Exotic Phases and Fractionalization in Frustrated Quantum Magnets

Jason Alicea

Christopher N. Varney, Kai Sun, Victor M. Galitski +1 more

Yu. E. Lozovik, O. I. Notych

Matthias Gohlke

Interactions between the microscopic constituents of a solid---a many-body system--- can lead to novel phases and exotic physical phenomena like fractionalization, topological order, quantum spin liquids, emergent gauge field, etc.. The concept of frustration provides a ground for such exotic phenomena. Frustration can prevent a many-body system from establishing long-range order down to the lowest temperatures due to competing interactions. Instead, competing interactions may result in disordered and liquid-like phases of matter that provide the vacuum for fractional excitations. The absence of any order parameter in strongly frustrated systems---due to not breaking any symmetry spontaneously--- immediately raises the question about possible experimental probes of spin-liquids and their fractional excitations. Dynamic probes, like inelastic neutron scattering or Raman scattering, provide an experimental method to detect signatures of fractionalised quasiparticles. The energy and momentum transferred in a scattering event is split between the fractional quasiparticles. On the theory side, computing such dynamical signatures beyond one spatial dimension is generally a difficult task. In this thesis, numerical methods like density matrix renormalisation group and matrix product states are used to study strongly frustrated magnets and their dynamics in a non-perturbative way. This thesis covers two physical models in the context of frustration and emergent gauge fields. Firstly, the Kitaev model of spin-1/2 degrees of freedom subject to strongly anisotropic spin exchange. The Kitaev model features quantum spin liquid ground states with fractionalization of spins into Majorana fermions and Z_2-fluxes---the visons of an emergent Z_2 gauge theory. The main questions addressed here concern the stability of the quantum spin liquid phase upon adding perturbations relevant in magnetic compounds such as Heisenberg or the symmetric-offdiagonal Gamma exchange. Applying a magnetic field drives the Kitaev model into a topologically ordered phase. The excitations and dynamical signatures within the spin liquid, the topologically ordered phase, and within ordered phases are studied. Secondly, a classical minimal model of the proton configuration in water ice is studied. The ice rules, a local constraint describing the low energy manifold, result in emergent Maxwell's equation. Upon applying an external electric field along certain axis, a polarization plateau occurs in which the remaining degrees of freedom can be described by dimers on two-dimensional lattices.

Wilhelm Kadow, Ivan Morera, Eugene Demler +1 more

Separating electrons into emergent fractional quasiparticles is a hallmark of exotic quantum phases of matter with strong interactions. Understanding under which circumstances fractionalized excitations appear is a major conceptual challenge and can help realize long sought-after states, such as quantum spin liquids. Here, we identify a distinct mechanism for fractionalization. Starting from the plaquette-ordered ground state of an SU(4) symmetric t-J model at quarter filling on frustrated triangular lattices, we reveal a compelling interplay between order and fractionalization as a function of doping. For hole doping, we find that the kinetic frustration can be relieved by fractionalizing the holes into fermionic spinons and bosonic holons: the holons minimize their kinetic energy when the spinons form a spinon Fermi surface. We support this mechanism analytically in the large-N limit as well as numerically by simulating the SU(4) case with matrix product states on cylinder geometries and with variational Monte Carlo methods on system sizes up to 40x40. Conversely, electron doping drives the system into a ferromagnetic phase, akin to Nagaoka's theorem. We discuss possible experimental realizations in moiré heterostructures as well as ultracold atoms, and propose dynamical probes to search for key characteristics of the fractionalized quasiparticles.

Frédéric Mila