arXiv subjects

R. Moessner

Publications and source records attributed to R. Moessner.

At least 145 records · Page 8Linked to original sources

arXiv2004

Dipolar spin correlations in classical pyrochlore magnets

We study spin correlations for the highly frustrated classical pyrochlore lattice antiferromagnets with O(N) symmetry in the limit T->0. We conjecture that a local constraint obeyed by the extensively degenerate ground states dictates a dipolar form for the asymptotic spin correlations, at all N $\ne$ 2 for which the system is paramagnetic down to T=0. We verify this conjecture in the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion about the solvable N=infinity limit. Remarkably, the N=infinity formulae are an excellent fit, at all distances, to the correlators at N=3 and even at N=1. Thus we obtain a simple analytical expression also for the correlations of the equivalent models of spin ice and cubic water ice, I_h.

cond-mat.dis-nn↗

arXiv2004

Magnetization process of spin ice in a [111] magnetic field

Spin ice in a magnetic field in the [111] direction displays two magnetization plateaux, one at saturation and an intermediate one with finite entropy. We study the crossovers between the different regimes from a point of view of (entropically) interacting defects. We develop an analytical theory for the nearest-neighbor spin ice model, which covers most of the magnetization curve. We find that the entropy is non-monotonic, exhibiting a giant spike between the two plateaux. This regime is described by a monomer-dimer model with tunable fugacities. At low fields, we develop an RG treatment for the extended string defects, and we compare our results to extensive Monte Carlo simulations. We address the implications of our results for cooling by adiabatic (de)magnetization.

cond-mat.stat-mech↗

arXiv2004

On bipartite Rokhsar-Kivelson points and Cantor deconfinement

Quantum dimer models on bipartite lattices exhibit Rokhsar-Kivelson (RK) points with exactly known critical ground states and deconfined spinons. We examine generic, weak, perturbations around these points. In d=2+1 we find a first order transition between a ``plaquette'' valence bond crystal and a region with a devil's staircase of commensurate and incommensurate valence bond crystals. In the part of the phase diagram where the staircase is incomplete, the incommensurate states exhibit a gapless photon and deconfined spinons on a set of finite measure, almost but not quite a deconfined phase in a compact U(1) gauge theory in d=2+1! In d=3+1 we find a continuous transition between the U(1) resonating valence bond (RVB) phase and a deconfined staggered valence bond crystal. In an appendix we comment on analogous phenomena in quantum vertex models, most notably the existence of a continuous transition on the triangular lattice in d=2+1.

cond-mat.stat-mech↗

arXiv2004

Valence-bond crystal in a {111} slice of the pyrochlore antiferromagnet

We investigate theoretically the ordering effect of quantum spin fluctuations in a Heisenberg antiferromagnet on a two-dimensional network of corner sharing tetrahedra. This network is obtained as a {111} slice of the highly frustrated pyrochlore lattice, from which it inherits the equivalence of all three pairs of opposite bonds of each tetrahedron. The lowest-order (in 1/S) quantum corrections partially lift the huge degeneracy of the classical ground state and select an ensemble of states with long-range valence-bond order.

cond-mat.str-el↗

arXiv2003

Coulomb and Liquid Dimer Models in Three Dimensions

We study classical hard-core dimer models on three-dimensional lattices using analytical approaches and Monte Carlo simulations. On the bipartite cubic lattice, a local gauge field generalization of the height representation used on the square lattice predicts that the dimers are in a critical Coulomb phase with algebraic, dipolar, correlations, in excellent agreement with our large-scale Monte Carlo simulations. The non-bipartite FCC and Fisher lattices lack such a representation, and we find that these models have both confined and exponentially deconfined but no critical phases. We conjecture that extended critical phases are realized only on bipartite lattices, even in higher dimensions.

cond-mat.stat-mech↗

arXiv2003

Bond order from disorder in the planar pyrochlore magnet

We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.

cond-mat.str-el↗

arXiv2003

Three dimensional resonating valence bond liquids and their excitations

We show that there are two types of RVB liquid phases present in three-dimensional quantum dimer models, corresponding to the deconfining phases of U(1) and Z_2 gauge theories in d=3+1. The former is found on the bipartite cubic lattice and is the generalization of the critical point in the square lattice quantum dimer model found originally by Rokhsar and Kivelson. The latter exists on the non-bipartite face-centred cubic lattice and generalizes the RVB phase found earlier by us on the triangular lattice. We discuss the excitation spectrum and the nature of the ordering in both cases. Both phases exhibit gapped spinons. In the U(1) case we find a collective, linearly dispersing, transverse excitation, which is the photon of the low energy Maxwell Lagrangian and we identify the ordering as quantum order in Wen's sense. In the Z_2 case all collective excitations are gapped and, as in d=2, the low energy description of this topologically ordered state is the purely topological BF action. As a byproduct of this analysis, we unearth a further gapless excitation, the pi0n, in the square lattice quantum dimer model at its critical point.

