Critical spin liquid at 1/3 magnetization in a spin-1/2 triangular antiferromagnet

Although magnetically ordered at low temperatures, the spin-1/2 triangular antiferromagnet Cs_2CuCl_4 exhibits remarkable spin dynamics that strongly suggest proximity to a spin liquid phase. Here we address the question of whether a proximate spin liquid may also occur in an applied magnetic field, leaving a similar imprint on the dynamical spin correlations of this material. Specifically, we explore a spatially anisotropic Heisenberg spin-1/2 triangular antiferromagnet at 1/3 magnetization from a dual vortex perspective, and indeed find a new ``critical'' spin liquid phase described by QED3 with an emergent SU(6) symmetry. A number of nontrivial predictions are given for the dynamical spin structure factor in this ``algebraic vortex liquid'' phase, which can be tested experimentally via inelastic neutron scattering. We also discuss how the well-studied ``up-up-down'' magnetization plateaus can be captured within our approach, and further predict the existence of a stable gapless solid phase in a weakly ordered up-up-down state. Finally, we predict several anomalous ``roton'' minima in the excitation spectrum in the regime of lattice anisotropy where the canted Neel state appears.Comment: 5 pages, 2 figures; expanded intro & discussion of theory; minor correction to structure facto

Construction of Lagrangian local symmetries for general quadratic theory

We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of so-called structure matrices of the Dirac formalism are obtained. The procedure fulfilled in terms of initial variables of the theory, and do not implies either separation of constraints on first and second class subsets or any other choice of basis for constraints

Improved extended Hamiltonian and search for local symmetries

We analyze a structure of the singular Lagrangian $L$ with first and second class constraints of an arbitrary stage. We show that there exist an equivalent Lagrangian (called the extended Lagrangian $\tilde L$) that generates all the original constraints on second stage of the Dirac-Bergmann procedure. The extended Lagrangian is obtained in closed form through the initial one. The formalism implies an extension of the original configuration space by auxiliary variables. Some of them are identified with gauge fields supplying local symmetries of $\tilde L$. As an application of the formalism, we found closed expression for the gauge generators of $\tilde L$ through the first class constraints. It turns out to be much more easy task as those for $L$. All the first class constraints of $L$ turn out to be the gauge symmetry generators of $\tilde L$. By this way, local symmetries of $L$ with higher order derivatives of the local parameters decompose into a sum of the gauge symmetries of $\tilde L$. It proves the Dirac conjecture in the Lagrangian framework

Monopole Quantum Numbers in the Staggered Flux Spin Liquid

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-T_c. 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.Comment: 9 pages, 0 figures; minor clarification

Generalization of the Extended Lagrangian Formalism on a Field Theory and Applications

Formalism of extended Lagrangian represent a systematic procedure to look for the local symmetries of a given Lagrangian action. In this work, the formalism is discussed and applied to a field theory. We describe it in detail for a field theory with first-class constraints present in the Hamiltonian formulation. The method is illustrated on examples of electrodynamics, Yang-Mills field and non-linear sigma model.Comment: 17 pages, to be published in Phys. Rev.

Monopole operators in three-dimensional N=4 SYM and mirror symmetry

We study non-abelian monopole operators in the infrared limit of three-dimensional SU(N_c) and N=4 SU(2) gauge theories. Using large N_f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators which are (anti-)chiral primaries and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified.Comment: 23 pages, LaTex; v2: section 3.4 modified, section 3.5 extended, references adde

Algebraic spin liquid as the mother of many competing orders

We study the properties of a class of two-dimensional interacting critical states -- dubbed algebraic spin liquids -- that can arise in two-dimensional quantum magnets. A particular example that we focus on is the staggered flux spin liquid, which plays a key role in some theories of underdoped cuprate superconductors. We show that the low-energy theory of such states has much higher symmetry than the underlying microscopic spin system. This symmetry has remarkable consequences, leading in particular to the unification of a number of seemingly unrelated competing orders. The correlations of these orders -- including, in the staggered flux state, the Neel vector and the order parameter for the columnar and box valence-bond solid states -- all exhibit the SAME slow power-law decay. Implications for experiments in the pseudogap regime of the cuprates and for numerical calculations on model systems are discussed.Comment: Minor changes; final published version. 17 pages, 3 figure

Deconfinement in the presence of a Fermi surface

U(1) gauge theory of non-relativistic fermions interacting via compact U(1) gauge fields in the presence of a Fermi surface appears as an effective field theory in low dimensional quantum antiferromagnetism and heavy fermion liquids. We investigate deconfinement of fermions near the Fermi surface in the effective U(1) gauge theory. Our present analysis benchmarks the recent investigation of quantum electrodynamics in two space and one time dimensions ($QED_3$) by Hermele et al. [Phys. Rev. B {\bf 70}, 214437 (2004)]. Utilizing a renormalization group analysis, we show that the effective U(1) gauge theory with a Fermi surface has a stable charged fixed point. Remarkably, the renormalization group equation for an internal charge $e$ (the coupling strength between non-relativistic fermions and U(1) gauge fields) reveals that the conductivity $\sigma$ of fermions near the Fermi surface plays the same role as the flavor number $N$ of massless Dirac fermions in $QED_3$. This leads us to the conclusion that if the conductivity of fermions is sufficiently large, instanton excitations of U(1) gauge fields can be suppressed owing to critical fluctuations of the non-relativistic fermions at the charged fixed point. As a result a critical field theory of non-relativistic fermions interacting via noncompact U(1) gauge fields is obtained at the charged fixed point

Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice

There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appear to be a plethora of low energy excitations, predominantly singlets but also spin carrying, which suggest that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-1/2 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux-smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED$_3$) with an emergent $\mathrm{SU}(8)$ flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.Comment: 14 pages, 8 figure

Holographic Anyons in the ABJM Theory

We consider the holographic anyons in the ABJM theory from three different aspects of AdS/CFT correspondence. First, we identify the holographic anyons by using the field equations of supergravity, including the Chern-Simons terms of the probe branes. We find that the composite of Dp-branes wrapped over CP3 with the worldvolume magnetic fields can be the anyons. Next, we discuss the possible candidates of the dual anyonic operators on the CFT side, and find the agreement of their anyonic phases with the supergravity analysis. Finally, we try to construct the brane profile for the holographic anyons by solving the equations of motion and Killing spinor equations for the embedding profile of the wrapped branes. As a by product, we find a BPS spiky brane for the dual baryons in the ABJM theory.Comment: 1+33 pages, 3 figures; v2 discussion for D4-D6 case added, references added; v3 comments adde