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Register a new userFate of CP(N-1) fixed points with q-monopoles
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We present an extensive quantum Monte Carlo study of the Neel-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 Neel-VBS transition is realized. On increasing $Ngeq 4$, we observe that the transition becomes continuous and with the {em 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 $mathbb{CP}^{N-1}$ fixed points with $q$-monopoles.
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We study fixed points of the easy-plane $mathbb{CP}^{N-1}$ field theory by combining quantum Monte Carlo simulations of lattice models of easy-plane SU($N$) superfluids with field theoretic renormalization group calculations, by using ideas of deconfined criticality. From our simulations, we present evidence that at small $N$ our lattice model has a first order phase transition which progressively weakens as $N$ increases, eventually becoming continuous for large values of $N$. Renormalization group calculations in $4-epsilon$ dimensions provide an explanation of these results as arising due to the existence of an $N_{ep}$ that separates the fate of the flows with easy-plane anisotropy. When $N<N_{ep}$ the renormalization group flows to a discontinuity fixed point and hence a first order transition arises. On the other hand, for $N > N_{ep}$ the flows are to a new easy-plane $mathbb{CP}^{N-1}$ fixed point that describes the quantum criticality in the lattice model at large $N$. Our lattice model at its critical point thus gives efficient numerical access to a new strongly coupled gauge-matter field theory.
The topological charge distribution P(Q) is calculated for lattice ${rm CP}^{N-1}$ models. In order to suppress lattice cut-off effects we employ a fixed point (FP) action. Through transformation of P(Q) we calculate the free energy $F(theta)$ as a function of the $theta$ parameter. For N=4, scaling behavior is observed for P(Q), $F(theta)$ as well as the correlation lengths $xi(Q)$. For N=2, however, scaling behavior is not observed as expected. For comparison, we also make a calculation for the ${rm CP}^{3}$ model with standard action. We furthermore pay special attention to the behavior of P(Q) in order to investigate the dynamics of instantons. For that purpose, we carefully look at behavior of $gamma_{it eff}$, which is an effective power of P(Q)($sim exp(-CQ^{gamma_{it eff}})$), and reflects the local behavior of P(Q) as a function of Q. We study $gamma_{it eff}$ for two cases, one of which is the dilute gas approximation based on the Poisson distribution of instantons and the other is the Debye-Huckel approximation of instanton quarks. In both cases we find similar behavior to the one observed in numerical simulations.
We construct a family of warped AdS_5 compactifications of IIB supergravity that are the holographic duals of the complete set of N=1 fixed points of a Z_2 quiver gauge theory. This family interpolates between the T^{1,1} compactification with no three-form flux and the Z_2 orbifold of the Pilch-Warner geometry which contains three-form flux. This family of solutions is constructed by making the most general Ansatz allowed by the symmetries of the field theory. We use Killing spinor methods because the symmetries impose two simple projection conditions on the Killing spinors, and these greatly reduce the problem. We see that generic interpolating solution has a nontrivial dilaton in the internal five-manifold. We calculate the central charge of the gauge theories from the supergravity backgrounds and find that it is 27/32 of the parent N=2, quiver gauge theory. We believe that the projection conditions that we derived here will be useful for a much larger class of N=1 holographic RG-flows.
We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time our results directly apply to Kitaevs honeycomb model in a vortex superlattice.
We study the famous example of weakly first order phase transitions in the 1+1D quantum Q-state Potts model at Q>4. We numerically show that these weakly first order transitions have approximately conformal invariance. Specifically, we find entanglement entropy on considerably large system sizes fits perfectly with the universal scaling law of this quantity in the conformal field theories (CFTs). This supports that the weakly first order transitions is proximate to complex fixed points, which are described by recent conjectured complex CFTs. Moreover, the central charge extracted from this fitting is close to the real part of the complex central charge of these complex CFTs. We also study the conformal towers and the drifting behaviors of these conformal data (e.g., central charge and scaling dimensions).
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