We study thermodynamic properties as well as the dynamical spin and quadrupolar structure factors of the O(3)-symmetric spin-1 Heisenberg model with bilinear-biquadratic exchange interactions on the triangular lattice. Based on a sign-problem-free quantum Monte Carlo approach, we access both the ferromagnetic and the ferroquadrupolar ordered, spin nematic phase as well as the SU(3)-symmetric point which separates these phases. Signatures of Goldstone soft-modes in the dynamical spin and the quadrupolar structure factors are identified, and the properties of the low-energy excitations are compared to the thermodynamic behavior observed at finite temperatures as well as to Schwinger-boson flavor-wave theory.
We examine the entanglement properties of the spin-half Heisenberg model on the two-dimensional square-lattice bilayer based on quantum Monte Carlo calculations of the second Renyi entanglement entropy. In particular, we extract the dominant area-law contribution to the bipartite entanglement entropy that shows a non-monotonous behavior upon increasing the inter-layer exchange interaction: a local maximum in the area-law coefficient is located at the quantum critical point separating the antiferromagnetically ordered region from the disordered dimer-singlet regime. Furthermore, we consider subleading logarithmic corrections to the Renyi entanglement entropy scaling. Employing different subregion shapes, we isolate the logarithmic corner term from the logarithmic contribution due to Goldstone modes that is found to be enhanced in the limit of decoupled layers. At the quantum critical point, we estimate a contribution of $0.016(1)$ due to each $90^{circ}$ corner. This corner term at the SU(2) quantum critical point deviates from the Gaussian theory value, while it compares well with recent numerical linked cluster calculations on the bilayer model.
It is argued that the subtle crossover from decoherence-dominated classical magnetism to fluctuation-dominated quantum magnetism is experimentally accessible in graphene nanoribbons. We show that the width of a nanoribbon determines whether the edge magnetism is on the classical side, on the quantum side, or in between. In the classical regime, decoherence is dominant and leads to static spin polarizations at the ribbon edges, which are well described by mean-field theories. The quantum Zeno effect is identified as the basic mechanism which is responsible for the spin polarization and thereby enables the application of graphene in spintronics. On the quantum side, however, the spin polarization is destroyed by dynamical processes. The great tunability of graphene magnetism thus offers a viable route for the study of the quantum-classical crossover.
We analyze the thermodynamics of the atomic and (nematic) pair superfluids appearing in the attractive two-dimensional Bose-Hubbard model with a three-body hard-core constraint that has been derived as an effective model for cold atoms subject to strong three-body losses in optical lattices. We show that the thermal disintegration of the pair superfluidity is governed by the proliferation of fractional half-vortices leading to a Berezinskii-Kosterlitz-Thousless transition with unusual jump in the helicity modulus. In addition to the (conventional) Berezinskii-Kosterlitz-Thousless transition out of the atomic superfluid, we furthermore identify a direct thermal phase transition separating the pair and the atomic superfluid phases, and show that this transition is continuous with critical scaling exponents consistent with those of the two-dimensional Ising universality class. We exhibit a direct connection between the partial loss of quasi long-range order at the Ising transition between the two superfluids and the parity selection in the atomic winding number fluctuations that distinguish the atomic from the pair superfluid.
We analyze the nucleation of supersolid order out of the superfluid ground state of bosons on the triangular lattice. While the stability of supersolidity against phase separation in this system is by now well established for nearest-neighbor and long-range dipolar interactions, relevant for two-dimensional arrays of ultra-cold polar molecules, here we address directly the nature of the superfluid-to-supersolid transition. Based on symmetry arguments and quantum Monte Carlo simulations, we conclude that this quantum phase transition is driven first-order beyond the line of particle-hole symmetry. Along this line, the transition is continuous and its scaling behavior consistent with the three-dimensional (3D) XY universality class. We relate this finding to a 3D Z6 clock model description of the enlarged symmetry of the solid order parameter field. In the generic case however, the symmetry reduces to that of a 3D Z3 clock model, which reflects the first-order nature of the generic superfluid-to-supersolid quantum phase transition on the triangular lattice.
We examine the equilibrium properties of lattice bosons with attractive on-site interactions in the presence of a three-body hard-core constraint that stabilizes the system against collapse and gives rise to a dimer superfluid phase formed by virtual hopping processes of boson pairs. Employing quantum Monte Carlo simulations, the ground state phase diagram of this system on the square lattice is analyzed. In particular, we study the quantum phase transition between the atomic and dimer superfluid regime and analyze the nature of the superfluid-insulator transitions. Evidence is provided for the existence of a tricritical point along the saturation transition line, where the transition changes from being first-order to a continuous transition of the dilute bose gas of holes. The Berzinskii-Kosterlitz-Thouless transition from the dimer superfluid to the normal fluid is found to be consistent with an anomalous stiffness jump, as expected from the unbinding of half-vortices.
We explore the phase diagram of ultracold bosonic polar molecules confined to a planar optical lattice of triangular geometry. External static electric and microwave fields can be employed to tune the effective interactions between the polar molecules into a regime of extended two- and three-body repulsions of comparable strength, leading to a rich quantum phase diagram. In addition to various solid phases, an extended supersolid phase is found to persist deep into the three-body dominated regime. While three-body interactions break particle-hole symmetry explicitly, a characteristic supersolid-supersolid quantum phase transition is observed, which indicates the restoration of particle-hole symmetry at half-filling. We revisit the spatial structure of the supersolid at this filling, regarding the existence of a further supersolid phase with three inequivalent sublattices, and provide evidence that this state is excluded also at finite temperatures.
Using the adaptive time-dependent density matrix renormalization group, we study the time evolution of density correlations of interacting spinless fermions on a one-dimensional lattice after a sudden change in the interaction strength. Over a broad range of model parameters, the correlation function exhibits a characteristic light-cone-like time evolution representative of a ballistic transport of information. Such behavior is observed both when quenching an insulator into the metallic region and also when quenching within the insulating region. However, when a metallic state beyond the quantum critical point is quenched deep into the insulating regime, no indication for ballistic transport is observed. Instead, stable domain walls in the density correlations emerge during the time evolution, consistent with the predictions of the Kibble-Zurek mechanism.
