European Commission logo
English English
CORDIS - EU research results

Topological Matter and Crystal Symmetry: From Microscopic Structure to Phenomenology

Project description

A wide-ranging theory of topological states of matter

Topological states of matter are characterised by subtle structures in the quantum entanglement between different degrees of freedom. New tools are required to analyse their properties. The EU-funded TMCS project aims to develop tools to identify, simulate and experimentally detect these structures/phases. The project will build a broad theory of strongly correlated topological states of matter in two and three dimensions. It will use non-symmorphic crystal symmetry as an organising principle to identify systems that are appropriate candidates to host fractionalised states of matter and study its influence on competing orders. The ultimate goal is to create an altered understanding of two- and three-dimensional topological phases and develop new classes of analytical and numerical tools.


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.

Host institution

Net EU contribution
€ 1 499 622,00
OX1 2JD Oxford
United Kingdom

See on map

South East (England) Berkshire, Buckinghamshire and Oxfordshire Oxfordshire
Activity type
Higher or Secondary Education Establishments
Total cost
€ 1 499 622,00

Beneficiaries (1)