We present results of extensive finite-temperature Quantum Monte Carlo simulations on a SU(2) symmetric S = 1/2 quantum antiferromagnet with a four-spin interaction [Sandvik, Phys. Rev. Lett. 98, 227202 (2007)]. Our simulations, which are free of the sign-problem and carried out on lattices containing in excess of 1.6 × 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.Research into the possible ground states of SU(2) symmetric quantum antiferromagnets has thrived over the last two decades, motivated to a large extent by the undoped parent compounds of the cuprate superconductors. In these materials, the Cu sites can be well described as S = 1/2 spins on a two-dimensional (2D) square lattice that interact with an anti-ferromagnetic exchange, the archetypal model for which is the Heisenberg model. By now, it is well established [1] that the ground state of this model with nearest-neighbor interaction has Néel order that spontaneously breaks the SU(2) symmetry. Two logical questions immediately arise: What possible paramagnetic ground states can be reached by tuning competing interactions that destroy the Néel state? Are there universal quantum-critical points (QCP) that separate these paramagnets from the Néel phase?An answer to the first question is to disorder the Néel state by the proliferation of topological defects in the Néel order parameter [2]. It was shown by Read and Sachdev [3] that the condensation of these defects in the presence of quantum Berry phases results in a fourfold degenerate paramagnetic ground state, which breaks square-lattice symmetry due to the formation of a crystal of valence bonds -a valence-bond solid (VBS) phase. An answer to the second question was posed in recent work by Senthil et al.[4], where the possibility of a direct continuous Néel-to-VBS transition was proposed. The natural field theoretic description of this 'deconfined quantum critical point' is written in terms of certain fractionalized fields that are confined on either side of the QCP and become 'deconfined' precisely at the critical point. As is familiar from the general study of QCPs, these fractional excitations are expected to influence the physics in a large fan-shaped region that extends above the critical point at finite-T [5] (see Fig. 1).It is clearly of great interest to find models that harbor a direct Néel-VBS QCP and that can be studied without approximation on large lattices. Currently, the best candidate is the 'JQ' model, introduced by Sandvik [6], which is an S = 1/2, SU(2) invariant antiferromagnet (ii) In the 'quantum critical fan', there is scaling behavior characteristic of a z = 1 QCP; (iii) An accurate estimate of the scaling dimension of the Néel field establishes that this transition is not in the O(3) universality class; and, (iv) The paramagnetic ground state for sufficiently small J/Q is a V...

Soon after the discovery of high temperature superconductivity, Anderson [6] presented influential ideas on its connection to a novel type of insulator, in which the electron falls apart into emergent fractional particles which separately carry its spin and charge. These ideas have been extensively developed [7], and can explain the nodal zero-energy electron states in the superconductor. However, it is now known that the actual cuprate insulators are not of this type, and instead have conventional antiferromagnetic order, with the electron spins aligned in a checkerboard pattern on the square lattice. A separate set of ideas [8] take the presence of antiferromagnetic order in the insulator seriously, but require a specific effort to induce zero energy nodal electrons in the superconductor.Our theory of algebraic charge liquids (ACLs) uses the the recently developed theoretical

We synthesize and study single crystals of a new double-perovskite Sr2YIrO6. Despite two strongly unfavorable conditions for magnetic order, namely, pentavalent Ir5+(5d4) ions which are anticipated to have Jeff=0 singlet ground states in the strong spin-orbit coupling (SOC) limit and geometric frustration in a face-centered cubic structure formed by the Ir5+ ions, we observe this iridate to undergo a novel magnetic transition at temperatures below 1.3 K. We provide compelling experimental and theoretical evidence that the origin of magnetism is in an unusual interplay between strong noncubic crystal fields, local exchange interactions, and "intermediate-strength" SOC. Sr2YIrO6 provides a rare example of the failed dominance of SOC in the iridates.

We present an extensive quantum Monte Carlo study of the Néel to valence-bond solid (VBS) phase transition on rectangular- and honeycomb-lattice SU(N) antiferromagnets in sign-problem-free models. We find that in contrast to the honeycomb lattice and previously studied square-lattice systems, on the rectangular lattice for small N, a first-order Néel-VBS transition is realized. On increasing N≥4, we observe that the transition becomes continuous and with the same universal exponents as found on the honeycomb and square lattices (studied here for N=5, 7, 10), providing strong support for a deconfined quantum critical point. Combining our new results with previous numerical and analytical studies, we present a general phase diagram of the stability of CPN-1 fixed points with q monopoles.

We consider relativistic U(1) gauge theories in 2 + 1 dimensions, with N b species of complex bosons and N f species of Dirac fermions at finite temperature. The quantum phase transition between the Higgs and Coulomb phases is described by a conformal field theory (CFT). At large N b and N f , but for arbitrary values of the ratio N b /N f , we present computations of various critical exponents and universal amplitudes for these CFTs. We make contact with the different spin-liquids, charge-liquids and deconfined critical points of quantum magnets that these field theories describe. We compute physical observables that may be measured in experiments or numerical simulations of insulating and doped quantum magnets.