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Register a new userNovel Topological Phases and Self-Correcting Memories in Interacting Anyon Systems
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Authors
James R. Wootton
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Recent studies have shown that topological models with interacting anyonic quasiparticles can be used as self-correcting quantum memories. Here we study the behaviour of these models at thermal equilibrium. It is found that the interactions allow topological order to exist at finite temperature, not only in an extension of the ground state phase but also in a novel form of topologically ordered phase. Both phases are found to support self-correction in all models considered, and the transition between them corresponds to a change in the scaling of memory lifetime with system size.
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We show that semiconductor nanowires coupled to an s-wave superconductor provide a playground to study effects of interactions between different topological superconducting phases supporting Majorana zero-energy modes. We consider quasi-one dimensional system where the topological phases emerge from different transverse subbands in the nanowire. In a certain parameter space, we show that there is a multicritical point in the phase diagram where the low-energy theory is equivalent to the one describing two coupled Majorana chains. We study effect of interactions as well as symmetry-breaking perturbations on the topological phase diagram in the vicinity of this multicritical point. Our results shed light on the stability of the topological phase around the multicritical point and have important implications for the experiments on Majorana nanowires.
The construction and classification of symmetry-protected topological (SPT) phases in interacting bosonic and fermionic systems have been intensively studied in the past few years. Very recently, a complete classification and construction of space group SPT phases were also proposed for interacting bosonic systems. In this paper, we attempt to generalize this classification and construction scheme systematically into interacting fermion systems. In particular, we construct and classify point group SPT phases for 2D interacting fermion systems via lower-dimensional block-state decorations. We discover several intriguing fermionic SPT states that can only be realized in interacting fermion systems (i.e., not in free-fermion or bosonic SPT systems). Moreover, we also verify the recently conjectured crystalline equivalence principle for 2D interacting fermion systems. Finally, the potential experimental realization of these new classes of point group SPT phases in 2D correlated superconductors is addressed.
We study theoretically the effects of long-range and on-site Coulomb interactions on the topological phases and transport properties of spin-orbit-coupled quasi-one-dimensional quantum wires imposed on an s-wave superconductor. The electrostatic potential and charge density distributions are computed self-consistently within the Hartree approximation. Due to the finite width of the wires and the charge repulsion, the potential and density distribute inhomogeneously in the transverse direction and tend to accumulate along the lateral edges where the hard-wall confinement is assumed. This result has profound effects on the topological phases and the differential conductance of the interacting quantum wires and their hybrid junctions with superconductors. Coulomb interactions renormalize the chemical potential, and alter the topological phases strongly by enhancing the topological regimes and producing jagged boundaries. Moreover, the multicritical points connecting different topological phases from high-index subbands are modified remarkably in striking contrast to the predictions of the two-band model. We further suggest the possible non-magnetic topological phase transitions manipulated externally with the aid of long-range interactions. Finally, the transport properties of normal-superconductor junctions are also examined and interaction impacts on the emergence of Majorana fermions and the strength of Majorana zero-bias peaks are revealed.
Topological quantum computing is believed to be inherently fault-tolerant. One mathematical justification would be to prove that ground subspaces or ground state manifolds of topological phases of matter behave as error correction codes with macroscopic distance. While this is widely assumed and used as a definition of topological phases of matter in the physics literature, besides the doubled abelian anyon models in Kitaevs seminal paper, no non-abelian models are proven to be so mathematically until recently. Cui et al extended the theorem from doubled abelian anyon models to all Kitaev models based on any finite group. Those proofs are very explicit using detailed knowledge of the Hamiltonians, so it seems to be hard to further extend the proof to cover other models such as the Levin-Wen. We pursue a totally different approach based on topological quantum field theories (TQFTs), and prove that a lattice implementation of the disk axiom and annulus axiom in TQFTs as essentially the equivalence of TQO1 and TQO2 conditions. We confirm the error correcting properties of ground subspaces for topological lattice Hamiltonian schemas of the Levin-Wen model and Dijkgraaf-Witten TQFTs by providing a lattice version of the disk axiom and annulus of the underlying TQFTs. The error correcting property of ground subspaces is also shared by gapped fracton models such as the Haah codes. We propose to characterize topological phases of matter via error correcting properties, and refer to gapped fracton models as lax-topological.
Measurement plays a quintessential role in the control of quantum systems. Beyond initialization and readout which pertain to projective measurements, weak measurements in particular, through their back-action on the system, may enable various levels of coherent control. The latter ranges from observing quantum trajectories to state dragging and steering. Furthermore, just like the adiabatic evolution of quantum states that is known to induce the Berry phase, sequential weak measurements may lead to path-dependent geometric phases. Here we measure the geometric phases induced by sequences of weak measurements and demonstrate a topological transition in the geometric phase controlled by measurement strength. This connection between weak measurement induced quantum dynamics and topological transitions reveals subtle topological features in measurement-based manipulation of quantum systems. Our protocol could be implemented for classes of operations (e.g. braiding) which are topological in nature. Furthermore, our results open new horizons for measurement-enabled quantum control of many-body topological states.
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