Ground-state and spectral properties of an asymmetric Hubbard ladder

Abdelwahab, Anas; Jeckelmann, Eric; Hohenadler, Martin

doi:10.1103/physrevb.91.155119

Cited by 11 publications

(35 citation statements)

References 53 publications

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“…13, the pair binding energy seems to reach its maximum E pb ≈ 0.22t for U ≈ 8 where the spin gap E s is also the largest. Again this behavior is similar to the observation made for homogeneous symmetric [19] and anti-symmetric [31] two-leg Hubbard ladders. One can conclude that the pair binding energy is intimately related to the behavior of the spin gap energy [32].…”

Section: B 3-3-2-2 Alternating Rung Geometrysupporting

confidence: 88%

Magnetic properties of alternating Hubbard ladders

et al. 2021

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We investigate the Hubbard Hamiltonian on ladders where the number of sites per rung alternates between two and three. These geometries are bipartite, with a non-equal number of sites on the two sublattices. Thus they share a key feature of the Hubbard model in a class of lattices which Lieb has shown analytically to exhibit long-range ferrimagnetic order, while being amenable to powerful numeric approaches developed for quasi-one-dimensional geometries. The Density Matrix Renormalization Group (DMRG) method is used to obtain the ground state properties, e.g. excitation gaps, charge and spin densities as well as their correlation functions at half-filling. We show the existence of long-range ferrimagnetic order in the one-dimensional ladder geometries.Our work provides detailed quantitative results which complement the general theorem of Lieb for generalized bipartite lattices. It also addresses the issue of how the alternation between quasi-long range order and spin liquid behavior for uniform ladders with odd and even numbers of legs might be affected by a regular alternation pattern.

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Section: B 3-3-2-2 Alternating Rung Geometrysupporting

confidence: 88%

Magnetic properties of alternating Hubbard ladders

et al. 2021

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“…Their properties are sometimes ascribed to Luttinger liquids and sometimes to anisotropic 2D Fermi liquids. One of the main reasons for these controversies is a poor understanding of the influence of the 3D substrate [13,15,[26][27][28] on 1D conductors. Isolated 1D conductors are known to be Luttinger liquids [9][10][11], whereas the above experimental realizations raise the question of the stability of Luttinger liquids coupled to an environment [10,26,29].…”

Section: Introductionmentioning

confidence: 99%

Correlated atomic wires on substrates. II. Application to Hubbard wires

2017

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In the first part of our theoretical study of correlated atomic wires on substrates, we introduced lattice models for a one-dimensional quantum wire on a three-dimensional substrate and their approximation by quasi-one-dimensional effective ladder models [arXiv:1704.07350]. In this second part, we apply this approach to the case of a correlated wire with a Hubbard-type electronelectron repulsion deposited on an insulating substrate. The ground-state and spectral properties are investigated numerically using the density-matrix renormalization group method and quantum Monte Carlo simulations. As a function of the model parameters, we observe various phases with quasi-one-dimensional low-energy excitations localized in the wire, namely paramagnetic Mott insulators, Luttinger liquids, and spin-1/2 Heisenberg chains. The validity of the effective ladder models is assessed by studying the convergence with the number of legs and comparing to the full three-dimensional model. We find that narrow ladder models accurately reproduce the quasi-onedimensional excitations of the full three-dimensional model but predict only qualitatively whether excitations are localized around the wire or delocalized in the three-dimensional substrate.

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“…Thus we now turn to the density distribution of low-energy excitations to gain more information. Similar quantities have already proven to be useful to understand the ground state of inhomogeneous ladder systems [16,17,31,32].…”

Section: Excitation Densitymentioning

confidence: 89%

Effective narrow ladder model for two quantum wires on a semiconducting substrate

Abdelwahab,

Jeckelmann

2021

Preprint

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We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.

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Ground-state and spectral properties of an asymmetric Hubbard ladder

Cited by 11 publications

References 53 publications

Magnetic properties of alternating Hubbard ladders

Magnetic properties of alternating Hubbard ladders

Correlated atomic wires on substrates. II. Application to Hubbard wires

Effective narrow ladder model for two quantum wires on a semiconducting substrate

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