Recent scanning tunneling microscopy (STM) experiments on underdoped cuprates have displayed modulations in the local electronic density of states, which are centered on a Cu-O-Cu bond [Kohsaka et al., Science 315, 1380 (2007)]. As a paradigm of the pinning of such bond-centered ordering in strongly correlated systems, we present the theory of valence bond solid (VBS) correlations near a single impurity in a square lattice antiferromagnet. The antiferromagnet is assumed to be in the vicinity of a quantum transition from a magnetically ordered N'eel state to a spin-gap state with long-range VBS order. We identify two distinct classes of impurities: (i) local modulation in the exchange constants and (ii) a missing or additional spin, for which the impurity perturbation is represented by an uncompensated Berry phase. The ``boundary'' critical theory for these classes is developed. In the second class, we find a VBS pinwheel around the impurity, accompanied by a suppression in the VBS susceptibility. Implications for numerical studies of quantum antiferromagnets and for STM experiments on the cuprates are noted.
We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type, the spin-lattice coupling-induced VBS state can occur when
2S is not an integer multiple of the coordination number
z.
S=2 spins on the triangular lattice with
z=6 is discussed as an example. Within the Schwinger boson mean-field theory the ground state is derived as the direct product of states, one of which represents the conventional long-range ordered spins, and the other given by the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ modulation of the valence bond amplitudes. Excitation spectrum for the modulated valence bond state is worked out within the single-mode approximation. The spectrum offers a new collective mode, distinct from the spin wave excitations of the magnetically ordered ground state, and observable in neutron scattering.
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∕2 (if the system without the impurity had an even number of
S=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∕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∕2 spin per unit cell, which are described by a ``deconfined'' field theory of spinons.
We use quantum Monte Carlo methods to study the ground-state phase diagram of a
S=1/2 honeycomb lattice magnet in which a nearest-neighbor antiferromagnetic exchange
J (favoring N\'eel order) competes with two different multispin interaction terms: a six-spin interaction
Q3 that favors columnar valence-bond solid (VBS) order, and a four-spin interaction
Q2 that favors staggered VBS order. For ${Q}_{3}\ensuremath{\sim}{Q}_{2}\ensuremath{\gg}J$, we establish that the competition between the two different VBS orders stabilizes N\'eel order in a large swath of the phase diagram even when
J is the smallest energy scale in the Hamiltonian. When ${Q}_{3}\ensuremath{\gg}({Q}_{2},J)$ $\mathrm{[}{Q}_{2}\ensuremath{\gg}({Q}_{3},J)\text{]}$, this model exhibits at zero temperature phase transition from the N\'eel state to a columnar (staggered) VBS state. We establish that the N\'eel-columnar VBS transition is continuous for all values of
Q2, and that critical properties along the entire phase boundary are well characterized by critical exponents and amplitudes of the noncompact
CP1 (NCCP1) theory of deconfined criticality, similar to what is observed on a square lattice. However, a surprising threefold anisotropy of the phase of the VBS order parameter at criticality, whose presence was recently noted at the
Q2=0 deconfined critical point, is seen to persist all along this phase boundary. We use a classical analogy to explore this by studying the critical point of a three-dimensional
XY model with a fourfold anisotropy field which is known to be weakly irrelevant at the three-dimensional
XY critical point. In this case, we again find that the critical anisotropy appears to saturate to a nonzero value over the range of sizes accessible to our simulations.
Using a loop–cluster algorithm we investigate the spin- Heisenberg antiferromagnet on a square lattice with exchange coupling J and an additional four-spin interaction of strength Q . We confirm the existence of a phase transition separating antiferromagnetism at J / Q > J c / Q from a valence bond solid (VBS) state at J / Q < J c / Q . Although our Monte Carlo data are consistent with those of previous studies, we do not confirm the existence of a deconfined quantum critical point. Instead, using a flowgram method on lattices as large as 80 2 , we find evidence for a weak first-order phase transition. We also present a detailed study of the antiferromagnetic phase. For J / Q > J c / Q the staggered magnetization, the spin stiffness and the spinwave velocity of the antiferromagnet are determined by fitting Monte Carlo data to analytic results from the systematic low-energy effective field theory for magnons. Finally, we also investigate the physics of the VBS state at J / Q < J c / Q and we show that long but finite antiferromagnetic correlations are still present.
We present a detailed study of the destruction of SU(
N) magnetic order in square lattice bilayer antiferromagnets using unbiased quantum Monte Carlo numerical simulations and field theoretic techniques. We study phase transitions from an SU(
N) N\'eel state into two distinct quantum disordered ``valence-bond'' phases: a valence-bond liquid (VBL) with no broken symmetries and a lattice-symmetry-breaking valence-bond solid (VBS) state. For finite interlayer coupling, the cancellation of Berry phases between the layers has dramatic consequences on the two phase transitions: the N\'eel-VBS transition is first order for all $N\ensuremath{\ge}5$ accesible in our model, whereas the N\'eel-VBL transition is continuous for
N=2 and first order for $N\ensuremath{\ge}4$; for
N=3 the N\'eel-VBL transition show no signs of first-order behavior.
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∕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 spin liquid: the critical theory has deconfined excitations interacting with an emergent
U(1) gauge force. We comment on the broader implications of our results for the study of quantum criticality in correlated electron systems.