Spontaneous PT symmetry breaking and quantum phase transitions in dimerized spin chains

Abstract

The occurrence of parity-time reversal ($\mathcal{P}\mathcal{T}$) symmetry breaking is discussed in a non-Hermitian spin chain. The Hermiticity of the model is broken by the presence of an alternating, imaginary, transverse magnetic field. A full real spectrum, which occurs if and only if all the eigenvectors are $\mathcal{P}\mathcal{T}$ symmetric, can appear only in presence of dimerization, i.e. only if the hopping amplitudes between nearest-neighbor spins assume alternate values along the chain. In order to make a connection between such system and the Hermitian world, we study the critical magnetic properties of the model and look for the conditions that would allow to observe the same phase diagram in the absence of the imaginary field. Such procedure amounts to renormalizing the spin-spin coupling amplitudes.

References in corpus (13)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Exact PT-Symmetry Is Equivalent to Hermiticity
• Physical Aspects of Pseudo-Hermitian and $PT$-Symmetric Quantum Mechanics
• Solutions of PT symmetric tight-binding chain and its equivalent Hermitian counterpart
• On Pseudo-Hermitian Hamiltonians and Their Hermitian Counterparts
• PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
• Physics counterpart of the PT non-hermitian tight-binding chain
• A spin chain model with non-Hermitian interaction: The Ising quantum spin chain in an imaginary field
• Ground-state factorization and quantum phase transition in dimerized spin chains
• PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
• Separability and entanglement in finite dimer-type chains in general transverse fields

Cited by in corpus (29)

• Heralded magnetism in non-Hermitian atomic systems
• Quantum Geometric Tensor in $\mathcal{P}\mathcal{T}$-Symmetric Quantum Mechanics
• Spontaneous PT symmetry breaking in non-Hermitian coupled cavities array
• Non-Hermitian bidirectional robust transport
• Non-Hermitian anisotropic XY model with intrinsic rotation-time reversal symmetry
• Convective and absolute PT symmetry breaking in tight-binding lattices
• PT-symmetric deformations of integrable models
• Proposal for Observing Yang-Lee Criticality in Rydberg Atomic Arrays
• Non-Hermitian Dynamics in the Quantum Zeno Limit
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• Self-sustained emission in semi-infinite non-Hermitian systems at the exceptional point
• Hermitian dynamics in a class of pseudo-Hermitian networks
• A physical interpretation for the non-Hermitian Hamiltonian
• Probability-preserving evolution in a non-Hermitian two-band model
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• Quantum battery with non-Hermitian charging
• Nonadiabatic robust excitation transfer assisted by an imaginary gauge field
• Scaling behavior and phase diagram of a PT-symmetric non-Hermitian Bose-Hubbard system
• Dynamic magnetization in non-Hermitian quantum spin system
• Generation of Bell, W and GHZ states via exceptional points in non-Hermitian quantum spin systems
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain
• Exotic entanglement for non-Hermitian Jaynes-Cummings Hamiltonians
• Chern number in Ising models with spatially modulated real and complex fields
• Physics of PT-Symmetric Quantum Systems at Finite Temperature
• Detecting exceptional points through dynamics in non-Hermitian systems
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Effective non-Hermitian physics for degenerate ground states of a nonHermitian Ising model with $\mathcal{R}\mathcal{T}$ symmetry
• Interplay between nonclassicality and $\mathcal{P}\mathcal{T}$ symmetry in an effective two level system with open system effects
• Interferometric Geometric Phases of $\mathcal{P}\mathcal{T}$-symmetric Quantum Mechanics