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arXiv:cond-mat/9311045 · Physical Review Letters

Universal magnetic properties of frustrated quantum antiferromagnets in two dimensions

Andrey V. Chubukov, T. Senthil, Subir Sachdev A

Published Mar 28, 1994• 133 citations
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Abstract

We present a theory of frustrated, two-dimensional, quantum antiferromagnets in the vicinity of a quantum transition from a noncollinear, magnetically ordered ground state to a quantum-disordered phase. Using a sigma model for bosonic, spin-1/2, spinon fields, we obtain universal scaling forms for a variety of observables. Our results are compared with numerical data on the spin-1/2 triangular antiferromagnet.

DOI
10.1103/physrevlett.72.2089

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•Jan 1, 2012•0 citations
We present a theory of frustrated, two-dimensional, quantum antiferromagnets in the vicinity of a quantum transition from a noncollinear, magnetically ordered ground state to a quantum-disordered phase. Using a sigma model for bosonic, spin-1/2, spinon fields, we obtain universal scaling forms for a variety of observables. Our results are compared with numerical data on the spin-1/2 triangular antiferromagnet.
We study frustrated, two-dimensional, quantum antiferromagnets in the vicinity of a quantum transition from a non-collinear, magnetically-ordered ground state to a quantum disordered phase. The general scaling properties of this transition are described. A detailed study of a particular field-theoretic model of the transition, with bosonic spin-1/2 spinon fields, is presented. Explicit universal scaling forms for a variety of observables are obtained and the results are compared with numerical data on the spin-1/2 triangular antiferromagnet. Universal properties of an alternative field-theory, with confined spinons, are also briefly noted.
Consider a d-dimensional antiferromagnet with a quantum disordered ground state and a gap to bosonic excitations with nonzero spin. In a finite external magnetic field, this antiferromagnet will undergo a phase transition to a ground state with nonzero magnetization, describable as the condensation of a dilute gas of bosons. The finite-temperature properties of the Bose gas in the vicinity of this transition are argued to obey a hypothesis of zero scale-factor universality for d2, with logarithmic violations in d=2. Scaling properties of various experimental observables are computed in an expansion in \ensuremath{\epsilon}=2-d, and exactly in d=1.
We present a general approach to understanding the quantum phases and phase transitions of quantum antiferromagnets in two spatial dimensions. We begin with the simplest spin-liquid state, the Z2{Z}_{2}Z2​ spin liquid, whose elementary excitations are spinons and visons, carrying Z2{Z}_{2}Z2​ electric and magnetic charges, respectively. Their dynamics is expressed in terms of a doubled U(1) Chern-Simons theory, which correctly captures the ``topological'' order of the Z2{Z}_{2}Z2​ spin-liquid state. We show that the same theory also yields a description of the variety of ordered phases obtained when one or more of the elementary excitations condense. Field theories for the transitions and multicritical points between these phases are obtained. We survey experimental results on antiferromagnets on the anisotropic triangular lattice, and make connections between their phase diagrams and our results.
The behavior of ordered quantum Heisenberg antiferromagnets is analyzed from the nonlinear \ensuremath{\sigma} model in two and three dimensions. Many thermodynamic and dynamic properties are found to be universal at low temperatures and small magnetic fields. Finite-size effects are also investigated in detail; the results should be useful for analyzing numerical work on two-dimensional (2D) quantum antiferromagnets. The X-Y phase transition in 2D which is induced by a magnetic field is discussed. Applications to the ordered phase of solid 3He^{3}\mathrm{He}3He are also given.
We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional Heisenberg antiferromagnet is related to a phase transition of the hard-square model on the square lattice, which belongs to the two-dimensional Ising model universality class. It manifests itself in a logarithmic (low-) temperature singularity of the specific heat of the spin system observed for magnetic fields just below the saturation field.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.