Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain

Abstract

We construct the exact solution of a non-Hermitian $\mathcal{PT}$-symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases we refer to as $A$ and $B$ phases. In the $B$ type phase, the $\mathcal{PT}$- symmetry remains unbroken and it consists of eigenstates with only real energies, whereas the $A$ type phase contains a $\mathcal{PT}$-symmetry broken sector comprised of eigenstates with only complex energies and a sector of unbroken $\mathcal{PT}$-symmetry with eigenstates of real energies. The $\mathcal{PT}$-symmetry broken sector consists of pairs of eigenstates whose energies are complex conjugates of each other. The existence of two sectors in the $A$ type phase is associated with the exponentially localized bound states at the edges with complex energies which are described by boundary strings. We find that both $A$ and $B$ type phases can be further divided into sub-phases which exhibit different ground states. We also compute the bound state wavefunction in one magnon sector and find that as the imaginary value of the boundary parameter is increased, the exponentially localized wavefunction broadens thereby protruding more into the bulk, which indicates that exponentially localized bound states may not be stabilized for large imaginary values of the boundary parameter.

arXiv comment28 pages and 4 figures

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• Kondo effect in the isotropic Heisenberg spin chain
• A spin chain with non-Hermitian $\mathcal{PT}-$symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge
• Edge modes and boundary impurities in the anisotropic Heisenberg spin chain
• The Kondo effect in the quantum $XX$ spin chain
• Breakdown of Linear Spin-Wave Theory in a Non-Hermitian Quantum Spin Chain
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Oscillation probabilities for a PT-symmetric non-Hermitian two-state system
• Dissipative Kondo physics in the Anderson Impurity Model with two-body losses
• Interacting many-body non-Hermitian systems as Markov chains