Spin nematics, valence-bond solids and spin liquids in SO(NN) quantum spin models on the triangular lattice

We introduce a simple model of SO($N$) spins with two-site interactions which is amenable to quantum Monte-Carlo studies without a sign problem on non-bipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small $N$, a valence-bond solid (VBS) at large $N$ and a quantum spin liquid at intermediate $N$. By the introduction of a sign-free four-site interaction we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions

Marshall-positive SU(NN) quantum spin systems and classical loop models: A practical strategy to design sign-problem-free spin Hamiltonians

We consider bipartite SU($N$) spin Hamiltonians with a fundamental representation on one sublattice and a conjugate to fundamental on the other sublattice. By mapping these antiferromagnets to certain classical loop models in one higher dimension, we provide a practical strategy to write down a large family of SU($N$) symmetric spin Hamiltonians that satisfy Marshall's sign condition. This family includes all previously known sign-free SU($N$) spin models in this representation and in addition provides a large set of new models that are Marshall positive and can hence be studied efficiently with quantum Monte Carlo methods. As an application of our idea to the square lattice, we show that in addition to Sandvik's $Q$-term, there is an independent non-trivial four-spin $R$-term that is sign-free. Using numerical simulations, we show how the $R$-term provides a new route to the study of quantum criticality of N\'eel order

New easy-plane CPN−1\mathbb{CP}^{N-1} fixed points

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.Comment: 12 pages, 9 figure

Numerical studies of various Neel-VBS transitions in SU(N) anti-ferromagnets

In this manuscript we review recent developments in the numerical simulations of bipartite SU(N) spin models by quantum Monte Carlo (QMC) methods. We provide an account of a large family of newly discovered sign-problem free spin models which can be simulated in their ground states on large lattices, containing O(10^5) spins, using the stochastic series expansion method with efficient loop algorithms. One of the most important applications so far of these Hamiltonians are to unbiased studies of quantum criticality between Neel and valence bond phases in two dimensions -- a summary of this body of work is provided. The article concludes with an overview of the current status of and outlook for future studies of the "designer" Hamiltonians.Comment: Mini-review article for the proceedings of CCP 2014 (Boston

Quantum criticality in SU(3) and SU(4) anti-ferromagnets

We study the quantum phase transition out of the Neel state in SU(3) and SU(4) generalizations of the Heisenberg anti-ferromagnet with a sign problem free four spin coupling (so-called JQ model), by extensive quantum Monte Carlo simulations. We present evidence that the SU(3) and SU(4) order parameters and the SU(3) and SU(4) stiffness' go to zero continuously without any evidence for a first order transition. However, we find considerable deviations from simple scaling laws for the stiffness even in the largest system sizes studied. We interpret these as arising from multiplicative scaling terms in these quantities which affect the leading behavior, i.e., they will persist in the thermodynamic limit unlike the conventional additive corrections from irrelevant operators. We conjecture that these multiplicative terms arise from dangerously irrelevant operators whose contributions to the quantities of interest are non-analytic

First-order superfluid to valence bond solid phase transitions in easy-plane SU(NN) magnets for small-NN

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 $N\leq 5$ 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 $N\leq 5$. 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-$N$.Comment: 8 pages, 8 figures, 1 tabl

Spin nematic ground state of the triangular lattice S=1 biquadratic model

Motivated by the spate of recent experimental and theoretical interest in Mott insulating S=1 triangular lattice magnets, we consider a model S=1 Hamiltonian on a triangular lattice interacting with rotationally symmetric biquadratic interactions. We show that the partition function of this model can be expressed in terms of configurations of three colors of tightly-packed, closed loops with {\em non-negative} weights, which allows for efficient quantum Monte Carlo sampling on large lattices. We find the ground state has spin nematic order, i.e. it spontaneously breaks spin rotation symmetry but preserves time reversal symmetry. We present accurate results for the parameters of the low energy field theory, as well as finite-temperature thermodynamic functions

Spin Nematics, Valence-Bond Solids, and Spin Liquids in SO(\u3cem\u3eN\u3c/em\u3e) Quantum Spin Models on the Triangular Lattice

We introduce a simple model of SO(N) spins with two-site interactions which is amenable to quantum Monte Carlo studies without a sign problem on nonbipartite lattices. We present numerical results for this model on the two-dimensional triangular lattice where we find evidence for a spin nematic at small N, a valence-bond solid at large N, and a quantum spin liquid at intermediate N. By the introduction of a sign-free four-site interaction, we uncover a rich phase diagram with evidence for both first-order and exotic continuous phase transitions

Spin excitations in fluctuating stripe phases of doped cuprate superconductors

Using a phenomenological lattice model of coupled spin and charge modes, we determine the spin susceptibility in the presence of fluctuating stripe charge order. We assume the charge fluctuations to be slow compared to those of the spins, and combine Monte Carlo simulations for the charge order parameter with exact diagonalization of the spin sector. Our calculations unify the spin dynamics of both static and fluctuating stripe phases and support the notion of a universal spin excitation spectrum in doped cuprate superconductors.Comment: 4 pages, 4 figs, minor changes, final version as publishe