Quantum and Thermal Transitions Out of the Supersolid Phase of a 2D Quantum Antiferromagnet

We investigate the thermodynamic properties of a field-induced supersolid phase in a 2D quantum antiferromagnet model. Using quantum Monte Carlo simulations, a very rich phase diagram is mapped out in the temperature—magnetic-field plane, with an extended supersolid region where a diagonal (solid) order coexists with a finite XY spin stiffness (superfluid). The various quantum and thermal transitions out of the supersolid state are characterized. Experimental consequences in the context of field-induced magnetization plateau materials are briefly discussed.

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Nicolas Laflorencie, Frédéric Mila
2007
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https://infoscience.epfl.ch/record/267587?ln=fr

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Supersolid phase induced by correlated hopping in spin-1/2 frustrated quantum magnets

Julien Dorier, Frédéric Mila

We show that correlated hopping of triplets, which is often the dominant source of kinetic energy in dimer-based frustrated quantum magnets, produces a remarkably strong tendency to form supersolid phases in a magnetic field. These phases are characterized by simultaneous modulation and ordering of the longitudinal and transverse magnetization, respectively. Using quantum Monte Carlo and a semiclassical approach for an effective hard-core boson model with nearest-neighbor repulsion on a square lattice, we prove, in particular, that a supersolid phase can exist even if the repulsion is not strong enough to stabilize an insulating phase at half-filling. Experimental implications for frustrated quantum antiferromagnets in a magnetic field at zero and finite temperature are discussed.

2008

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Zero-temperature Monte Carlo study of the noncoplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice

Frédéric Mila, Karlo Penc, Sandro Wenzel

We investigate the ground-state properties of the highly degenerate noncoplanar phase of the classical bilinear-biquadratic Heisenberg model on the triangular lattice with Monte Carlo simulations. For that purpose, we introduce an Ising pseudospin representation of the ground states, and we use a simple Metropolis algorithm with local updates, as well as a powerful cluster algorithm. At sizes that can be sampled with local updates, the presence of long-range order is surprisingly combined with an algebraic decay of correlations and the complete disordering of the chirality. It is only thanks to the investigation of unusually large systems (containing similar to 10(8) spins) with cluster updates that the true asymptotic regime can be reached and that the system can be proven to consist of equivalent (i.e., equally ordered) sublattices. These large-scale simulations also demonstrate that the scalar chirality exhibits long-range order at zero temperature, implying that the system has to undergo a finite-temperature phase transition. Finally, we show that the average distance in the order parameter space, which has the structure of an infinite Cayley tree, remains remarkably small between any pair of points, even in the limit when the real space distance between them tends to infinity.

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Thermodynamic properties of highly frustrated quantum spin ladders: Influence of many-particle bound states

Frédéric Mila, Bruce Normand

Quantum antiferromagnets have proven to be some of the cleanest realizations available for theoretical, numerical, and experimental studies of quantum fluctuation effects. At finite temperatures, however, the additional effects of thermal fluctuations in the restricted phase space of a low-dimensional system have received much less attention, particularly the situation in frustrated quantum magnets, where the excitations may be complex collective (bound or even fractionalized) modes. We investigate this problem by studying the thermodynamic properties of the frustrated two-leg S=12 spin ladder, with particular emphasis on the fully frustrated case. We present numerical results for the magnetic specific heat and susceptibility, obtained from exact diagonalization and quantum Monte Carlo studies, which we show can be rendered free of the sign problem even in a strongly frustrated system and which allow us to reach unprecedented sizes of L=200 ladder rungs. We find that frustration effects cause an unconventional evolution of the thermodynamic response across the full parameter regime of the model. However, close to the first-order transition they cause a highly anomalous reduction in temperature scales with no concomitant changes in the gap; the specific heat shows a very narrow peak at very low energies and the susceptibility rises abruptly at extremely low temperatures. Unusually, the two quantities have different gaps over an extended region of the parameter space. We demonstrate that these results reflect the presence of large numbers of multiparticle bound-state excitations, whose energies fall below the one-triplon gap in the transition region.

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