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Quantum spin liquids host novel emergent excitations, such as monopoles of an emergent gauge field. Here, we study the hierarchy of monopole operators that emerges at quantum critical points (QCPs) between a two-dimensional Dirac spin liquid and various ordered phases. This is described by a confinement transition of quantum electrodynamics in two spatial dimensions (QED3 Gross-Neveu theories). Focusing on a spin ordering transition, we get the scaling dimension of monopoles at leading order in a large-N expansion, where 2N is the number of Dirac fermions, as a function of the monopoles total magnetic spin. Monopoles with a maximal spin have the smallest scaling dimension while monopoles with a vanishing magnetic spin have the largest one, the same as in pure QED3. The organization of monopoles in multiplets of the QCPs symmetry group SU(2) x SU(N) is shown for general N.
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Monopole operators are studied at certain quantum critical points between a Dirac spin liquid and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction term. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED$_{3}$-GN), while for the transition to the Z$_{2}$ QSL it is a superconducting pairing term (QED$_{3}$-Z$_{2}$GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to sub-leading order in 1/N. For monopoles with a minimal topological charge q = 1/2, the scaling dimension is 2N*0.26510 at leading-order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the Z$_{2}$ case. Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in QED$_{3}$ is also obtained and we find a sub-leading contribution of $-$0.038138(5), which is slightly different from the value $-$0.0383 first obtained in the literature. The scaling dimension of a QED$_{3}$-GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED$_{3}$-GN with 2N = 2 flavors and the CP$^{1}$ model. Additionally, non-minimally charged monopoles with equal charges on both sides of the duality have similar scaling dimensions. By studying the large-q asymptotics of the scaling dimensions in QED$_{3}$, QED$_{3}$-GN, and QED$_{3}$-Z$_{2}$GN we verify that the constant O(q$^{0}$) coefficient precisely matches the universal prediction for CFTs with a global U(1) symmetry.
If spin liquids have been famously defined by what they are not, i.e. ordered, the past years have seen the frontier between order and spin liquid starting to fade, with a growing number of materials whose low-temperature physics cannot be explained without co-existence of (partial) magnetic order and spin fluctuations. Here we study an example of such co-existence in the presence of magnetic dipolar interactions, related to spin ice, where the order is long range and the fluctuations support a Coulomb gauge field. Topological defects are effectively coupled via energetic and entropic Coulomb interactions, the latter one being stronger than for the spin-ice ground state. Depending on whether these defects break the divergence-free condition of the Coulomb gauge field or the long-range order, they are respectively categorized as monopoles - as in spin ice - or monopole holes, in analogy with electron holes in semiconductors. The long-range order plays the role of a fully-occupied valence band, while the Coulomb spin liquid can be seen as an empty conducting band. These results are discussed in the context of other lattices and models which support a similar co-existence of Coulomb gauge field and long-range order. We conclude this work by explaining how dipolar interactions lift the spin liquid degeneracy at very low energy scale by maximizing the number of flippable plaquettes, in light of the equivalent quantum dimer model.
The spin-1/2 triangular lattice antiferromagnet YbMgGaO$_{4}$ has attracted recent attention as a quantum spin-liquid candidate with the possible presence of off-diagonal anisotropic exchange interactions induced by spin-orbit coupling. Whether a quantum spin-liquid is stabilized or not depends on the interplay of various exchange interactions with chemical disorder that is inherent to the layered structure of the compound. We combine time-domain terahertz spectroscopy and inelastic neutron scattering measurements in the field polarized state of YbMgGaO$_{4}$ to obtain better microscopic insights on its exchange interactions. Terahertz spectroscopy in this fashion functions as high-field electron spin resonance and probes the spin-wave excitations at the Brillouin zone center, ideally complementing neutron scattering. A global spin-wave fit to all our spectroscopic data at fields over 4T, informed by the analysis of the terahertz spectroscopy linewidths, yields stringent constraints on $g$-factors and exchange interactions. Our results paint YbMgGaO$_{4}$ as an easy-plane XXZ antiferromagnet with the combined and necessary presence of sub-leading next-nearest neighbor and weak anisotropic off-diagonal nearest-neighbor interactions. Moreover, the obtained $g$-factors are substantially different from previous reports. This works establishes the hierarchy of exchange interactions in YbMgGaO$_{4}$ from high-field data alone and thus strongly constrains possible mechanisms responsible for the observed spin-liquid phenomenology.
A key problem in the field of quantum criticality is to understand the nature of quantum phase transitions in systems of interacting itinerant fermions, motivated by experiments on a variety of strongly correlated materials. Much attention has been paid in recent years to two-dimensional (2D) materials in which itinerant fermions acquire a pseudo-relativistic Dirac dispersion, such as graphene, topological insulator surfaces, and certain spin liquids. This article reviews the phenomenology and theoretical description of quantum phase transitions in systems of 2D Dirac fermions.
At sufficiently low temperatures, condensed-matter systems tend to develop order. An exception are quantum spin-liquids, where fluctuations prevent a transition to an ordered state down to the lowest temperatures. While such states are possibly realized in two-dimensional organic compounds, they have remained elusive in experimentally relevant microscopic two-dimensional models. Here, we show by means of large-scale quantum Monte Carlo simulations of correlated fermions on the honeycomb lattice, a structure realized in graphene, that a quantum spin-liquid emerges between the state described by massless Dirac fermions and an antiferromagnetically ordered Mott insulator. This unexpected quantum-disordered state is found to be a short-range resonating valence bond liquid, akin to the one proposed for high temperature superconductors. Therefore, the possibility of unconventional superconductivity through doping arises. We foresee its realization with ultra-cold atoms or with honeycomb lattices made with group IV elements.
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