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arXiv:1011.4827 · Physical Review B

Quantum destruction of spiral order in two-dimensional frustrated magnets

Subhro Bhattacharjee

Published Sep 15, 2011• 9 citations
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Abstract

We study the fate of spin-$1/2$ spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a ${Z}_{2}$ character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the ${Z}_{2}$ vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.

DOI
10.1103/physrevb.84.104430

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We study the fate of spin-1/21/21/2 spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a Z2{Z}_{2}Z2​ character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the Z2{Z}_{2}Z2​ vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for this latter phase transition and apply it to a lattice model. This transition potentially provides a new example of a Landau-forbidden deconfined quantum critical point.
Recently it was argued that quantum phase transitions can be radically different from classical phase transitions with, as a highlight, the "deconfined critical points" exhibiting fractionalization of quantum numbers due to Berry phase effects. Such transitions are supposed to occur in frustrated (" J 1 - J 2 ") quantum magnets. We have developed a novel renormalization approach for such systems which is fully respecting the underlying lattice structure. According to our findings, another profound phenomenon is around the corner: a fluctuation-induced (order-out-of-disorder) first-order transition. This has to occur for large spin and we conjecture that it is responsible for the weakly first-order behavior recently observed in numerical simulations for frustrated S = 1/2 systems.
Two-dimensional quantum antiferromagnets are believed to host phases of matter whose excitations are more fundamental than those of the ordered phases. When combining two such spin systems in a bilayer, strong interaction between the emergent excitations can produce phases not realized in either of its subsystems. We show that the critical fluctuations of a two-dimensional spin-liquid state can induce a deconfined quantum critical point in a proximate antiferromagnet. The most relevant coupling between the associated effective field theories is given by a mixed Chern-Simons term of the emergent gauge fields in each layer. This describes a topological current-current interaction. In contrast to the local spin-spin interaction, it strongly modifies the renormalization group flow of the theory describing the N\'eel--valence-bond-solid transition of the antiferromagnet. In particular, the protected coupling constant associated with it implies nontrivial quantum critical scaling characterized by a nonuniversal power-law divergence of the correlation length in the critical domain and Berezinskii-Kosterlitz-Thouless divergence approaching it.
Antiferromagnetic quantum spin systems can exhibit a transition between collinear and spiral ground states, driven by frustration. Classically this is a smooth crossover and the crossover point is termed a Lifshitz point. Quantum fluctuations change the nature of the transition. In particular, it has been argued previously that in the two-dimensional (2D) case a spin liquid (SL) state is developed in the vicinity of the Lifshitz point, termed a Lifshitz SL. In the present work, using a field theory approach, we solve the Lifshitz quantum phase transition problem for the 2D frustrated XY model. Specifically, we show that, unlike the SU(2)SU(2)SU(2) symmetric Lifshitz case, in the XY model, the SL exists only at the critical point. At zero temperature we calculate nonuniversal critical exponents in the N\'eel and in the spin spiral state and relate these to properties of the SL. We also solve the transition problem at a finite temperature and discuss the role of topological excitations.
We present the critical theory of a number of zero-temperature phase transitions of quantum antiferromagnets and interacting boson systems in two dimensions. The most important example is the transition of the S=1∕2S=1∕2S=1∕2 square lattice antiferromagnet between the N\'eel state (which breaks spin rotation invariance) and the paramagnetic valence bond solid (which preserves spin rotation invariance but breaks lattice symmetries). We show that these two states are separated by a second-order quantum phase transition. This conflicts with Landau-Ginzburg-Wilson theory, which predicts that such states with distinct broken symmetries are generically separated either by a first-order transition, or by a phase with co-existing orders. The critical theory of the second-order transition is not expressed in terms of the order parameters characterizing either state, but involves fractionalized degrees of freedom and an emergent, topological, global conservation law. A closely related theory describes the superfluid-insulator transition of bosons at half filling on a square lattice, in which the insulator has a bond density wave order. Similar considerations are shown to apply to transitions of antiferromagnets between the valence bond solid and the Z2{Z}_{2}Z2​ spin liquid: the critical theory has deconfined excitations interacting with an emergent U(1)\mathrm{U}(1)U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.