Exactly Solvable Quasi-hermitian Transverse Ising Model

Abstract

A non-hermitian deformation of the one-dimensional transverse Ising model is shown to have the property of quasi-hermiticity. The transverse Ising chain is obtained from the starting non-hermitian Hamiltonian through a similarity transformation. Consequently, both the models have identical eigen-spectra, although the eigen-functions are different. The metric in the Hilbert space, which makes the non-hermitian model unitary and ensures the completeness of states, has been constructed explicitly. Although the longitudinal correlation functions are identical for both the non-hermitian and the hermitian Ising models, the difference shows up in the transverse correlation functions, which have been calculated explicitly and are not always real. A proper set of hermitian spin operators in the Hilbert space of the non-hermitian Hamiltonian has been identified, in terms of which all the correlation functions of the non-hermitian Hamiltonian become real and identical to that of the standard transverse Ising model. Comments on the quantum phase transitions in the non-hermitian model have been made.

RevTeX 6 pages, no figures; Added discussions and references, version to appear in Journal of Physics A

References in corpus (22)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• Dynamics of quantum phase transition: exact solution in quantum Ising model
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Quantum Phase Transitions and Bipartite Entanglement
• Must a Hamiltonian be Hermitian?
• Reaction-Diffusion Processes, Critical Dynamics and Quantum Chains
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• The ODE/IM Correspondence
• Quasi-exactly solvable quartic potential
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Multipartite Entanglement Signature of Quantum Phase Transitions
• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
• New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain
• Non-Hermitian oscillator Hamiltonian and su(1,1): a way towards generalizations
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Level statistics of a pseudo-Hermitian Dicke model
• On the Real Spectra of Calogero Model with Complex Coupling
• Generalized Swanson models and their solutions
• Quantum Phase Transition in a Pseudo-hermitian Dicke model

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