Quantum critical scaling behavior of deconfined spinons

Abstract

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if N is large enough. We argue that nonperturbatively this result should persist down to N = 2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent η for the decay of the two-spin correlation function to first-order in ǫ = 4 − d. We also note the scaling relation η = d + 2(1 − ϕ/ν) connecting the exponent η for the decay to the correlation length exponent ν and the crossover exponent ϕ. The most remarkable incarnation of the LandauGinzburg theory of phase transitions is the one embodied by Wilson's renormalization group (RG) [1]. According to this point of view, the Landau-Ginzburg theory is uniquely determined by the effective coupling constants obtained by integrating out high-energy modes. In this way, the large distance scaling behavior of different physical quantities is governed by the fixed points in the space of coupling constants. This is the so called LandauGinzburg-Wilson (LGW) paradigm of phase transitions [2]. The LGW paradigm is known to fail in a number of quantum phase transitions. One prominent example is the transition between the Néel state to a valence bond solid (VBS) state in a two-dimensional Mott insulator [3]. This transition features a quantum critical point (QCP), which is at odds with the LGW scenario that would predict a first-order phase transition. The crucial observation in this context is that both phases break symmetries in distinct spaces: the Néel state breaks the SU(2) symmetry of the Hamiltonian, while the paramagnetic VBS state breaks lattice symmetries. A continuous such order-order phase transition would not be captured by a LGW-like point of view [4].For an SU(2) Heisenberg antiferromagnet the spinons z α are the elementary constituents of the spin orientation field n. We have n a = z † σ a z, a = 1, 2, 3, where z = (z 1 , z 2 ) and σ a are the Pauli matrices. This is the so called CP 1 representation of the SU(2) spins. There is an inherent local gauge invariance in this representation, since n remains invariant when the spinon fields change by a local phase factor, i.e., z α → e iθ(x) z α . Thus, it seems to be natural to effectively describe a Mott insulator through a gauge theory coupled to "spinon matter". The gauge field here is an emergent photon: it is dynamically generated as a consequence of the local gauge invariance of n in terms of the spinon fields. Note that only expectation values of gauge-invariant operators can be nonzero, in agreement with Elitzur's theorem [5]. The VB...

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