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arXiv:1002.1375 · Physical Review B

Impurity spin texture at a deconfined quantum critical point

Argha Banerjee, Kedar Damle, Fabien Alet

Published Oct 26, 2010• 68 citations
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Abstract

The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N\'eel ordered phase and a valence-bond solid phase in square lattice $S=1/2$ antiferromagnets. Using a newly developed $T=0$ quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.

DOI
10.1103/physrevb.82.155139

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The spin texture surrounding a nonmagnetic impurity in a quantum antiferromagnet is a sensitive probe of the novel physics of a class of quantum phase transitions between a N'eel ordered phase and a valence-bond solid phase in square lattice S=1/2S=1/2S=1/2 antiferromagnets. Using a newly developed T=0T=0T=0 quantum Monte Carlo technique, we compute this spin texture at these transitions and find that it does not obey the universal scaling form expected at a scale invariant quantum critical point. We also identify the precise logarithmic form of these scaling violations. Our results are expected to yield important clues regarding the probable theory of these unconventional transitions.
We study the impurity physics at a continuous quantum phase transition from an SU(3) symmetric N\'eel-ordered state to a valence-bond-solid state that breaks lattice symmetries, using quantum Monte Carlo techniques. This continuous transition is expected to be an example of ``deconfined criticality'' in an SU(3) symmetric system. We find that the spin-texture induced by a missing-spin defect at the transition takes on a finite-size scaling form consistent with expectations from standard scaling arguments at a scale-invariant quantum critical point, albeit with significant subleading power-law finite size corrections that we analyze in detail. Together with recently found logarithmic violations of scaling at similar continuous transitions in the SU(2) case, our results provide indirect evidence of the existence of operators that become marginal as NNN is reduced to 222 in the field theoretical description of these deconfined critical points.
We describe the spin distribution in the vicinity of a nonmagnetic impurity in a two-dimensional antiferromagnet undergoing a transition from a magnetically ordered N\'eel state to a paramagnet with a spin gap. The quantum critical ground state in a finite system has total spin S=1∕2S=1∕2S=1∕2 (if the system without the impurity had an even number of S=1∕2S=1∕2S=1∕2 spins), and recent numerical studies in a double layer antiferromagnet [K. H. H\"oglund et al., Phys. Rev. Lett. 98, 087203 (2007)] have shown that the spin has a universal spatial form delocalized across the entire sample. We present the field theory describing the uniform and staggered magnetizations in this spin texture for two classes of antiferromagnets: (i) the transition from a N\'eel state to a paramagnet with local spin singlets, in models with an even number of S=1∕2S=1∕2S=1∕2 spins per unit cell, which are described by a O(3) Landau-Ginzburg-Wilson field theory; and (ii) the transition from a N\'eel state to a valence bond solid, in antiferromagnets with a single S=1∕2S=1∕2S=1∕2 spin per unit cell, which are described by a ``deconfined'' field theory of spinons.
We present results of extensive finite-temperature quantum Monte Carlo simulations on a SU(2) symmetric S=1/2 quantum antiferromagnet with four-spin interaction [A. W. Sandvik, Phys. Rev. Lett. 98, 227202 (2007)10.1103/PhysRevLett.98.227202]. Our simulations, which are free of the sign problem and carried out on lattices containing in excess of 1.6 x 10(4) spins, indicate that the four-spin interaction destroys the Néel order at an unconventional z = 1 quantum critical point, producing a valence-bond solid paramagnet. Our results are consistent with the "deconfined quantum criticality" scenario.
Motivated by recent Monte Carlo simulations of H\"oglund and Sandvik (arXiv:0808.0408), we study edge response in square lattice quantum antiferromagnets. We use the O(3) nonlinear $\ensuremath{\sigma}$ model to compute the decay asymptotics of the staggered magnetization, energy density, and local magnetic susceptibility away from the edge. We find that the total edge susceptibility is negative and diverges logarithmically as the temperature $T\ensuremath{\rightarrow}0$. We confirm the predictions of the continuum theory by performing a 1/S1/S1/S expansion of the microscopic Heisenberg model with the edge. We propose a qualitative explanation of the edge dimerization seen in Monte Carlo simulations by a theory of valence-bond-solid correlations in the N\'eel state. We also discuss the extension of the latter theory to the response of a single nonmagnetic impurity, and its connection to the theory of the deconfined critical point.
We generalize the SU(N=2) S=1/2 square-lattice quantum magnet with nearest-neighbor antiferromagnetic coupling (J(1)) and next-nearest-neighbor ferromagnetic coupling (J(2)) to arbitrary N. For all N>4, the ground state has valence-bond-solid order for J(2)=0 and Néel order for J(2)/J(1)≫1, allowing us access to the transition between these types of states for large N. Using quantum Monte Carlo simulations, we show that both order parameters vanish at a single quantum-critical point, whose universal exponents for large enough N (here up to N=12) approach the values obtained in a 1/N expansion of the noncompact CP(N-1) field theory. These results lend strong support to the deconfined quantum-criticality theory of the Néel-valence-bond-solid transition.
Abstract Berry phase interference arguments that underlie the theory of deconfined quantum criticality (DQC) for S = 1 / 2 antiferromagnets have also been invoked to allow for continuous transitions in S = 1 magnets including a Néel to (columnar) valence bond solid (cVBS) transition. We provide a microscopic model realization of this transition on the square lattice consisting of Heisenberg exchange ( J H ) and biquadratic exchange ( J B ) that favor a Néel phase, and a designed Q -term ( Q B ) interaction which favors a cVBS through large-scale quantum Monte Carlo (QMC) simulations. For J H = 0 , this model is equivalent to the SU(3) JQ model with a Néel-cVBS transition that has been argued to be DQC through QMC. Upon turning on J H which brings down the symmetry to SU(2), we find multiple signatures—a single critical point, high quality collapse of correlation ratios and order parameters, ‘U(1)-symmetric’ cVBS histograms and lack of double-peak in order parameter histograms for largest sizes studied near the critical point—that are highly suggestive of a continuous transition scenario. However, Binder analysis finds negative dips that grow sub-extensively that we interpret as these transitions rather being pseudocritical. This, along with recent results on spin- 1 2 models, suggests that deconfined pseudocriticality is the more generic scenario.