Algebraic spin liquids, which are exotic gapless spin states preserving all microscopic symmetries, have been widely studied due to potential realizations in frustrated quantum magnets and the cuprates. At low energies, such putative phases are described by quantum electrodynamics in
2+1 dimensions. While significant progress has been made in understanding this nontrivial interacting field theory and the associated spin physics, one important issue which has proved elusive is the quantum numbers carried by so-called monopole operators. Here we address this issue in the ``staggered flux'' spin liquid which may be relevant to the pseudogap regime in high
Tc. Employing general analytical arguments supported by simple numerics, we argue that proximate phases encoded in the monopole operators include the familiar Neel and valence bond solid orders, as well as other symmetry-breaking orders closely related to those previously explored in the monopole-free sector of the theory. Surprisingly, we also find that one monopole operator carries trivial quantum numbers, and briefly discuss its possible implications.
We propose that underdoped high-
Tc superconductors are described by an algebraic spin liquid (ASL) at high energies, which undergoes a spin-charge recombination transition at low energies. The spin correlation in the ASL is calculated via its effective theory---a system of massless Dirac fermions coupled to a U(1) gauge field. We find that without fine-tuning any parameters the gauge interaction strongly enhances the staggered spin correlation even in the presence of a large single-particle pseudogap. This allows us to show that the ASL plus spin-charge recombination picture can explain many highly unusual properties of underdoped high-
Tc superconductors.
In the past few decades, tremendous efforts have been made toward understanding the exotic physics emerging from competition between various ordering tendencies in strongly correlated systems. Employing state-of-the-art quantum Monte Carlo simulation, we investigate an interacting SU(N) fermionic model with varying interaction strength and value of N, and we unveil the ground-state phase diagram of the model exhibiting a plethora of exotic phases. For small values of N-namely, N=2, 3-the ground state is an antiferromagnetic (AFM) phase, whereas in the large-N limit, a staggered valence bond solid (VBS) order is dominant. For intermediate values of N such as N=4, 5, remarkably, our study reveals that distinct VBS orders appear in the weak and strong coupling regimes. More fantastically, the competition between staggered and columnar VBS ordering tendencies gives rise to a Mott insulating phase without spontaneous symmetry breaking (SSB), existing in a large interacting parameter regime, which is consistent with a gapped quantum spin liquid. Our study not only provides a platform to investigate the fundamental physics of quantum many-body systems-it also offers a novel route toward searching for exotic states of matter such as quantum spin liquid in realistic quantum materials.
The algebraic spin liquid is a long-sought-after phase of matter characterized by the absence of quasiparticle excitations, a low-energy description in terms of emergent Dirac fermions and gauge fields interacting according to
(2+1)-dimensional quantum electrodynamics
(QED3), and power-law correlations with universal exponents. The prototypical algebraic spin liquid is the Affleck-Marston $\ensuremath{\pi}$-flux phase, originally proposed as a possible ground state of the spin-
21 Heisenberg model on the two-dimensional square lattice. While the latter model is now known to order antiferromagnetically at zero temperature, recent sign-problem-free quantum Monte Carlo simulations of spin-
21 fermions coupled to a compact
U(1) gauge field on the square lattice have shown that quantum fluctuations can destroy N\'eel order and drive a direct quantum phase transition to the $\ensuremath{\pi}$-flux phase. We show this transition is in the universality class of the chiral Heisenberg
QED3-- Gross-Neveu-Yukawa model with a single
SU(2) doublet of four-component Dirac fermions (i.e.,
Nf=1), pointing out important differences with the corresponding putative transition on the kagome lattice. Using an $\ensuremath{\epsilon}$ expansion below four space-time dimensions to four-loop order, and a large-
Nf expansion up to second order, we show the transition is continuous and compute various thermodynamic and susceptibility critical exponents at this transition, setting the stage for future numerical determinations of these quantities. As a by-product of our analysis, we also obtain charge-density-wave and valence-bond-solid susceptibility exponents at the semimetal-N\'eel transition for interacting fermions on the honeycomb lattice.
In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the
S=1/2 kagome lattice Heisenberg antiferromagnet. Furthermore, this state, which lacks a spin gap, is appealing in light of recent experiments on herbertsmithite
[ZnCu3(OH)6Cl2]. Here, we study the properties of this ASL in more detail using both the low-energy effective field theory and Gutzwiller-projected wave functions of fermionic spinons. We identify the competing orders of the ASL, which are observables having slowly decaying power-law correlations---among them we find a set of magnetic orders lying at the
M points of the Brillouin zone, the familiar $\mathbit{q}=0$ magnetic ordered state, the ``Hastings'' valence-bond solid (VBS) state, and a pattern of vector spin-chirality ordering corresponding to one of the Dzyaloshinskii--Moriya (DM) interaction terms present in herbertsmithite. Identification of some of these orders requires an understanding of the quantum numbers of magnetic monopole operators in the ASL. We discuss the detection of the magnetic and VBS competing orders in experiments. While we primarily focus on a clean system without DM interaction, we consider the effects of small DM interaction and argue that, surprisingly, it leads to spontaneously broken time-reversal symmetry (for DM interaction that preserves
XY spin rotation symmetry, there is also
XY magnetic order). Our analysis of the projected wave function provides an estimate of the ``Fermi velocity''
vF that characterizes all low-energy excitations of the ASL---this allows us to estimate the specific heat, which compares favorably with experiments. We also study the spin and bond correlations of the projected wave function and compare these results with those of the effective field theory. While the spin correlations in the effective field theory and wave function seem to match rather well (although not completely), the bond correlations are more puzzling. We conclude with a discussion of experiments in herbertsmithite and make several predictions.
We describe spin correlations in the vicinity of a generalized impurity in a wide class of fractionalized spin liquid states. We argue that the primary characterization of the impurity is its electric charge under the gauge field describing singlet excitations in the spin liquid. We focus on two gapless
U(1) spin liquids described by
(2+1)-dimensional conformal field theories (CFT): the staggered flux (sF) spin liquid, and the deconfined critical point between the N\'eel and valence-bond-solid (VBS) states. In these cases, the electric charge is argued to be an exactly marginal perturbation of the CFT. Consequently, the impurity susceptibility has a
1∕T temperature dependence, with an anomalous Curie constant, which is a universal number associated with the CFT. One unexpected feature of the CFT of the sF state is that an applied magnetic field does not induce any staggered spin polarization in the vicinity of the impurity (while such a staggered magnetization is present for the N\'eel-VBS case). These results differ significantly from earlier theories of vacancies in the sF state, and we explicitly demonstrate how our gauge theory corrects these works. We discuss implications of our results for the cuprate superconductors, organic Mott insulators, and graphene.