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Register a new userReal-complex transition driven by quasiperiodicity: a new universality class beyond $mathcal{PT}$ symmetric one
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We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. Firstly, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential tuning parameter $a$. The localization property of $|a|<1$ can be directly mapping to that of $|a|>1$, the analytical expression of the mobility edge of $|a|>1$ is therefore obtained through spectral properties of $|a|<1$. More impressive, we prove rigorously that even if the phase $theta eq 0$ in quasiperiodic potentials, the model becomes non-$mathcal{PT}$ symmetric, however, there still exists a new type of real-complex transition driven by non-Hermitian disorder, which is a new universality class beyond $mathcal{PT}$ symmetric class.
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We study the delocalization dynamics of interacting disordered hard-core bosons for quasi-1D and 2D geometries, with system sizes and time scales comparable to state-of-the-art experiments. The results are strikingly similar to the 1D case, with slow, subdiffusive dynamics featuring power-law decay. From the freezing of this decay we infer the critical disorder $W_c(L, d)$ as a function of length $L$ and width $d$. In the quasi-1D case $W_c$ has a finite large-$L$ limit at fixed $d$, which increases strongly with $d$. In the 2D case $W_c(L,L)$ grows with $L$. The results are consistent with the avalanche picture of the many-body localization transition.
We study a one-dimensional $p$-wave superconductor subject to non-Hermitian quasiperiodic potentials. Although the existence of the non-Hermiticity, the Majorana zero mode is still robust against the disorder perturbation. The analytic topological phase boundary is verified by calculating the energy gap closing point and the topological invariant. Furthermore, we investigate the localized properties of this model, revealing that the topological phase transition is accompanied with the Anderson localization phase transition, and a wide critical phase emerges with amplitude increments of the non-Hermitian quasiperiodic potentials. Finally, we numerically uncover a non-conventional real-complex transition of the energy spectrum, which is different from the conventional $mathcal{PT}$ symmetric transition.
Non-hermitian, $mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $mathcal{PT}$ symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that $mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $mathcal{PT}$ symmetric phases.
We investigate the dynamical evolution of a parity-time ($mathcal{PT}$) symmetric extension of the Aubry-Andr{e} (AA) model, which exhibits the coincidence of a localization-delocalization transition point with a $mathcal{PT}$ symmetry breaking point. One can apply the evolution of the profile of the wave packet and the long-time survival probability to distinguish the localization regimes in the $mathcal{PT}$ symmetric AA model. The results of the mean displacement show that when the system is in the $mathcal{PT}$ symmetry unbroken regime, the wave-packet spreading is ballistic, which is different from that in the $mathcal{PT}$ symmetry broken regime. Furthermore, we discuss the distinctive features of the Loschmidt echo with the post-quench parameter being localized in different $mathcal{PT}$ symmetric regimes.
We study the cross-stitch flat band lattice with a $mathcal{PT}$-symmetric on-site potential and uncover mobility edges with exact solutions. Furthermore, we study the relationship between the $mathcal{PT}$ symmetry broken point and the localization-delocalization transition point, and verify that mobility edges in this non-Hermitian model is available to signal the $mathcal{PT}$ symmetry breaking.
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