Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics Conference Series

Dual algebraic structures for pairing models

FRANCESCO IACHELLO

Published Aug 24, 2012• 1 citation
Publisher

Abstract

Duality relations for pairing models are discussed in an unified framework for bosons and fermions. Quantum phase transitions for pairing systems are studied and analogies and differences between bosonic and fermionic systems are highlighted.
DOI
10.1088/1742-6596/380/1/012001

Related papers

Analysis of quantum phase transition in some different Curie-Weiss models: a unified approach

Carla Maria Pontes Carneiro, G. Q. Pellegrino

A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum Hamiltonian by an appropriate factor, rewriting the Hamiltonian in terms of $SU(2)$ operators only, and obtention of a classical Hamiltonian. $SU(2)$ operators are obtained from creation and annihilation operators as linear combinations in the case of fermions and as an inverse Holstein-Primakoff transformation in the case of bosons. This scheme is successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.

arXiv:1712.07634•Dec 20, 2017•0 citations

Dual algebraic structures for the two-level pairing model

M. A. Caprio, Jacob H. Skrabacz, FRANCESCO IACHELLO

Duality relations are explicitly established relating the Hamiltonians and basis classification schemes associated with the number-conserving unitary and number-nonconserving quasispin algebras for the two-level system with pairing interactions. These relations are obtained in a unified formulation for both bosonic and fermionic systems, with arbitrary and, in general, unequal degeneracies for the two levels. Illustrative calculations are carried out comparing the bosonic and fermionic quantum phase transitions.

arXiv:1102.1482•Journal of Physics A Mathematical and Theoretical•Jan 28, 2011•42 citations

Pairing of bosons in the condensed state of the boson-fermion model

A. S. Alexandrov

arXiv:cond-mat/0407238•The European Physical Journal B•May 1, 2004•4 citations

Quantum Phase Transitions of Two-species Bosons(New Development of Numerical Simulations in Low-Dimensional Quantum Systems: From Density Matrix Renormalization Group to Tensor Network Formulations)

Pochung Chen, Min-Fong Yang

物性研究•Mar 5, 2011•0 citations

Topological dualities via tensor networks

Carolin Wille, Jens Eisert, Alexander Altland

The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly associated to different areas of physics -- that of long range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically non-local, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this work, we propose a unified approach to this duality, whose main protagonist is a tensor network (TN) assuming the role of an intermediate translator. Introducing a fourth node into the net of dualities offers several advantages: the formulation is integrative in that all links of the duality are treated on an equal footing, (unlike in field theoretical approaches) it is formulated with lattice precision, a feature that becomes key in the mapping of correlation functions, and their possible numerical implementation. Finally, the passage from bosons to fermions is formulated entirely within the two-dimensional TN framework where it assumes an intuitive and technically convenient form. We illustrate the predictive potential of the formalism by exploring the fate of phase transitions, point and line defects, topological boundary modes, and other structures under the mapping between system classes. Having condensed matter readerships in mind, we introduce the construction pedagogically in a manner assuming only minimal familiarity with the concept of TNs.

arXiv:2309.13118•Sep 22, 2023•0 citations

Effect of a fermion on quantum phase transitions in bosonic systems

FRANCESCO IACHELLO, A. Leviatan, D. Petrellis

arXiv:1111.0781•Physics Letters B•Oct 17, 2011•54 citations
A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum Hamiltonian by an appropriate factor, rewriting the Hamiltonian in terms of SU(2)SU(2)SU(2) operators only, and obtention of a classical Hamiltonian. SU(2)SU(2)SU(2) operators are obtained from creation and annihilation operators as linear combinations in the case of fermions and as an inverse Holstein-Primakoff transformation in the case of bosons. This scheme is successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.
Duality relations are explicitly established relating the Hamiltonians and basis classification schemes associated with the number-conserving unitary and number-nonconserving quasispin algebras for the two-level system with pairing interactions. These relations are obtained in a unified formulation for both bosonic and fermionic systems, with arbitrary and, in general, unequal degeneracies for the two levels. Illustrative calculations are carried out comparing the bosonic and fermionic quantum phase transitions.
The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly associated to different areas of physics -- that of long range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically non-local, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this work, we propose a unified approach to this duality, whose main protagonist is a tensor network (TN) assuming the role of an intermediate translator. Introducing a fourth node into the net of dualities offers several advantages: the formulation is integrative in that all links of the duality are treated on an equal footing, (unlike in field theoretical approaches) it is formulated with lattice precision, a feature that becomes key in the mapping of correlation functions, and their possible numerical implementation. Finally, the passage from bosons to fermions is formulated entirely within the two-dimensional TN framework where it assumes an intuitive and technically convenient form. We illustrate the predictive potential of the formalism by exploring the fate of phase transitions, point and line defects, topological boundary modes, and other structures under the mapping between system classes. Having condensed matter readerships in mind, we introduce the construction pedagogically in a manner assuming only minimal familiarity with the concept of TNs.