Designing a symmetry-protected molecular device

Büsser, C. A.; Feiguin, Adrian

doi:10.1103/physrevb.86.165410

Cited by 6 publications

(5 citation statements)

References 42 publications

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“…94,95 The method can also become a powerful tool to study quantum chemistry problems in which a magnetic atom is embedded into a system that may be described by a Hückellike theory. 96 Moreover, one could use it in conjunction with ab initio band structure calculations, incorporating the information about the bulk system into the effective 1D chain, and the hybridization terms in the structure of the seed state, paving the way toward realistic first-principles modeling and a better understanding of correlation effects in quantum impurity problems.…”

Section: Discussionmentioning

confidence: 99%

Lanczos transformation for quantum impurity problems ind-dimensional lattices: Application to graphene nanoribbons

Büsser¹,

Martins

Feiguin

2013

Phys. Rev. B

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We present a completely unbiased and controlled numerical method to solve quantum impurity problems in d-dimensional lattices. This approach is based on a canonical transformation, of the Lanczos form, where the complete lattice Hamiltonian is exactly mapped onto an equivalent one-dimensional system, in the same spirit as Wilson's numerical renormalization, and Haydock's recursion method. We introduce many-body interactions in the form of a Kondo or Anderson impurity and we solve the low-dimensional problem using the density matrix renormalization group. The technique is particularly suited to study systems that are inhomogeneous, and/or have a boundary. The resulting dimensional reduction translates into a reduction of the scaling of the entanglement entropy by a factor L d−1 , where L is the linear dimension of the original d-dimensional lattice. This allows one to calculate the ground state of a magnetic impurity attached to an L × L square lattice and an L × L × L cubic lattice with L up to 140 sites. We also study the localized edge states in graphene nanoribbons by attaching a magnetic impurity to the edge or the center of the system. For armchair metallic nanoribbons we find a slow decay of the spin correlations as a consequence of the delocalized metallic states. In the case of zigzag ribbons, the decay of the spin correlations depends on the position of the impurity. If the impurity is situated in the bulk of the ribbon, the decay is slow as in the metallic case. On the other hand, if the adatom is attached to the edge, the decay is fast, within few sites of the impurity, as a consequence of the localized edge states, and the short correlation length. The mapping can be combined with ab initio band structure calculations to model the system, and to understand correlation effects in quantum impurity problems starting from first principles.

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Section: Discussionmentioning

confidence: 99%

Lanczos transformation for quantum impurity problems ind-dimensional lattices: Application to graphene nanoribbons

Büsser¹,

Martins

Feiguin

2013

Phys. Rev. B

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“…A simple folding transformation 28,29 allows us to map it onto an equivalent chain of length L + 1 and an impurity coupled to the first site (r 0 = 0):…”

Section: Model and Methodsmentioning

confidence: 99%

“…Without loss of generality, we model the conduction electrons by a one dimensional tight-binding chain with open boundary conditions of size 2L + 1 (L even) and the impurity connected to the site in the middle 9 . A simple folding transformation 28,29 allows us to map it onto an equivalent chain of length L + 1 and an impurity coupled to the first site (r 0 = 0):…”

Section: Model and Methodsmentioning

confidence: 99%

Unveiling the internal entanglement structure of the Kondo singlet

Yang

Feiguin

2017

Phys. Rev. B

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We disentangle all the individual degrees of freedom in the quantum impurity problem to deconstruct the Kondo singlet, both in real and energy space, by studying the contribution of each individual free electron eigenstate. This is a problem of two spins coupled to a bath, where the bath is formed by the remaining conduction electrons. Being a mixed state, we resort to the "concurrence" to quantify entanglement. We identify "projected natural orbitals" that allow us to individualize a single-particle electronic wave function that is responsible of more than 90% of the impurity screening. In the weak coupling regime, the impurity is entangled to an electron at the Fermi level, while in the strong coupling regime, the impurity counterintuitively entangles mostly with the high energy electrons and disentangles completely from the low-energy states carving a "hole" around the Fermi level. This enables one to use concurrence as a pseudo order parameter to compute the characteristic "size" of the Kondo cloud, beyond which electrons are are weakly correlated to the impurity and are dominated by the physics of the boundary.

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“…They become local operators by folding the chain around the bond (L, L + 1) that transforms it into a ladder with 2 legs and L rungs. The folding trick has played an important role in the study of quantum impurity problems [40][41][42]. Equation (4) shows that the bcs state is the product of bonding and antibonding states on the rungs.…”

Section: The Rainbow XX Modelmentioning

confidence: 99%

Symmetry protected phases in inhomogeneous spin chains

et al. 2019

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It has been shown recently that inhomogenous spin chains can exhibit exotic phenomena such as the breaking of the area law of the entanglement entropy. An example is given by the rainbow model where the exchange coupling constants decrease from the center of the chain. Here we show that by folding the chain around its center, the long-range entanglement becomes short-range which can lead to topological phases protected by symmetries (SPT). The phases are trivial for bond-centered foldings, and non trivial for site-centered ones. In the latter case, the folded spin 1/2 chain with U (1) symmetry belongs to the Su-Schrieer-Heeger class, while the folded chain with SU (2) symmetry is in the Haldane phase. Finally, we extend these results to higher spin chains where we find a correspondence between the symmetry protection of gapped and gapless phases.

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Designing a symmetry-protected molecular device

Cited by 6 publications

References 42 publications

Lanczos transformation for quantum impurity problems ind-dimensional lattices: Application to graphene nanoribbons

Lanczos transformation for quantum impurity problems ind-dimensional lattices: Application to graphene nanoribbons

Unveiling the internal entanglement structure of the Kondo singlet

Symmetry protected phases in inhomogeneous spin chains

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