Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains

• URL: http://arxiv.org/abs/2211.00679v1
• Date: Tue, 1 Nov 2022 18:10:12 GMT
• Title: Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
• Authors: Grigory A. Starkov, Mikhail V. Fistoul, Ilya M. Eremin
• Abstract summary: We present a theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian $mathcalPmathcalT$-symmetric superconducting qubits chains. A non-Hermitian part of the Hamiltonian is implemented via imaginary staggered textitlongitudinal magnetic field. We obtain two quantum phases for $J0$, namely, $mathcalPmathcalT$-symmetry broken antiferromagnetic state and $mathcalPmathcalT$-symmetry preserved paramagnetic state
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a theoretical study of quantum phases and quantum phase transitions occurring in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric superconducting qubits chains described by a transverse-field Ising spin model. A non-Hermitian part of the Hamiltonian is implemented via imaginary staggered \textit{longitudinal } magnetic field, which corresponds to a local staggered gain and loss terms. By making use of a direct numerical diagonalization of the Hamiltonian for spin chains of a finite size $N$, we explore the dependencies of the energy spectrum, including the energy difference between the first excited and the ground states, the spatial correlation function of local polarization ($z$-component of local magnetization) on the adjacent spins interaction strength $J$ and the local gain (loss) parameter $\gamma$. A scaling procedure for the coherence length $\xi$ allows us to establish a complete quantum phase diagram of the system. We obtain two quantum phases for $J<0$, namely, $\mathcal{P}\mathcal{T}$-symmetry broken antiferromagnetic state and $\mathcal{P}\mathcal{T}$-symmetry preserved paramagnetic state, and the quantum phase transition line between them is the line of exception points. For $J>0$ the $\mathcal{P}\mathcal{T}$-symmetry of the ground state is retained in a whole region of parameter space of $J$ and $\gamma$, and a system shows \textit{two} intriguing quantum phase transitions between ferromagnetic and paramagnetic states for a fixed parameter $\gamma > 1$. We also provide the qualitative quantum phase diagram $\gamma-J$ derived in the framework of the Bethe-Peierls approximation that is in a good accord with numerically obtained results.

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