论文标题
量子相转换中的非 - 富人$ \ MATHCAL {P} \ MATHCAL {T} $ - 对称横向式旋转链
Quantum phase transitions in non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric transverse-field Ising spin chains
论文作者
论文摘要
我们提出了一项理论研究，该研究是对在非铁级$ \ MATHCAL {p} \ MATHCAL {T} $ - 对称的超导量子链链中发生的量子相和量子相变的理论研究。哈密顿式的一个非武者部分是通过假想的交错\ textit {纵向}磁场实现的，该磁场对应于局部交错的增益和损失项。 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 $γ$.相干长度$ξ$的缩放过程使我们能够建立系统的完整量子相图。我们获得了$ j <0 $的两个量子阶段，即，$ \ Mathcal {p} \ Mathcal {t} $ - 对称破碎的反铁磁性状态和$ \ Mathcal {p} \ Mathcal {t} $ - 对称保留的paramagnetic状态，以及量子相对的量子相位，以及它们之间的量子量线，它们之间的量子量为单位。对于$ j> 0 $，$ \ mathcal {p} \ mathcal {t} $ - 基础状态的对称性保留在$ j $和$ j $的参数空间的整个区域中，并且一个系统显示\ textit {textit {twiT}吸引量子相位的量子相位过渡，并在固定parameter for ofermagnetic和paramagnet contention for nesive of pargemeter o a viensepers parmeter parmeters parmeter $ $ umg之间。我们还提供了定性量子相图$γ-J $在伯特 - 皮埃尔斯近似框架中得出的，这与数值获得的结果非常好。
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 $γ$. A scaling procedure for the coherence length $ξ$ 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 $γ$, and a system shows \textit{two} intriguing quantum phase transitions between ferromagnetic and paramagnetic states for a fixed parameter $γ> 1$. We also provide the qualitative quantum phase diagram $γ-J$ derived in the framework of the Bethe-Peierls approximation that is in a good accord with numerically obtained results.
