Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than $\text{SU}(2)$. Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with $\text{SU}(3)$ symmetry. Using a combination of homotopy analysis and analytic field theory we identify a family of solitonic wave functions characterized by integer charge $\mathbf{Q}=({Q}_{A},{Q}_{B},{Q}_{C})$, with ${Q}_{A}+{Q}_{B}+{Q}_{C}=0$. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that solitons with charge $\mathbf{Q}=(1,1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}2)$ spontaneously decay into a pair of solitons with elementary topological charge, and emergent interactions. This result suggests that it could be possible to realize a class of interacting soliton, with no classical analog, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge group $\text{U}(1)\ifmmode\times\else\texttimes\fi{}\text{U}(1)$.
Cold atoms bring new opportunities to study quantum magnetism, and in particular, to simulate quantum magnets with symmetry greater than SU(2). Here we explore the topological excitations which arise in a model of cold atoms on the triangular lattice with SU(3) symmetry. Using a combination of homotopy analysis and analytic field theory we identify a family of solitonic wave functions characterized by integer charge Q=(QA,QB,QC), with QA+QB+QC=0. We use a numerical approach, based on a variational wave function, to explore the stability of these solitons on a finite lattice. We find that solitons with charge Q=(1,1,\ensuremath−2) spontaneously decay into a pair of solitons with elementary topological charge, and emergent interactions. This result suggests that it could be possible to realize a class of interacting soliton, with no classical analog, using cold atoms. It also suggests the possibility of a new form of quantum spin liquid, with gauge group U(1)\ifmmode×\else\texttimes\fiU(1).
Theory of Dirac spin liquids on spin-S triangular lattice: possible application to α-CrOOH(D)
Triangular lattice quantum antiferromagnet has recently emerged to be a promising playground for realizing Dirac spin liquids (DSLs) -- a class of highly entangled quantum phases hosting emergent gauge fields and gapless Dirac fermions. While previous theories and experiments focused mainly on S=1/2 spin systems, more recently signals of a DSL were detected in an S=3/2 system α-CrOOH(D). In this work we develop a theory of DSLs on triangular lattice with spin-S moments. We argue that in the most natural scenario, a spin-S system realizes a U(2S) DSL, described at low energy by gapless Dirac fermions coupled with an emergent U(2S) gauge field (also known as U(2S) QCD3). An appealing feature of this scenario is that at sufficiently large S, the U(2S) QCD becomes intrinsically unstable toward spontaneous symmetry breaking and confinement. The confined phase is simply the 120∘ coplanar magnetic order, which agrees with semiclassical (large-S) results on simple Heisenberg-like models. Other scenarios are nevertheless possible, especially at small S when quantum fluctuations are strong. For S=3/2, we argue that a U(1) DSL is also theoretically possible and phenomenologically compatible with existing measurements. One way to distinguish the U(3) DSL from the U(1) DSL is to break time-reversal symmetry, for example by adding a spin chirality term Si⋅(Sj×Sk) in numerical simulations: the U(1) DSL becomes the standard Kalmeyer-Laughlin chiral spin liquid with semion/anti-semion excitation; the U(3) DSL, in contrast, becomes a non-abelian chiral spin liquid described by the SU(2)3 topological order, with Fibonacci-like anyons.
Topological Spin Liquid Phase in the Spin-1/2 Triangular Heisenberg Model
We study the spin-1/2 Heisenberg model on the triangular lattice with the antiferromagnetic first (J1) and second nearest-neighbor (J2) interactions using density matrix renormalization group. By studying the spin correlation function, we find a 120◦ magnetic order phase for J2 . 0.08J1 and a stripe antiferromagnetic phase for J2 & 0.16J2. Between these two phases, we identify a gapped spin liquid phase characterized by the exponential decaying spin and dimer correlations, as well as finite spin singlet and triplet excitation gaps. We also find two topological degenerating ground states in two topological sectors. Furthermore, we detect the signature of the fractionalization by following the evolution of different ground states with inserting spin flux into the cylinder system. While the sector with spinon is found to respect the time reveral symmetry, the even sector without a spinon may break such a symmetry. We discuss the implications of numerical results for the nature of the topological spin liquid phase.
