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 N\'eel 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.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 N\'eel 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.

arXiv:cond-mat/0502215Physical Review BSep 2, 2005262 citations

Order and disorder in a model quantum magnet

D. Bitko

Jan 1, 19975 citations

Emergence of New States in Low-Dimensional Quantum Magnets

Gang Su

한국자기학회 학술연구발표회 논문개요집Dec 1, 20100 citations

Competing orders, nonlinear sigma models, and topological terms in quantum magnets

T. Senthil, Matthew P. A. Fisher

A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson (LGW) paradigm in describing the competing phases and phase transitions of two-dimensional quantum magnets. In this paper, we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examples that are studied include weakly coupled quasi-one-dimensional spin chains, deconfined critical points in fully two-dimensional magnets, and two-component massless ${\mathrm{QED}}_{3}$ . A prominent role is played by an anisotropic O(4) nonlinear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We speculate that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson (LGW) paradigm in describing the competing phases and phase transitions of two-dimensional quantum magnets. In this paper, we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examples that are studied include weakly coupled quasi-one-dimensional spin chains, deconfined critical points in fully two-dimensional magnets, and two-component massless ${\mathrm{QED}}_{3}$. A prominent role is played by an anisotropic O(4) nonlinear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We speculate that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.

arXiv:cond-mat/0510459Physical Review BAug 8, 2006226 citations

Magnetic Field Effects in Low-Dimensional Quantum Magnets

Adam Iaizzi

Springer thesesJan 1, 20186 citations

{\mathrm{QED}}_{3}

. A prominent role is played by an anisotropic O(4) nonlinear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We speculate that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.