A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field

Castro-Alvaredo, Olalla A.; Fring, Andreas

doi:10.1088/1751-8113/42/46/465211

Cited by 74 publications

(70 citation statements)

References 48 publications

(134 reference statements)

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“…It is the simplest non-unitary model in this infinite class of models, which are all characterized by the condition p − q > 1, and whose corresponding Hamiltonians are all expected to be non-Hermitian. The PT -symmetry of the model was exploited in Castro-Alvaredo & Fring [22].…”

Section: Pt -Symmetrically Deformed Quantum Spin Chainsmentioning

confidence: 99%

PT -symmetric deformations of integrable models

Fring

2013

Phil. Trans. R. Soc. A.

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We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of Calogero-Moser-Sutherland type and non-linear integrable field equations of Korteweg-de-Vries type. The quantum spin chain discussed is related to the first example in the series of the non-unitary models of minimal conformal field theories. For the Calogero-Moser-Sutherland models we provide three alternative deformations: A complex extension for models related to all types of Coxeter/Weyl groups; models describing the evolution of poles in constrained real valued field equations of non linear integrable systems and genuine deformations based on antilinearly invariant deformed root systems. Deformations of complex nonlinear integrable field equations of KdV-type are studied with regard to different kinds of PT-symmetrical scenarios. A reduction to simple complex quantum mechanical models currently under discussion is presented.Comment: 21 pages, 3 figure

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Section: Pt -Symmetrically Deformed Quantum Spin Chainsmentioning

confidence: 99%

PT -symmetric deformations of integrable models

Fring

2013

Phil. Trans. R. Soc. A.

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“…Within the context of PT -symmetric theory, non-hermitian spin chains have been studied in Refs. [8,9].…”

Section: Xxz Spin-chainmentioning

confidence: 99%

On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space

Ghosh¹

2010

J. Phys. A: Math. Theor.

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A class of pseudo-hermitian quantum system with an explicit form of the positive-definite metric in the Hilbert space is presented. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. The examples considered include simple harmonic oscillators with complex angular frequencies, Stark(Zeeman) effect with non-hermitian interaction, non-hermitian general quadratic form of N boson(fermion) operators, symmetric and asymmetric XXZ spin-chain in complex magnetic field, non-hermitian Haldane-Shastry spin-chain and LipkinMeshkov-Glick model.

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“…Within the context of PT -symmetric theory, non-hermitian spin chains have been studied in Refs. [4,7,8].…”

Section: Pseudo-hermitian Xxz Spin-chainmentioning

confidence: 99%

“…A few prototype examples from a vast list of such systems are contained in Refs. [1,2,3,4,5,6,7,8,9,10,11]. The real difficulty in giving a complete description of these systems lies in finding the exact positive-definite metric in the Hilbert space.…”

Section: Introductionmentioning

confidence: 99%

Constructing Exactly Solvable Pseudo-hermitian Many-Particle Quantum Systems by Isospectral Deformation

Ghosh¹

2010

Int J Theor Phys

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A class of non-Dirac-hermitian many-particle quantum systems admitting entirely real spectra and unitary time-evolution is presented. These quantum models are isospectral with Dirac-hermitian systems and are exactly solvable. The general method involves a realization of the basic canonical commutation relations defining the quantum system in terms of operators those are hermitian with respect to a pre-determined positive definite metric in the Hilbert space. Appropriate combinations of these operators result in a large number of pseudo-hermitian quantum systems admitting entirely real spectra and unitary time evolution. Examples of a pseudo-hermitian rational Calogero model and XXZ spin-chain are considered.

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A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field

Cited by 74 publications

References 48 publications

PT -symmetric deformations of integrable models

PT -symmetric deformations of integrable models

On the construction of a pseudo-Hermitian quantum system with a pre-determined metric in the Hilbert space

Constructing Exactly Solvable Pseudo-hermitian Many-Particle Quantum Systems by Isospectral Deformation

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