Spin liquids : mean field and beyond

Abstract

Spin liquids are fluid-like ground states of spin systems, where spins do not order at zero temperature. These states have long-range entanglement and concomitant exotic properties, such as fractionalized excitations and emergent gauge field. In this thesis we use mean field approach and its extensions to address spin liquid states of spin-1 system which has no analogue for spin-1/2. Also, we consider impurity as a probe of spin-1 system, and spinon-phonon interactions in Dirac spin liquid. In Chapter 2, using a fermionic representation for spin-1 system, we find a state where one flavor of spinons has a Fermi surface, while other flavors are gapped out by d + id topological pairing [1]. Despite the existence of a Fermi surface, this ground state has fully gapped bulk spin excitations. Within Variational Monte Carlo techniques we study phase diagram of different spin-1 generalizations of Heisenberg model [2]. For an SU(3)-invariant model with sufficiently strong ring-exchange terms, we find a d+id paired quantum spin liquid with a Fermi surface of deconfined spinons. Chapter 3 addressed the behavior of Kondo S = 1/2 impurity embedded in a two-dimensional S = 1 U(1) spin liquid with a Fermi surface [3]. This problem contains an interplay between non-Fermi-liquid behavior induced by a gauge field, and a non-Fermi-liquid fixed point in the overscreened Kondo problem. We find that the gauge field leads to observable changes in the physical properties of the system at the overscreened Kondo fixed point. Thus, realization of overscreened Kondo physics in U(1) spin liquid can be used as a probe of fermionic spinons. Finally, in Chapter 4 we study the interaction of Dirac spinons with S = 1/2 with lattice vibrations [4]. We establish the general procedure for deriving spinon-phonon interactions which is based on a symmetry considerations, and illustrate it for different algebraic spin liquids. Despite all considered algebraic spin liquids have identical low energy description, spinon-phonon interaction probes the microscopic details and is set by representation of projective symmetry group. We estimate the attenuation of ultrasound, and discuss its experimental prospectives as probe of spinons.