Progress of Theoretical Physics Supplement

Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the α-XY Model(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)

Shin‐itiro Goto, Yoshiyuki Y. Yamaguchi

Published Jun 5, 2006• 0 citations

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Progress of Theoretical Physics Supplement

Non-Universal Finite Size Effects with Universal Infinite-Size Free Energy for the α-XY Model(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)

Shin‐itiro Goto, Yoshiyuki Y. Yamaguchi

Published Jun 5, 2006• 0 citations

OpenAlex

Related papers

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Shin‐itiro Goto, Yoshiyuki Y. Yamaguchi

arXiv:cond-mat/0512381Physica A Statistical Mechanics and its ApplicationsApr 8, 20051 citation

Quantum Fisher Information and q-Deformed Relative Entropies : Additivity vs Nonadditivity(COMPLEXITY AND NONEXTENSIVITY:NEW TRENDS IN STATISTICAL MECHANICS)

Hiroshi Hasegawa

Progress of Theoretical Physics SupplementJun 5, 20060 citations

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Carlos Wexler, Cintia Mariela Lapilli, Peter Pfeifer

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Minoru Takahashi

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Exceptional point rings and $\mathcal{P}\mathcal{T}$ -symmetry in the non-Hermitian XY modelExceptional point rings and $$\mathcal{P}\mathcal{T}$$-symmetry in the non-Hermitian XY model

Robert A. Henry, Dongchang Liu, Murray T. Batchelor

Abstract The XY spin chain is a paradigmatic example of a model solved by free fermions, in which the energy eigenspectrum is built from combinations of quasi-energies. In this article, we show that by extending the XY model’s anisotropy parameter $\lambda$ λ to complex values, it is possible for two of the quasi-energies to become degenerate. In the non-Hermitian XY model, these quasi-energy degeneracies give rise to exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. The distinct $\lambda$ λ values at which EPs appear form concentric rings in the complex plane which are shown in the infinite system size limit to converge to the unit circle coinciding with the boundary between distinct topological phases. The non-Hermitian model is also seen to possess a line of broken $\mathcal{P}\mathcal{T}$ P T symmetry along the pure imaginary $\lambda$ λ -axis. For finite systems, there are four EP values on this broken $\mathcal{P}\mathcal{T}$ P T -symmetric line if the system size is a multiple of 4.Abstract The XY spin chain is a paradigmatic example of a model solved by free fermions, in which the energy eigenspectrum is built from combinations of quasi-energies. In this article, we show that by extending the XY model’s anisotropy parameter $$\lambda$$ λ to complex values, it is possible for two of the quasi-energies to become degenerate. In the non-Hermitian XY model, these quasi-energy degeneracies give rise to exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. The distinct $$\lambda$$ λ values at which EPs appear form concentric rings in the complex plane which are shown in the infinite system size limit to converge to the unit circle coinciding with the boundary between distinct topological phases. The non-Hermitian model is also seen to possess a line of broken $$\mathcal{P}\mathcal{T}$$ P T symmetry along the pure imaginary $$\lambda$$ λ -axis. For finite systems, there are four EP values on this broken $$\mathcal{P}\mathcal{T}$$ P T -symmetric line if the system size is a multiple of 4.

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Exceptional point rings and

\mathcal{P}\mathcal{T}

-symmetry in the non-Hermitian XY model

\lambda

λ to complex values, it is possible for two of the quasi-energies to become degenerate. In the non-Hermitian XY model, these quasi-energy degeneracies give rise to exceptional points (EPs) where eigenvalues and their corresponding eigenvectors coalesce. The distinct

\lambda

λ values at which EPs appear form concentric rings in the complex plane which are shown in the infinite system size limit to converge to the unit circle coinciding with the boundary between distinct topological phases. The non-Hermitian model is also seen to possess a line of broken

\mathcal{P}\mathcal{T}

P T symmetry along the pure imaginary

\lambda

λ -axis. For finite systems, there are four EP values on this broken

\mathcal{P}\mathcal{T}

P T -symmetric line if the system size is a multiple of 4.