Geometric phase and phase diagram for a non-Hermitian quantum X Y model

2017

Phys. Rev. B

Transport of quantum or classical waves in open systems is known to be strongly affected by non-Hermitian terms that arise from an effective description of system-enviroment interaction. A simple and paradigmatic example of non-Hermitian transport, originally introduced by Hatano and Nelson two decades ago [N. Hatano and D.R. Nelson, Phys. Rev. Lett. 77, 570 (1996)], is the hopping dynamics of a quantum particle on a one-dimensional tight-binding lattice in the presence of an imaginary vectorial potential. The imaginary gauge field can prevent Anderson localization via non-Hermitian delocalization, opening up a mobility region and realizing robust transport immune to disorder and backscattering. Like for robust transport of topologically-protected edge states in quantum Hall and topological insulator systems, non-Hermitian robust transport in the HatanoNelson model is unidirectional. However, there is not any physical impediment to observe robust bidirectional non-Hermitian transport. Here it is shown that in a quasi-one dimensional zigzag lattice, with non-Hermitian (imaginary) hopping amplitudes and a synthetic gauge field, robust transport immune to backscattering can occur bidirectionally along the lattice.

Section: Introductionmentioning

confidence: 99%

Non-Hermitian bidirectional robust transport

2017

Phys. Rev. B

“…Non-Hermitian Hamiltonians are widely used as effective models to describe open quantum and classical systems [4,5,6], or are introduced to provide complex extensions of the ordinary quantum mechanics such as in the PT -symmetric quantum mechanics [7,8,9,10]. The increasing interest devoted to non-Hermitian dynamics has motivated the extension of the arsenal of perturbation mathematical tools into the non-Hermitian realm 1 [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Several results have been found concerning extensions and breakdown of the adiabatic theorem [13,15,16,34,38,39], Berry phase [12,14,…”

Section: Introductionmentioning

confidence: 99%

“…The increasing interest devoted to non-Hermitian dynamics has motivated the extension of the arsenal of perturbation mathematical tools into the non-Hermitian realm 1 [11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42]. Several results have been found concerning extensions and breakdown of the adiabatic theorem [13,15,16,34,38,39], Berry phase [12,14,17,18,22,26,27,32,33] and shortcuts to adiabaticity [30,36,…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions

Valle

2017

Annals of Physics

The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial an final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint HamiltonianĤ 0 , induced by a time-dependent non-Hermitian interaction f (t)Ĥ 1 . In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be asymmetric for exchange of initial and final states. In particular, for a temporal shape f (t) of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form ofĤ 0 andĤ 1 . As an application of our results, we provide important physical insights into the asymmetric (chiral) behavior of dynamical encircling of an exceptional point in two-and three-level non-Hermitian systems.

“…However, the quantum phase transition induced interface state still remains with almost no frequency change and its field is most concentrated at the first A site of the right sub-lattice, evidently demonstrating that the interface state by quantum phase transition is robust against global topological disorders. This topology-insensitive property overcomes the limitation of the stringent topological dependence in topological photonics where topological disorder may destroy the topological phase transition and thus ruin its induced interface state 39 .…”

mentioning

confidence: 97%

Robust Light State by Quantum Phase Transition in Non-Hermitian Optical Materials

Zhao

Feng

2015

Sci Rep

Robust light transport is the heart of optical information processing, leading to the search for robust light states by topological engineering of material properties. Here, it is shown that quantum phase transition, rather than topology, can be strategically exploited to design a novel robust light state. We consider an interface between parity-time (PT) symmetric media with different quantum phases and use complex Berry phase to reveal the associated quantum phase transition and topological nature. While the system possesses the same topological order within different quantum phases, phase transition from PT symmetry to PT breaking across the interface in the synthetic non-Hermitian metamaterial system facilitates novel interface states, which are robust against a variety of gain/loss perturbations and topological impurities and disorder. The discovery of the robust light state by quantum phase transition may promise fault-tolerant light transport in optical communications and computing.