations

Abstract

We consider fermions on a one-dimensional superlattice, represented by a repeated pattern of repulsive (i.e., positive Hubbard $U$) and free (i.e., $U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) 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.

DOI: 10.1103/physrevlett.76.1126

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Physical Review Letters

Electronic Correlations in One-Dimensional Superlattices

Thereza Paiva, Raimundo R. dos Santos

Published Feb 12, 1996• 31 citations

Publisher

Abstract

We consider fermions on a one-dimensional superlattice, represented by a repeated pattern of repulsive (i.e., positive Hubbard

U

) and free (i.e.,

U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}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.

DOI: 10.1103/physrevlett.76.1126

Related papers

Multiperiodic magnetic structures in Hubbard superlattices

André Luiz Malvezzi, Thereza Paiva, Raimundo R. dos Santos

We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard- $U$ couplings arranged in a repeated pattern of repulsive (i.e., $U>0)$ and free $(U=0)$ 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.We consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-$U$ couplings arranged in a repeated pattern of repulsive (i.e., $U>0)$ and free $(U=0)$ 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.

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Liangliang Zhang, Jin Huang, Cheng-Bo Duan +1 more

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 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.

Chinese Physics BJun 25, 20155 citations

We consider fermions on a one-dimensional superlattice, represented by a repeated pattern of repulsive (i.e., positive Hubbard

U

) and free (i.e.,

U\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0

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 consider fermions in one-dimensional superlattices (SL's), modeled by site-dependent Hubbard-

U

couplings arranged in a repeated pattern of repulsive (i.e.,

U>0)

and free

(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.

(U>0)

and free

(U=0)

sites. Density matrix renormalization group diagonalization of finite systems (up to 120 sites) is used to calculate the charge-density correlation function and structure factor in the ground state. The modulation period can still be predicted through effective Fermi wave vectors

{k}_{F}^{*}

and densities, and we have found that it is much more sensitive to electron (or hole) doping, both because of the narrow range of densities needed to go from

{q}^{*}=0

to $\ensuremath{\pi}$, but also due to sharp $2{k}_{F}^{*}\ensuremath{-}4{k}_{F}^{*}$ transitions; these features render CDW's more versatile for actual applications in heterostructures than in homogeneous systems.

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

{L}_{U}

repulsive sites followed by

{L}_{0}

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,

{L}_{U}+{L}_{0}

) 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 study the formation of charge density waves (CDW's) in one-dimensional Hubbard superlattices, modeled by a repeated pattern of repulsive

(U>0)

and free

(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.