cond-mat.str-el↗

arXiv2003

Classical dimers on the triangular lattice

We study the classical hard-core dimer model on the triangular lattice. Following Kasteleyn's fundamental theorem on planar graphs, this problem is soluble by Pfaffians. This model is particularly interesting for, unlike the dimer problems on the bipartite square and hexagonal lattices, its correlations are short ranged with a correlation length of less than one lattice constant. We compute the dimer-dimer and monomer-monomer correlators, and find that the model is deconfining: the monomer-monomer correlator falls off exponentially to a constant value sin(pi/12)/sqrt(3) = .1494..., only slightly below the nearest-neighbor value of 1/6. We also consider the anisotropic triangular lattice model in which the square lattice is perturbed by diagonal bonds of one orientation and small fugacity. We show that the model becomes non-critical immediately and that this perturbation is equivalent to adding a mass term to each of two Majorana fermions that are present in the long wavelength limit of the square-lattice problem.

cond-mat.stat-mech↗

arXiv2003

Theory of the [111] magnetization plateau in spin ice

The application of a magnetic field along the [111] direction in the spin ice compounds leads to two magnetization plateaux, in the first of which the ground state entropy is reduced but still remains extensive. We observe that under reasonable assumptions, the remaining degrees of freedom in the low field plateau live on decoupled kagome planes, and can be mapped to hard core dimers on a honeycomb lattice. The resulting two dimensional state is critical, and we have obtained its residual entropy -- in good agreement with a recent experiments -- the equal time spin correlations as well as a theory for the dynamical spin correlations. Small tilts of the field are predicted to lead a vanishing of the entropy and the termination of the critical phase by a Kasteleyn transition characterized by highly anisotropic scaling. We discuss the thermally excited defects that terminate the plateau either end, among them an exotic string defect which restores three dimensionality.

cond-mat.stat-mech↗

arXiv2003

Interplay of quantum and thermal fluctuations in a frustrated magnet

We demonstrate the presence of an extended critical phase in the transverse field Ising magnet on the triangular lattice, in a regime where both thermal and quantum fluctuations are important. We map out a complete phase diagram by means of quantum Monte Carlo simulations, and find that the critical phase is the result of thermal fluctuations destabilising an order established by the quantum fluctuations. It is separated by two Kosterlitz-Thouless transitions from the paramagnet on one hand and the quantum-fluctuation driven three-sublattice ordered phase on the other. Our work provides further evidence that the zero temperature quantum phase transition is in the 3d XY universality class.

cond-mat.stat-mech↗

arXiv2002

On Ising and dimer models in two and three dimensions

Motivated by recent interest in 2+1 dimensional quantum dimer models, we revisit Fisher's mapping of two dimensional Ising models to hardcore dimer models. First, we note that the symmetry breaking transition of the ferromagetic Ising model maps onto a non-symmetry breaking transition in dimer language -- instead it becomes a deconfinement transition for test monomers. Next, we introduce a modification of Fisher's mapping in which a second dimer model, also equivalent to the Ising model, is defined on a generically different lattice derived from the dual. In contrast to Fisher's original mapping, this enables us to reformulate frustrated Ising models as dimer models with positive weights and we illustrate this by providing a new solution of the fully frustrated Ising model on the square lattice. Finally, by means of the modified mapping we show that a large class of three-dimensional Ising models are precisely equivalent, in the time continuum limit, to particular quantum dimer models. As Ising models in three dimensions are dual to Ising gauge theories, this further yields an exact map between the latter and the quantum dimer models. The paramagnetic phase in Ising language maps onto a deconfined, topologically ordered phase in the dimer models. Using this set of ideas, we also construct an exactly soluble quantum eight vertex model.

cond-mat.stat-mech↗

arXiv2002

Pocket Monte Carlo algorithm for classical doped dimer models

We study the correlations of classical hardcore dimer models doped with monomers by Monte Carlo simulation. We introduce an efficient cluster algorithm, which is applicable in any dimension, for different lattices and arbitrary doping. We use this algorithm for the dimer model on the square lattice, where a finite density of monomers destroys the critical confinement of the two-monomer problem. The monomers form a two-component plasma located in its high-temperature phase, with the Coulomb interaction screened at finite densities. On the triangular lattice, a single pair of monomers is not confined. The monomer correlations are extremely short-ranged and hardly change with doping.

