Disorder protected and induced local zero-modes in longer-range Kitaev chains

Abstract

We study the effects of disorder on a Kitaev chain with longer-range hopping and pairing terms which is capable of forming local zero energy excitations and, hence, serves as a minimal model for localization-protected edge qubits. The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes (MZMs) per edge. Using a semi-analytic approach corroborated by numerical calculations of the entanglement degeneracy, we show how phase boundaries evolve under the influence of disorder. While in general the 2 MZM region is stable with respect to moderate disorder, stronger values drive transition towards the topologically trivial phase. We uncover regions where the addition of disorder induces local zero-modes absent for the corresponding clean system. Interestingly, we discover that disorder destroys any direct transition between phases with zero and two MZMs by creating a tricritical point at the 2-0 MZM boundary of the clean system. Finally, motivated by recent experiments, we calculate the characteristic signatures of the disorder phase diagram as measured in dynamical local and non-local "qubit" correlation functions. Our work provides a minimal starting point to investigate the coherence properties of local qubits in the presence of disorder.The Kitaev superconductor p-wave chain [1] supports an inherently non-local ground state degeneracy, making it possible to create a qubit which is highly fault-tolerant to local decoherence processes [2] interesting for quantum information technology [3]. While the non-locality of the zero-mode offers this protection, it also poses an experimental challenge since non-local measurements are generally difficult [4,5]. Local qubits formed at the edge of topological chains can exhibit remarkable coherence properties when the bulk system is in a many-body localized state [6,7]. Intuitively, this can be understood from the localization of bulk excitations, which once excited thermally for example, typically decohere the qubit state. However, their detrimental effects may be suppressed in disordered systems due to lack of thermalization [6,8]. This potentially provides a route to achieve both stable qubits and better experimental controllability.Motivated by these ideas, we study the effects of disorder on the topological phase diagram for a minimal variant of the Kitaev chain which enables both local and nonlocal qubit formation [9]. (This system can also be viewed as a three-spin 'cluster' transverse-field Ising model via Jordan-Wigner transformation [10].) The Z classification [11] of the model allows two Majorana zero-modes (MZMs) to form on each side of the chain which can pair up to form a local zero-energy excitation [12]. Previous works have investigated the role of disorder in topological chains with MZMs [13-20] and found that the clean phase diagram is generally robust for weak values of disorder but strong disorder drives the system into a topologically trivial phase. While the issue is of central importance in conventional solid-state setups [21][22][23], recent...

Classification of topological insulators and superconductors out of equilibrium

“…Although we do not do so here, one could also consider quench protocols in which the final Hamiltonian is non-Hermitian, which captures certain gain and/or loss processes. In doing so, one must be careful to consider the relationship between symmetries of the initial state and the non-Hermitian Hamiltonian, the latter of which can have a more general set of symmetries 39 . Note, however, that this work is concerned with properties of the instantaneous wavefunction rather than the spectrum of the Hamiltonian, in contrast to previous studies of non-Hermitian topology [35][36][37][38] .…”

“…∈ Z 2 . As a toy model of such a system (analogous to the one used to demonstrate mixing in class DIII in 66 ), we use a semi-infinite extended Kitaev chain with beyond-nearest-neighbour hopping and pairing 39,67…”

Enhancing correlation times for edge spins through dissipation

“…However, in some instances it has been shown that engineered systemenvironment couplings can actually enhance or even generate quantum correlations, such as entanglement [9][10][11][12][13][14][15][16][17][18]. While robustness of coherence times for edge spins has been extensively studied in the presence of interactions or of integrability-breaking terms and also in the presence of disorder in the Hamiltonian [1,2,19], less is known about their behavior under irreversible open quantum dynamics [20][21][22][23][24]. In particular, it is not clear whether under Markovian (memory-less) dynamics these long edge time-correlations can be observed and general conditions for their existence are not known.…”

Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain

“…Very recently, the experimental observation of the topological Anderson insulator has been reported in 1D disordered atomic chain based * binzhou@hubu.edu.cn on the SSH model [64] and optical lattices [65]. In addition, the disorder-induced topological phases in TSCs have also attracted much attention [66][67][68][69]. Analogous to the topological Anderson insulator, Borchmann et al proposed the concept of the Anderson topological superconductor, a disorder-induced topological state in superconductor systems [66].…”

“…Analogous to the topological Anderson insulator, Borchmann et al proposed the concept of the Anderson topological superconductor, a disorder-induced topological state in superconductor systems [66]. Recently, Lieu et al studied disorder effects on Kitaev chain model with longer-range hopping and pairing terms, and presented the transformation of phase boundaries under the influence of disorder [68]. Moreover, the combined effects of disorder and interaction in the Kitaev chain model have also been investigated by several research groups [70][71][72][73][74].…”