Quantum phase transitions in Mott insulators do not fit easily into the Landau-Ginzburg-Wilson paradigm. A recently proposed alternative to it is the so-called deconfined quantum criticality scenario, providing a new paradigm for quantum phase transitions. In this context it has recently been proposed that a second-order phase transition would occur in a two-dimensional spin 1/2 quantum antiferromagnet in the deep easy-plane limit. A check of this conjecture is important for understanding the phase structure of Mott insulators. To this end we have performed large-scale Monte Carlo simulations on an effective gauge theory for this system, including a Berry-phase term that projects out the S=1/2 sector. The result is a first-order phase transition, thus contradicting the conjecture.
A high-order direct numerical simulation code (The Pencil Code) has been used together with the immersed boundary method on a Cartesian grid to simulate particle impaction on a cylinder in a crossflow. The direct numerical scheme concerns only the fluid flow, into which the particles are subsequently coupled through a one-way drag-coefficient law. The immersed boundary method is extended to work with high-order discretization, and the particle impaction efficiency has been measured for Stokes numbers ranging from 0.001 to 40 for a range of different Reynolds numbers. Three modes of impaction on the front side of the cylinder are identified, where, for the large-Stokes-number mode (St > 0.3), an alternative to the traditional Stokes number is presented that provides better scaling. The intermediate impaction mode has a very steep decrease in impaction efficiency as the Stokes number is decreased, and this is identified as the range of Stokes numbers where the viscous boundary layer starts to take effect. The third mode of front-side impaction is for the very small particles with St < 0.1 exactly following the flow but impacting on the cylinder due to their finite radii. There will not be any capture on the front side of the cylinder for impact angles larger than ~56° for this mode. Finally, it is found that the particle impaction on the back side of the cylinder is strongly dependent on the flow Reynolds number, where large Reynolds numbers lead to larger impaction efficiencies. The upper limiting Stokes number of back-side impaction is around 0.13, apparently irrespective of the Reynolds number.
We use analytical arguments and large-scale Monte Carlo calculations to investigate the nature of the phase transitions between distinct complex superfluid phases in a two-component Bose-Einstein condensate when a non-dissipative drag between the two components is being varied. We focus on understanding the role of topological defects in various phase transitions and develop vortex-matter arguments allowing an analytical description of the phase diagram. We find the behavior of fluctuation induced vortex matter to be much more complex and substantially different from that of single-component superfluids. We propose and investigate numerically a novel drag-induced "preemptive vortex loop proliferation" transition. Such a transition may be a quite generic feature in many multicomponent systems where symmetry is restored by a gas of several kinds of competing vortex loops.
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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