Olalla A Castro-Alvaredo and Andreas Fring 2009 J. Phys. A: Math. Theor. 42 465211 doi:10.1088/1751-8113/42/46/465211
A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field
Olalla A Castro-Alvaredo and Andreas Fring
Show affiliationsWe investigate a lattice version of the Yang–Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement 
-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken 
-symmetry, we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turn out to be unique with the sole assumption that the Dyson map is Hermitian. Finally, we analyse the magnetization of the chain in the z- and x-direction.
- PACS
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05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
75.10.Jm Quantized spin models
75.60.Ej Magnetization curves, hysteresis, Barkhausen and related effects
- MSC
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82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs
82C26 Dynamic and nonequilibrium phase transitions (general)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
- Subjects
- Dates
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Issue 46 (20 November 2009)
Received 2 July 2009, in final form 30 September 2009
Published 26 October 2009
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A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field
Olalla A Castro-Alvaredo and Andreas Fring 2009 J. Phys. A: Math. Theor. 42 465211
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