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Topological Matter and Crystal Symmetry: From Microscopic Structure to Phenomenology

Objective

This ERC project will build a wide-ranging theory of strongly-correlated topological states of matter in three dimensions, via analytical, numerical, and phenomenological approaches. It will use non-symmorphic crystal symmetry as an organizing principle to identify systems that are good candidates to host fractionalized states of matter. Via slave-particle mean-field theories used in concert with symmetry analysis, it will provide a systematic classification of different possible spin-charge-separated, topologically ordered, and broken-symmetry states in correlated Mott insulators and heavy-fermion materials. This mean-field study of model Hamiltonians will be wedded to a sophisticated new variational tensor-network scheme for simulating physically-realistic systems. Separately, an analytical classification of gapless ‘U(1)’ quantum spin liquids with emergent photon excitations will be implemented. Variational trial wavefunctions will also be developed to access a new class of interacting 'topological quantum paramagnets’ with gapless edge states.

The symmetry analysis will be coupled to two phenomenological studies. One will examine unconventional surface state properties of topological semimetals, and extend these to the interacting regime. Another will develop a spectroscopic theory for topological matter with symmetry, leveraging results from the parton approach where possible. Experimental input from studies of nematic quantum Hall states and photoemission studies of Weyl semimetals will provide feedback to this effort.

A final thrust of activity will focus on newly-proposed fracton states of matter not captured by usual theories of topological order, and will employ both analytical parton techniques and numerical quantum Monte Carlo simulations.

At its close, this project will deliver a dramatically altered understanding of three dimensional topological phases and provide a new class of analytical and numerical tools as a platform for future studies.

Call for proposal

ERC-2018-STG
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Host institution

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
Address
Wellington Square University Offices
OX1 2JD Oxford
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 499 622

Beneficiaries (1)

THE CHANCELLOR, MASTERS AND SCHOLARS OF THE UNIVERSITY OF OXFORD
United Kingdom
EU contribution
€ 1 499 622
Address
Wellington Square University Offices
OX1 2JD Oxford
Activity type
Higher or Secondary Education Establishments