Periodic Reporting for period 4 - TopInSy (Novel phases of matter emerging from topology, interactions, and symmetries)
Berichtszeitraum: 2020-10-01 bis 2022-01-31
The discovery of how the interplay of topology and symmetry can govern quantum mechanical behaviour has reshaped our understanding of the forms matter can take. We have learned that topological insulators exist whose electrical insulation in the bulk protects a highly conducting "skin". Topological superconductors have been discovered where a superconducting bulk implies the emergence of novel exotic particles, so-called Majorana fermions.
These early examples are mostly based on the physics of weakly interacting electrons. They have already seen a number of striking experimental demonstrations and form the basis of exciting lines of research, including experimental programmes towards the potential use of Majorana fermions for quantum computation.
This project investigated systems displaying phenomena governed by topology and symmetry, but where interactions play an important role. Strong interactions can not only lead to qualitatively different behaviour than that of weakly interacting electrons (including new forms of protected "skins" and exotic particles), but can also underpin topological phenomena based on systems with qualitatively different constituents, for example topological insulators of bosons (instead of electrons) which would be impossible without interactions.
The broad objectives of the project were: to theoretically study how the interplay of topology, interactions, and symmetries can lead to new forms of matter; how they can underpin new signatures in experiments; and to link to new directions in quantum technology.
Our work led to proposing novel ways to create, characterise, and experimentally detect such symmetric, interacting, topological matter, and also identified new forms in which such matter can emerge. We also established new links between these systems and topological quantum computing.
These early examples are mostly based on the physics of weakly interacting electrons. They have already seen a number of striking experimental demonstrations and form the basis of exciting lines of research, including experimental programmes towards the potential use of Majorana fermions for quantum computation.
This project investigated systems displaying phenomena governed by topology and symmetry, but where interactions play an important role. Strong interactions can not only lead to qualitatively different behaviour than that of weakly interacting electrons (including new forms of protected "skins" and exotic particles), but can also underpin topological phenomena based on systems with qualitatively different constituents, for example topological insulators of bosons (instead of electrons) which would be impossible without interactions.
The broad objectives of the project were: to theoretically study how the interplay of topology, interactions, and symmetries can lead to new forms of matter; how they can underpin new signatures in experiments; and to link to new directions in quantum technology.
Our work led to proposing novel ways to create, characterise, and experimentally detect such symmetric, interacting, topological matter, and also identified new forms in which such matter can emerge. We also established new links between these systems and topological quantum computing.
Our work on creating these novel forms of matter included studying how precursors of fractional topological insulators (two-dimensional electronic matter arising from interactions, topology, and time-reversal symmetry) can arise in fermionic ladder systems and showing that such precursors may serve as ingredients for creating full-fledged two-dimensional fractional topological insulators. We also showed how geometrical twists in other fermionic ladder systems can lead to robust dynamical features linked to generalisations of Majorana fermions at the boundaries. We also proposed ways to create topological boundary dynamics directly. In particular, for high-complexity boundary dynamics corresponding to the so-called Sachdev-Ye-Kitaev (SYK) model (of great recent interest due to links to quantum information scrambling and gravity), we devised a realisation based on a Majorana topological quantum computer. We also described novel, intrinsically non-equilibrium, forms of topological quantum matter and showed how intermediate-term quantum computers may be used to create them.
The work on theoretical characterisation included studying how topological states, despite possessing certain non-local defining features, may be captured using tensor networks, an inherently local framework for describing and simulating quantum matter on classical computers. We have also developed a framework for uniting topological states with the inherently local phenomenon of many-body localisation (insulating behaviour arising from interactions and quantum interference). Our framework characterises such topological many-body localised systems in terms of weakly interacting local objects emerging from ingredients in topological quantum error correction. This allowed us to study topological order at high energies (in contrast to the usual setting of the lowest achievable energy), and to combine it with generalised forms of symmetries to describe and characterise the above mentioned intrinsically non-equilibrium topological systems. We also showed how this framework can be used to characterise topological many-body localised systems in computer simulations. Another approach to characterise topological states is via their boundary. Our work included establishing how boundary features link to bulk characteristics in topological superconductors with rotation symmetry. We also characterised the high-complexity boundary systems corresponding to the SYK model. Our results include establishing the symmetry classification of these systems and the striking finding of boundary supersymmetry.
Our work on detection included showing that the fractional topological insulator precursors mentioned above, despite living on a quasi-one-dimensional ladder, already display certain quantised signatures that one would normally expect only in full-fledged two-dimensional fractional topological insulators. We also established transport results on interacting devices supporting Majorana fermions. Such devices are leading candidates for demonstrating Majorana fermion topological qubits for quantum computing. Our results include the nonequilibrium conductance, the prediction of fractional charge quantisation in current fluctuations, and the study of the spatial structure of the sea of conduction electrons. We also studied signatures of topological boundaries linked to the SYK model, both in transport measurements and for probing the dynamics in our proposed Majorana fermion SYK realisation.
These and further works from this project have led to nearly 30 journal publications (with several more in preparation), and a similar number of presentations at seminars, summer schools, workshops, and conferences.
The work on theoretical characterisation included studying how topological states, despite possessing certain non-local defining features, may be captured using tensor networks, an inherently local framework for describing and simulating quantum matter on classical computers. We have also developed a framework for uniting topological states with the inherently local phenomenon of many-body localisation (insulating behaviour arising from interactions and quantum interference). Our framework characterises such topological many-body localised systems in terms of weakly interacting local objects emerging from ingredients in topological quantum error correction. This allowed us to study topological order at high energies (in contrast to the usual setting of the lowest achievable energy), and to combine it with generalised forms of symmetries to describe and characterise the above mentioned intrinsically non-equilibrium topological systems. We also showed how this framework can be used to characterise topological many-body localised systems in computer simulations. Another approach to characterise topological states is via their boundary. Our work included establishing how boundary features link to bulk characteristics in topological superconductors with rotation symmetry. We also characterised the high-complexity boundary systems corresponding to the SYK model. Our results include establishing the symmetry classification of these systems and the striking finding of boundary supersymmetry.
Our work on detection included showing that the fractional topological insulator precursors mentioned above, despite living on a quasi-one-dimensional ladder, already display certain quantised signatures that one would normally expect only in full-fledged two-dimensional fractional topological insulators. We also established transport results on interacting devices supporting Majorana fermions. Such devices are leading candidates for demonstrating Majorana fermion topological qubits for quantum computing. Our results include the nonequilibrium conductance, the prediction of fractional charge quantisation in current fluctuations, and the study of the spatial structure of the sea of conduction electrons. We also studied signatures of topological boundaries linked to the SYK model, both in transport measurements and for probing the dynamics in our proposed Majorana fermion SYK realisation.
These and further works from this project have led to nearly 30 journal publications (with several more in preparation), and a similar number of presentations at seminars, summer schools, workshops, and conferences.
Our results provide theoretical input for creating new forms of topological quantum matter in the laboratory, and our predictions on their signatures aid detecting them in experiments. The approaches we found to characterise such systems have uncovered new ways to identify them computer simulations, and introduced a framework using which one may expand the range of settings for the emergence of topological order. The conceptual links we established to quantum error correction, our predictions on detecting topological qubits, and our results on Majorana quantum computers can have impact for quantum computing.