Jordan-Wigner transformations for tree structures

Alexander Shnirman; Stefan Backens; Yuriy Makhlin

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Jordan-Wigner transformations for tree structures

Stefan Backens, Alexander Shnirman, Yuriy Makhlin

Other Condensed Matter · Submitted 5 Oct 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,493 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.65 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension.	background 1.00	0.04	0.04	asserted 1.00
s1	Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling.	contribution 1.00	0.93	0.78	asserted 1.00
s2	The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains.	method 1.00	0.78	0.10	asserted 1.00
s3	This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.	interpretation 0.97	0.54	0.20	asserted 0.79

What kind of paper the classifier reports this is: method or tool 0.96 · evidence from proof or derivation 0.93.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

The celebrated Jordan--Wigner transformation provides an efficient mapping between spin chains and fermionic systems in one dimension. Here we extend this spin-fermion mapping to arbitrary tree structures, which enables mapping between fermionic and spin systems with nearest-neighbor coupling. The mapping is achieved with the help of additional spins at the junctions between one-dimensional chains. This property allows for straightforward simulation of Majorana braiding in spin or qubit systems.

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References

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3 arXiv papers cite this in 3 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Cites it as background 2 papers

Since its discovery, the Jordan-Wigner transformation has been generalized to an entire family of exact free-fermion solutions [ref] , yielding new understanding for a wide class of spin models.

A Unified Graph-Theoretic Framework for Free-Fermion Solvability · Introduction · 0.87
It is also interesting from point of view of generalizations of Jordan-Wigner transformations to trees and more general graphs discussed in other works [ref] .

Clifford algebras, Spin groups and qubit trees · Introduction · 0.94

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