Derivation of $\mathcal{PT}$-symmetric Sine-Gordon model and its relevance to non-equilibrium

Abstract

The Parity-Time PT -symmetric non-Hermitian Sine-Gordon(nhSG) model derived from the nonequilibrium spin-boson model. We have derived the Keldysh rotation for spin operators, from which the SG model can be derived. We perform renormalization group calculations in the Keldysh fields and compare the fixed points and the flow of the effective couplings of nonequilibrium and non-Hermitian models. Also, we explicitly find the self-energies and compare the two methods to understand the regimes where PT symmetry preserved regime, and nonequilibrium regimes persist.RG flow of couplings of nonequilibrium model and non-hermitian model both capture the standard Berezinskii-Kosterlitz-Thouless(BKT) physics in a strong coupling regime.

Anderson Impurities In Edge States with Nonlinear Dispersion

“…In the above solution, F is an incomplete elliptic function of the first kind, and E is an elliptic function of the second kind. P and T are polynomial and transcendental functions, respectively.Similar elliptic functions are found to solve nonhermitian problem [34] to connect the nonequilibrium self-energy of an open system. The inset graph shows the non-interacting FP we got when we set either JY or K to negative otherwise, we have two impurities Kondo effect, where all couplings diverge.…”

“…Moreover, adding second-order self-energy to the original Hamiltonian leads to non-Hermitian physics [32]. In open systems, adding finite-order self-energies can also give rise to effective non-Hermitian models [33][34][35]. In a theoretical study, it has been shown that complex solutions emerge from various types of potentials and their symmetries [36].…”