Topological Matter and Crystal Symmetry: From Microscopic Structure to Phenomenology

Descripción del proyecto

Una teoría amplia de los estados topológicos de la materia

Los estados topológicos de la materia se caracterizan por estructuras sutiles en el entrelazamiento cuántico entre diferentes grados de libertad. Se necesitan nuevas herramientas para analizar sus propiedades. El objetivo del proyecto TMCS, financiado con fondos europeos, es desarrollar herramientas para identificar, simular y detectar estas estructuras o fases de forma experimental. El equipo del proyecto creará una teoría amplia de los estados topológicos sólidamente correlacionados de la materia en dos y tres dimensiones. Utilizará la simetría cristalina no simmórfica como principio de organización para determinar los sistemas que puedan ser apropiados para albergar estados fraccionados de la materia y estudiar su influencia en los órdenes que compiten entre sí. El objetivo final es alcanzar una comprensión alterada de las fases topológicas bidimensionales y tridimensionales y desarrollar nuevas clases de herramientas analíticas y numéricas.

Objetivo

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.