cond-mat.str-el↗

arXiv2002

Resonating valence bond liquid physics on the triangular lattice

We give an account of the short-range RVB liquid phase on the triangular lattice, starting from an elementary introduction to quantum dimer models including details of the overlap expansion used to generate them. The fate of the topological degeneracy of the state under duality is discussed, as well as recent developments including its possible relevance for quantum computing.

cond-mat.str-el↗

arXiv2002

Spin-Peierls phases in pyrochlore antiferromagnets

In the highly frustrated pyrochlore magnet spins form a lattice of corner sharing tetrahedra. We show that the tetrahedral ``molecule'' at the heart of this structure undergoes a Jahn-Teller distortion when lattice motion is coupled to the antiferromagnetism. We extend this analysis to the full pyrochlore lattice by means of Landau theory and argue that it should exhibit spin-Peierls phases with bond order but no spin order. We find a range of Neel phases, with collinear, coplanar and noncoplanar order. While collinear Neel phases are easiest to generate microscopically, we also exhibit an interaction that gives rise to a coplanar state instead.

cond-mat.str-el↗

arXiv2001

Order by distortion and string modes in pyrochlore antiferromagnet

We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S=1, and semiclassical analyses to argue that such couplings generate bond order via a spin--Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Neel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Neel phase, a dispersionless string-like magnon mode dominates the resulting excitation spectrum, providing a distinctive signature of the parent geometrically frustrated state. We comment on the experimental situation.

cond-mat.str-el↗

arXiv2001

Planar pyrochlore, quantum ice and sliding ice

We study quantum antiferromagnetism on the highly frustrated checkerboard lattice, also known as the square lattice with crossings. The quantum Heisenberg antiferromagnet on this lattice is of interest as a two-dimensional analog of the pyrochlore lattice magnet. By combining several approaches we conclude that this system is most likely ordered for all values of spin, $S$, with a Neel state for large $S$ giving way to a two-fold degenerate valence-bond solid for smaller $S$. We show next that the Ising antiferromagnet with a weak four-spin exchange, equivalent to square ice with the leading quantum dynamics, exhibits long range ``anti-ferroelectric'' order. As a byproduct of this analysis we obtain, in the system of weakly coupled ice planes, a sliding phase with XY symmetry.

cond-mat.stat-mech↗

arXiv2001

The phase diagram of the hexagonal lattice quantum dimer model

We discuss the phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice. In addition to the columnar and staggered valence bond solids which have been discussed in previous work, we establish the existence of a plaquette valence bond solid. The transition between the plaquette and columnar phases at $v/t=-0.2 \pm 0.05$ is argued to be first order. We note that this model should describe valence bond dominated phases of frustrated Heisenberg models on the hexagonal lattice and discuss its relation to recent exact diagonalisation work by J.B. Fouet etal on the J_1-J_2 model on the same lattice. Our results also shed light on the properties of the transverse field Ising antiferromagnet on the triangular lattice and the classical Ising antiferromagnet on the stacked triangular lattice, which are related to dimer models by duality.

cond-mat.stat-mech↗

arXiv2001

Short-ranged RVB physics, quantum dimer models and Ising gauge theories

Quantum dimer models are believed to capture the essential physics of antiferromagnetic phases dominated by short-ranged valence bond configurations. We show that these models arise as particular limits of Ising (Z_2) gauge theories, but that in these limits the system develops a larger local U(1) invariance that has different consequences on different lattices. Conversely, we note that the standard Z_2 gauge theory is a generalised quantum dimer model, in which the particular relaxation of the hardcore constraint for the dimers breaks the U(1) down to Z_2. These mappings indicate that at least one realization of the Senthil-Fisher proposal for fractionalization is exactly the short ranged resonating valence bond (RVB) scenario of Anderson and of Kivelson, Rokhsar and Sethna. They also suggest that other realizations will require the identification of a local low energy, Ising link variable {\it and} a natural constraint. We also discuss the notion of topological order in Z_2 gauge theories and its connection to earlier ideas in RVB theory. We note that this notion is not central to the experiment proposed by Senthil and Fisher to detect vortices in the conjectured Z_2 gauge field.

cond-mat.supr-con↗