Kitaev spin models from topological nanowire networks

We show that networks of topological nanowires can realize the physics of exactly solvable Kitaev spin models with two-body interactions. This connection arises from the description of the low-energy theory of both systems in terms of a tight-binding model of Majorana modes. In Kitaev spin models the Majorana description provides a convenient representation to solve the model, whereas in an array of topological nanowires it arises, because the physical Majorana modes localized at wire ends permit tunnelling between wire ends and across different Josephson junctions. We explicitly show that an array of junctions of three wires -- a setup relevant to topological quantum computing with nanowires -- can realize the Yao-Kivelson model, a variant of Kitaev spin models on a decorated honeycomb lattice. Translating the results from the latter, we show that the network can be constructed to give rise to collective states characterized by Chern numbers \nu = 0, +/-1 and +/-2, and that defects in an array can be associated with vortex-like quasi-particle excitations. Finally, we analyze the stability of the collective states as well as that of the network as a quantum information processor. We show that decoherence inducing instabilities, be them due to disorder or phase fluctuations, can be understood in terms of proliferation of the vortex-like quasi-particles.Comment: 15 pages, 9 figure

Enhancing the effect of quantum many-body scars on dynamics by minimising the effective dimension

Quantum many-body scarring is believed to be the mechanism behind long-lived coherent oscillations in interacting Rydberg atom chains. These persistent oscillations are due to the large overlap of the many-body scars with certain initial states. We show that the "effective dimension" is a useful measure for identifying non-thermalising initial states in many-body scarred systems. By minimising the effective dimension we find physically reasonable initial states of the Rydberg chain that lead to more pronounced and longer lived oscillations, accentuating the effect of the many-body scars on the dynamics.Comment: 6 pages (including references and appendix

Extreme many-body scarring in a quantum spin chain via weak dynamical constraints

It has recently been established that quantum many-body scarring can prevent the thermalisation of some isolated quantum systems, starting from certain initial states. One of the first models to show this was the so-called PXP Hamiltonian, which was used to theoretically model an experiment on a chain of strongly interacting Rydberg atoms. A defining feature of the PXP Hamiltonian is a set of dynamical constraints that make certain states inaccessible to the dynamics. In this paper we construct a class of spin chain models that are parameterised by a discrete variable $\ell$ that controls the "strength" of a dynamical constraint. We show that by increasing $\ell$ the constraint becomes weaker, in the sense that fewer states are excluded from the dynamics. The PXP Hamiltonian is special case for $\ell = 2$. By weakening the constraint to $\ell \geq 4$, however, we find a more extreme version of quantum scarring than in the PXP Hamiltonian, with the number of scar states growing exponentially in the system size.Comment: 6 + 3 page

Enhanced zero-bias Majorana peak in disordered multi-subband quantum wires

A recent experiment [Mourik et al., Science 336, 1003 (2012)] on InSb quantum wires provides possible evidence for the realization of a topological superconducting phase and the formation of Majorana bound states. Motivated by this experiment, we consider the signature of Majorana bound states in the differential tunneling conductance of multi-subband wires. We show that the weight of the Majorana-induced zero-bias peak is strongly enhanced by mixing of subbands, when disorder is added to the end of the quantum wire. We also consider how the topological phase transition is reflected in the gap structure of the current-voltage characteristic.Comment: 4+ pages, 5 figures, minor changes in the text and Fig. 5, references added; published versio

Low-energy subgap states in multichannel p-wave superconducting wires

One-dimensional p-wave superconductors are known to harbor Majorana bound states at their ends. Superconducting wires with a finite width W may have fermionic subgap states in addition to possible Majorana end states. While they do not necessarily inhibit the use of Majorana end states for topological computation, these subgap states can obscure the identification of a topological phase through a density-of-states measurement. We present two simple models to describe low-energy fermionic subgap states. If the wire's width W is much smaller than the superconductor coherence length ξ, the relevant subgap states are localized near the ends of the wire and cluster near zero energy, whereas the lowest-energy subgap states are delocalized if W≳ξ. Notably, the energy of the lowest-lying fermionic subgap state (if present at all) has a maximum for W∼ξ

Impossible measurements revisited

It is by now well-recognised that the na\"ive application of the projection postulate on composite quantum systems can induce signalling between their constituent components, indicative of a breakdown of causality in a relativistic spacetime context. Here we introduce a necessary and sufficient condition for an ideal measurement of an observable to be non-signalling. As well as being particularly simple, it generalises previous no-signalling conditions in that it allows for degeneracies and can be applied to all bounded self-adjoint operators. The condition is used to establish that arbitrary sums of local observables will not signal, in accordance with our expectations from relativistic quantum field theory. On the other hand, it is shown that the measurement of the tensor product of commuting local observables, for example bipartite operators of the form $A\otimes B$, can in fact signal, contrary to the widely-held belief that such measurements are always locally realisable. The implications for the notion of measurement in relativistic quantum field theory are addressed; it appears that the most straightforward application of the standard quantum formalism generically leads to violations of causality. We conclude that either the class of observables that can be measured should be restricted and/or that the na\"ive translation of the measurement framework of quantum theory, in particular the projection postulate, to quantum field theory should be re-evaluated