Quantum cluster algorithm for frustrated Ising models in a transverse field

Abstract

Working within the stochastic series expansion framework, we introduce and characterize a new quantum cluster algorithm for quantum Monte Carlo simulations of transverse field Ising models with frustrated Ising exchange interactions. As a demonstration of the capabilities of this new algorithm, we show that a relatively small, ferromagnetic next-nearest neighbour coupling drives the transverse field Ising antiferromagnet on the triangular lattice from an antiferromagnetic threesublattice ordered state at low temperature to a ferrimagnetic three-sublattice ordered state.

Singular ferromagnetic susceptibility of the transverse-field Ising antiferromagnet on the triangular lattice

“…Finally, we comment on the nature of the transition between the antiferromagnetic and ferrimagnetic three sublattice ordered states. In previous work which studied 11 relatively small samples at moderately low temperatures in the vicinity of this transition, the phase of the estimator for the three-sublattice order parameter, as measured in the Quantum Monte Carlo simulations, was seen to be distributed more or less uniformly in the interval (0, 2π). If this behaviour were to persist to larger sizes, it would be indicative of a power-law ordered phase that interpolates between the antiferromagnetic and ferrimagnetic three-sublattice ordered phases at nonzero temperature.…”

“…This is consistent with the fact that a relatively small value of second-neighbour ferromagnetic exchange J 2 < 0 is sufficient to access a nearby state with ferrimagnetic three-sublattice ordering at low temperature. 11 In the power-law ordered phase associated with the two-step melting of three-sublattice order, the static susceptibility χ Q , defined in Eq. (8) for a finite size L × L system, is expected to scale as…”

“…In recent work,11 , the Γ = 0.8, J 1 = 1.0, J 2 = −0.1 The ferrimagnetic three-sublattice order that characterizes the ground state in the presence of a second-neighbour ferromagnetic interaction J2 = −0.1 also melts in a two-step manner. Upper and lower transition temperatures T1 and T2, that demarcate the boundaries of the power law ordered phase associated with this two-step melting, are obtained by plotting χ Q L −2 versus T for different values of L and identifying the temperatures at which curves corresponding to different L cross.…”

Cluster algorithms for frustrated two-dimensional Ising antiferromagnets via dual worm constructions

“…In this context, it is worth nothing that the cluster construction strategy developed recently for frustrated transverse field Ising models in Ref. 41 reduces, in the limit of vanishingly small transverse field, to a version of the Kandel-Ben Av-Domany plaquettepercolation approach. Thus, generalizations to quantum systems appear to be more natural within that framework, rather than in the dual worm approach used here.…”

Intrinsic transverse field in frustrated quantum Ising magnets: Physical origin and quantum effects

“…For the triangular lattice, this model has been extensively simulated [31][32][33][34] where the dynamical correlation properties and effect of long-range dipolar interaction were numerically studied recently 39,40 . On the triangular lattice, the system does not have exotic ground state and the physics is well captured within the conventional symmetry breaking 32,33 and the associated spin wave like quasiparticle picture 20 . In contrast, for our Kagome system, we would encounter fractionalization [41][42][43] .…”