Spin-S Heisenberg quantum antiferromagnets on the kagome lattice offer, when placed in a magnetic field, a fantastic playground to observe exotic phases of matter with (magnetic analogs of) superfluid, charge, bond, or nematic orders, or a coexistence of several of the latter. In this context, we have obtained the (zero-temperature) phase diagrams up to S=2 directly in the thermodynamic limit owing to infinite projected entangled pair states, a tensor network numerical tool. We find incompressible phases characterized by a magnetization plateau versus field and stabilized by spontaneous breaking of point group or lattice translation symmetry(ies). The nature of such phases may be semiclassical, as the plateaus at the $\frac{1}{3}\mathrm{th},\left(1\ensuremath{-}\frac{2}{9S}\right)\mathrm{th}$, and $\left(1\ensuremath{-}\frac{1}{9S}\right)\mathrm{th}$ of the saturated magnetization (the latter followed by a macroscopic magnetization jump), or fully quantum as the spin-2191 plateau exhibiting a coexistence of charge and bond orders. Upon restoration of the spin rotation U(1) symmetry, a finite compressibility appears, although lattice symmetry breaking persists. For integer spin values we also identify spin gapped phases at low enough fields, such as the S=2 (topologically trivial) spin liquid with no symmetry breaking, neither spin nor lattice.
The formation of quantum spin liquids in frustrated magnets represents an exciting possibility due to the rather exotic features they harbor, including fractionalized excitations and emergent gauge fields. \nUnfortunately, they are notoriously difficult to study as there are often no good analytical methods available and quantum Monte Carlo simulations are hindered by the negative sign problem. \nThe Kitaev honeycomb model is a notable exception of a frustrated quantum model which is exactly solvable and which hosts a number of distinct quantum spin liquid ground states. \nAs such, it allows for a rare opportunity to study the physics of spin liquids with full analytical control. \n \nIn this thesis, we study the fractionalization of spin-1/2 moments into Majorana fermions and an emergent Z2 gauge field in a generalization of the Kitaev honeycomb model to a number of three-dimensional lattices. \nWhile the excitations of the gauge field are always gapped, the fermionic quasiparticles may exhibit a gapless dispersion, forming fully two-dimensional Fermi surfaces, symmetry protected nodal lines, or topological Weyl nodes. \nWe show that one can deduce rather general constraints on the possible gapless excitations by making use of an object called the projective symmetry group. \nIn doing so we provide a scheme for classifying the various gapless Kitaev spin liquids. \nA thorough analysis is carried out for a number of these spin liquids, primarily investigating the stability of the gapless modes and the novel features resulting from their sometimes non-trivial topology, as well as their effects on certain equal-time correlation functions.
Triangular-lattice quantum spin-liquid insulators are observed to undergo transitions to superconductivity under pressure or doping, and exhibit enhanced terahertz conductivity when driven by mid-infrared light. We present a general theoretical framework for the emergence of superconducting and charge-ordered phases from a U(1) Dirac spin liquid with fermionic spinons, as well as from its gapped Z2 and chiral descendants. Numerical studies have provided substantial evidence for these spin-liquid states. The spin-liquid phase hosts fractionalized Dirac spinons coupled to an emergent gauge field, whereas the superconducting and charge-ordered phases are conventional, with neither fractionalized excitations nor emergent gauge dynamics. The transition between these phases is driven by the Higgs condensation of spinless charge-e bosonic chargons (``doublons'' and ``holons''). We show that the projective symmetry group of the Dirac spinons uniquely determines the symmetry and dispersion of the chargons, allowing us to construct an effective low-energy theory near the chargon band minima. Gauge-invariant composites of the chargon Higgs fields provide the order parameters characterizing the phases. The resulting phase diagram contains a rich variety of ordered states, including d+id superconductivity, charge-density waves, bond-density waves, and pair-density waves.
Dynamics and stability of U(1) spin liquids beyond mean-field theory: Triangular-lattice J1-J2 Heisenberg model
Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalised spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response. We use a self-consistent mean-field theory combined with the random phase approximation (RPA) for the J1-J2 Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We show the continuum response at the Brillouin zone corners is described by a spinon-exciton hybridised with monopole gauge excitations. We further show that the transition from the QSL to 120-degree coplanar order is in the QED3 O(3)-GN universality class. We extend the method to chiral QSLs and XXZ anisotropy, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments in KYbSe2.