The authors construct here an exactly solvable \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}}-symmetric non-Hermitian Heisenberg spin chain with complex-conjugate boundary Kondo couplings. They show that the model exhibits three distinct boundary phases: dissipative Kondo screening with unbroken \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} symmetry, bound-mode phases featuring spontaneously broken \ensuremath{\mathcal{P}}\ensuremath{\mathcal{T}} symmetry and complex-conjugate eigenvalues, and an unscreened local-moment phase with a purely real spectrum. Benchmarking with non-Hermitian DMRG demonstrates quantitative agreement with Bethe ansatz, validating tensor-network methods for open quantum systems.
Abstract We construct the exact solution of a non-Hermitian P T -symmetric isotropic Heisenberg spin chain with integrable boundary fields. We find that the system exhibits two types of phases named A and B . In the B type phase, the P T symmetry remains unbroken and it comprises of eigenstates with only real energies, whereas the A type phase exhibits both P T symmetry broken and unbroken sectors, comprising of eigenstates with only complex and real energies respectively. The P T -symmetry broken sector comprises 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.
Abstract Nonequilibrium phase transitions in open dissipative systems can be described as instabilities in the spectra and wavefunctions of effective non-Hermitian Hamiltonians invariant under simultaneous parity (
P P ) and time-reversal (
T T ) transformations. The degree of non-Hermiticity reflects the strength of the external drive and dissipation, and the transition is described as a loss of the
PT PT symmetry of the solutions corresponding to stationary low-drive dynamics. This approach has been successfully applied to spin, superconducting, and Mott insulator systems. However, the microscopic foundations for the employed phenomenological models are currently lacking. Here we propose a microscopic mechanism leading to the
PT PT -symmetric effective model in the context of the nonequilibrium Mott transition in a dissipative Hubbard chain. Our model comprises a half-filled fermionic Hubbard chain subject to a constant electric field. The dissipation is introduced via the electron-phonon coupling. We obtain the explicit expressions for the non-Hermitian parameter in terms of the electron-phonon coupling strength and driving field. Analyzing the implications of microscopic model, we find a re-entrant Mott insulator with the increasing electric field for phonon density of states that increases slower than the square of the energy (such as in one or two dimensions), or varies non-monotonously with energy.