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arXiv:1812.04471 · iScience

Dissipative Majorana Quantum Wires

Yizhen Huang, Alejandro M. Lobos, Zi Cai

Published Oct 17, 2019• 5 citations
arXivHTMLPDF

Abstract

In this paper, we formulate and quantitatively examine the effect of dissipation on topological systems. We use a specific model of Kitaev quantum wire with an onsite Ohmic dissipation and perform a numerically exact method to investigate the effect of dissipation on the topological features of the system (e.g., the Majorana edge mode) at zero temperature. We find that even though the topological phase is robust against weak dissipation as it is supposed to be, it will eventually be destroyed by sufficiently strong dissipation via either a continuous quantum phase transition or a crossover depending on the symmetry of the system. The dissipation-driven quantum criticality has also been discussed.

DOI
10.1016/j.isci.2019.10.025

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In this paper, we formulate and quantitatively examine the effect of dissipation on topological systems. We use a specific model of Kitaev quantum wire with an onsite Ohmic dissipation and perform a numerically exact method to investigate the effect of dissipation on the topological features of the system (e.g., the Majorana edge mode) at zero temperature. We find that even though the topological phase is robust against weak dissipation as it is supposed to be, it will eventually be destroyed by sufficiently strong dissipation via either a continuous quantum phase transition or a crossover depending on the symmetry of the system. The dissipation-driven quantum criticality has also been discussed.
Robustness of edge states and non-Abelian excitations of topological states of matter promises quantum memory and quantum processing, which are naturally immune to microscopic imperfections such as static disorder. However, topological properties will not in general protect quantum systems from time-dependent disorder or noise. Here we take the example of a network of Kitaev wires with Majorana edge modes storing qubits to investigate the effects of classical noise in the crossover from the quasistatic to the fast fluctuation regime. We present detailed results for the Majorana edge correlations, and fidelity of braiding operations for both global and local noise sources preserving parity symmetry, such as random chemical potentials and phase fluctuations. While in general noise will induce heating and dephasing, we identify examples of long-lived quantum correlations in the presence of fast noise due to motional narrowing, where external noise drives the system rapidly between the topological and nontopological phases.
We discuss the effects of quantum and thermal fluctuations on the Majorana edge states in a topological atomic wire coupled to a superfluid molecular gas with gapless excitations. We find that the coupling between the Majorana edge states remains exponentially decaying with the length of the wire, even at finite temperatures smaller than the energy gap for bulk excitations in the wire. This exponential dependence is controlled solely by the localization length of the Majorana states. The fluctuations, on the other hand, provide the dominant contribution to the preexponential factor, which increases with temperature and the length of the wire. More important is that thermal fluctuations give rise to a decay of an initial correlation between Majorana edge states to its stationary value after some thermalization time. This stationary value is sensitive to the temperature and to the length of the wire, and, although vanishing in the thermodynamic limit, can still be feasible in a mesoscopic system at sufficiently low temperatures. The thermalization time, on the other hand, is found to be much larger than the typical time scales in the wire, and is sufficient for quantum operations with Majorana fermions before the temperature-induced decoherence sets in.
We present a comprehensive theoretical study of interacting and disordered topological phases of coupled Kitaev wires, which may support further realistic applications of Majorana fermions. We develop a variety of analytical, mathematical, and numerical methods for one- and two-coupled wires, associated with a topological marker accessible from real-space correlation functions on the wire(s). We verify the stability of the topological superconducting phase and quantify disorder effects close to the quantum phase transitions, e.g., through two-point correlation functions or using a renormalization group analysis of disorder. We show that the double critical Ising (DCI) phase---a fractional Majorana liquid characterized by a pair of half central charges and topological numbers---is stabilized by strong interactions against disorder, which respects the inversion symmetry between the wires (i.e., parity conservation on each wire). In the presence of an interwire hopping term, the DCI phase turns into a protected topological phase with a bulk gap. We study the localization physics developing along the critical line for weaker interactions.
An attempt is made to study the quantum criticality in non-Hermitian system with topological characterization. We use the zero mode solutions to characterize the topological phases and, criticality and also to construct the phase diagram. The Hermitian counterpart of the model Hamiltonian possess quite a few interesting features such as Majorana zero modes (MZMs) at criticality, unique topological phase transition on the critical line and hence these unique features are of an interest to study in the non-Hermitian case also. We observe a unique behavior of critical lines in presence of non-Hermiticity. We study the topological phase transitions in the non-Hermitian case using parametric curves which also reveal the gap closing point through exceptional points. We study bulk and edge properties of the system where at the edge, the stability dependence behavior of MZMs at criticality is studied and at the bulk we study the effect of non-Hermiticity on the topological phases by investigating the behavior of the critical lines. The study of non-Hermiticity on the critical lines revels the rate of receding of the topological phases with respect to the increase in the value of non-Hermiticity. This work gives a new perspective on topological quantum criticality in non-Hermitian quantum system.
We study a periodically driven one-dimensional Kitaev model in the presence of disorder. In the clean limit our model exhibits four topological phases corresponding to the existence or nonexistence of edge modes at zero and $\ensuremath{\pi}$ quasienergy. When potential disorder is added, the system parameters get renormalized and the system may exhibit a topological phase transition. When starting from the Majorana $\ensuremath{\pi}$ mode (MPM) phase, which hosts only edge Majoranas with quasienergy $\ensuremath{\pi}$, disorder induces a transition into a neighboring phase with both $\ensuremath{\pi}$ and zero modes on the edges. We characterize the disordered system using (i) exact diagonalization, (ii) Arnoldi mapping onto an effective tight-binding chain, and (iii) topological entanglement entropy.
We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.