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Register a new userNew easy-plane $mathbb{CP}^{N-1}$ fixed points
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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.
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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.
We present a study of the one-dimensional S=1 antiferromagnetic spin chain with large easy plane anisotropy, with special emphasis on field-induced quantum phase transitions. Temperature and magnetic field dependence of magnetization, specific heat, and thermal conductivity is presented using a combination of numerical methods. In addition, the original S=1 model is mapped into the low-energy effective S=1/2 XXZ Heisenberg chain, a model which is exactly solvable using the Bethe ansatz technique. The effectiveness of the mapping is explored, and we show that all considered quantities are in qualitative, and in some cases quantitative, agreement. The thermal conductivity of the considered S=1 model is found to be strongly influenced by the underlying effective description. Furthermore, we elucidate the low-lying electron spin resonance spectrum, based on a semi--analytical Bethe ansatz calculation of the effective S=1/2 model.
We consider the easy-plane limit of bipartite SU($N$) Heisenberg Hamiltonians which have a fundamental representation on one sublattice and the conjugate to fundamental on the other sublattice. For $N=2$ the easy plane limit of the SU(2) Heisenberg model is the well known quantum XY model of a lattice superfluid. We introduce a logical method to generalize the quantum XY model to arbitrary $N$, which keeps the Hamiltonian sign-free. We show that these quantum Hamiltonians have a world-line representation as the statistical mechanics of certain tightly packed loop models of $N$-colors in which neighboring loops are disallowed from having the same color. In this loop representation we design an efficient Monte Carlo cluster algorithm for our model. We present extensive numerical results for these models on the two dimensional square lattice, where we find the nearest neighbor model has superfluid order for $Nleq 5$ and valence-bond order for $N> 5$. By introducing SU($N$) easy-plane symmetric four-spin couplings we are able to tune across the superfluid-VBS phase boundary for all $Nleq 5$. We present clear evidence that this quantum phase transition is first order for $N=2$ and $N=5$, suggesting that easy-plane deconfined criticality runs away generically to a first order transition for small-$N$.
While the Mott transition from a Fermi liquid is correctly believed to obtain without the breaking of any continuous symmetry, we show that in fact a discrete emergent $mathbb Z_2$ symmetry of the Fermi surface is broken. The extra $mathbb Z_2$ symmetry of the Fermi liquid appears to be little known although it was pointed out by Anderson and Haldane and we use it here to classify all possible Fermi liquids topologically by invoking K-homology. It is this $mathbb Z_2$ symmetry breaking that signals the onset of particle-hole asymmetry, a widely observed phenomenon in strongly correlated systems. In addition from this principle, we are able to classify which interactions suffice to generate the $mathbb Z_2$-symmetry-broken phase. As this is a symmetry breaking in momentum space, the local-in-momentum space interaction of the Hatsugai-Kohmoto (HK) model suffices as well as the Hubbard interaction as it contains the HK interaction. Both lie in the same universality class as can be seen from exact diagonalization. We then use the Bott topological invariant to establish the stability of a Luttinger surface. Our proof demonstrates that the strongly coupled fixed point only corresponds to those Luttinger surfaces with co-dimension $p+1$ with $p$ odd. Because they both lie in the same universality class, we conclude that the Hubard and HK models are controlled by this fixed point.
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.
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