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arXiv:2302.13561 · Physical Review Research

Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains

Sharareh Sayyad, José Luis Lado

Published Jun 2, 2023• 17 citations
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Abstract

The interacting phase diagram of a non-Hermitian one-dimensional model featuring topologically different phases is demonstrated. Furthermore, the exact solution in the integrable regime, which has been extended to the nonintegrable regime by employing exact diagonalization and matrix product state methods, is presented. The present results are expected to pave a new pathway toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.

DOI
10.1103/physrevresearch.5.l022046

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The interacting phase diagram of a non-Hermitian one-dimensional model featuring topologically different phases is demonstrated. Furthermore, the exact solution in the integrable regime, which has been extended to the nonintegrable regime by employing exact diagonalization and matrix product state methods, is presented. The present results are expected to pave a new pathway toward characterizing non-Hermitian topology in realistic interacting quantum many-body systems.
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It was recently shown that an interacting Kitaev topological superconductor model is exactly solvable based on two-step Jordan-Wigner transformations together with one spin rotation. We generalize this model by including the dimerization, which is shown also to be exactly solvable. We analytically determine the topological phase diagram containing seven distinct phases. It is argued that the system is topological when a fermionic many-body Majorana zero-energy edge state emerges. It is intriguing that there are two tetracritical points, at each of which four distinct phases touch.
An Attempt is made to study the non-Hermitian effect on the topological quantum criticality and also in the physics of Majroana zero mode (MZMs). In this work, the effects and modifications done by the non-Hermitian factor γγγ on the topological phases, criticality and also in the MZMs is studied. We use the zero mode solutions (ZMS) to construct the phase diagram. We find a correspondence between Hermitian and non-Hermitian model Hamiltonian. The MZMs appear at criticality and has a stability dependence on the new passage created because of the introduction of non-Hermiticity. The multicritical points are also studied to understand their nature under the influence of non-Hemiticity. We also study the effect of non-Hermiticity on the topological phases.
We investigate the non-Hermitian Kitaev chain with non-reciprocal hopping amplitudes and asymmetric superconducting pairing. We work out the symmetry structure of the model and show that particle-hole symmetry (PHS) is preserved throughout the entire parameter regime. As a consequence of PHS, the topological phase transition point of a finite open chain coincides with that of the periodic (infinite) system. By explicitly constructing the zero-energy wave functions (Majorana modes), we show that Majorana modes necessarily occur as reciprocal localization pairs accumulating on opposite boundaries, whose combined probability density exhibits an exact cancellation of the non-Hermitian skin effect for the zero energy modes. Excited states, by contrast, generically display skin-effect localization, with particle and hole components accumulating at opposite ends of the system. At the level of bulk topology, we further construct a Z2\mathbb{Z}_2Z2​ topological invariant in restricted parameter regimes that correctly distinguishes the topological and trivial phases. Finally, we present the topological phase diagram of the non-Hermitian Kitaev chain across a broad range of complex parameters and delineate the associated phase boundaries.
We systematically study a Kitaev chain with imbalanced pair creation and annihilation, which is introduced by non-Hermitian pairing terms. An exact phase diagram shows that the topological phase is still robust under the influence of the conditional imbalance. The gapped phases are characterized by a topological invariant, the extended Zak phase, which is defined by the biorthonormal inner product. Such phases are destroyed at the points where the coalescence of ground states occurs, associated with the time-reversal symmetry breaking. We find that the Majorana edge modes also exist in an open chain in the time-reversal symmetry-unbroken region, demonstrating the bulk-edge correspondence in such a non-Hermitian system.
We study analytically topological properties of a noninteracting modified dimerized Kitaev chain and an exactly solvable interacting dimerized Kitaev chain under open boundary conditions by analyzing two introduced edge correlation functions. The interacting dimerized Kitaev chain at the symmetry point $\mathrm{\ensuremath{\Delta}}=t$ and the chemical potential $\ensuremath{\mu}=0$ can be exactly solved by applying two Jordan-Wigner transformations and a spin rotation, which permits us to calculate the edge correlation functions analytically. We demonstrate that the two edge correlation functions can be used to characterize the trivial, Su-Schrieffer-Heeger-like topological and topological superconductor phases of both the noninteracting and interacting systems and give their phase diagrams.