Spin supersolid in an anisotropic spin-one Heisenberg chain

Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2

Supersolid, an exotic quantum state of matter that consists of particles forming an incompressible solid structure while simultaneously showing superfluidity of zero viscosity1, is one of the long-standing pursuits in fundamental research2,3. Although the initial report of 4He supersolid turned out to be an artefact4, this intriguing quantum matter has inspired enthusiastic investigations into ultracold quantum gases5-8. Nevertheless, the realization of supersolidity in condensed matter remains elusive. Here we find evidence for a quantum magnetic analogue of supersolid-the spin supersolid-in the recently synthesized triangular-lattice antiferromagnet Na2BaCo(PO4)2 (ref. 9). Notably, a giant magnetocaloric effect related to the spin supersolidity is observed in the demagnetization cooling process, manifesting itself as two prominent valley-like regimes, with the lowest temperature attaining below 100 mK. Not only is there an experimentally determined series of critical fields but the demagnetization cooling profile also shows excellent agreement with the theoretical simulations with an easy-axis Heisenberg model. Neutron diffractions also successfully locate the proposed spin supersolid phases by revealing the coexistence of three-sublattice spin solid order and interlayer incommensurability indicative of the spin superfluidity. Thus, our results reveal a strong entropic effect of the spin supersolid phase in a frustrated quantum magnet and open up a viable and promising avenue for applications in sub-kelvin refrigeration, especially in the context of persistent concerns about helium shortages10,11.

Characteristic quantum phase in Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies

We investigate the ground-state phase diagram for a spin-one quantum Heisenberg antiferromagnetic chain with exchange and single-ion anisotropies in an external magnetic field by using the infinite time-evolving block decimation algorithm to compute the ground-state fidelity per lattice site. We detect all phase boundaries solely by computing the ground-state fidelity per lattice site, with the prescription that a phase transition point is attributed to a pinch point on the ground-state fidelity surface. Furthermore, the results indicate that a magnetization plateau corresponds to a fidelity plateau on the ground-state fidelity surface, thus offering an alternative route for investigating the magnetization processes of quantum many-body spin systems. We characterize all phases by using the local-order parameter, the spin correlation, the momentum distribution of the spin correlation structure factor, and mutual information as a function of the lattice distance. The commensurate and incommensurate phases are distinguished by the mutual information. In addition, the central charges at criticalities are identified by performing a finite-entanglement scaling analysis. The results show that all phase transitions between spin liquids and magnetization plateaus belong to the Pokrovsky-Talapov universality class.

Mixed-spin system with supersolid phases: magnetocaloric effect and thermal properties

Recently, it has been shown that two dimensional frustrated mixed-spin systems with anisotropic exchange interactions display supersolid phases in their ground state phase diagrams even in the absence of long-range interactions. In this paper, using cluster mean field theory, we investigate the effects of thermal fluctuations on the ground state phases of this kind of system and show that various thermal solids and thermal insulators emerge around the ground state solid and Mott insulating phases. We also study the thermodynamic properties and magnetocaloric effect of these systems and demonstrate that at low temperatures, a large cooling rate is seen in the vicinity of the solid-supersolid, solid-superfluid and Mott insulator-superfluid critical points, with the large accumulation of the entropy and the minimums of the isentropes. Our results show the sign change of the magnetocaloric parameter inside the solids and the Mott insulator, which is a characteristic of ordered phases.

Spin supersolid phase in coupled alternating spin chains

We study the ground state phase diagram of a two dimensional mixed-spin system of coupled alternating spin-1 and 1/2 chains with a stripe supersolid phase. Utilizing different analytical and numerical approaches such as mean field approximation, cluster mean field theory and linear spin wave theory, we demonstrate that our system displays a rich ground state phase diagram including novel stripe supersolid, solids with different fillings and super-counterfluid phases, in addition to a stripe solid with half filling, superfluid and Mott insulating phases. In order to find a minimal mixed-spin model for stripe supersolidity, in the second part of the paper we consider two kinds of mixed-spin system of coupled alternating spin-1 and 1/2 chains with (i) anisotropic nearest neighbor interactions, (ii) anisotropic hoppings and study their ground state phase diagrams. We demonstrate that, for the systems with uniform hoppings, the repulsive intra-chains interactions are necessary for stripe supersolidity. In this case the minimal two dimensional mixed-spin model is a system of spin-1 and spin-1/2 XXZ chains, interacting via Ising Hamiltonian. In the case of anisotropic hoppings, a system of coupled Ising chains is the minimal model.

Quenching the haldane gap in spin-1 Heisenberg antiferromagnets

We consider a quasi-one-dimensional system of spin-1 Heisenberg antiferromagnetic chains in two-dimensional and three-dimensional hypercubic lattices with interchain coupling J and uniaxial single-ion anisotropy D. Using large-scale numerical simulations, we map out the J-D phase diagram and investigate the low-lying excitations of the Haldane phase in the J≪1 limit. We also provide direct evidence that the Haldane phase remains a nontrivial symmetry-protected topological state for small but finite J.

Competing supersolid and Haldane insulator phases in the extended one-dimensional bosonic Hubbard model

The Haldane insulator is a gapped phase characterized by an exotic nonlocal order parameter. The parameter regimes at which it might exist, and how it competes with alternate types of order, such as supersolid order, are still incompletely understood. Using the stochastic Green function quantum Monte Carlo algorithm and density matrix renormalization group, we study numerically the ground state phase diagram of the one-dimensional bosonic Hubbard model with contact and near neighbor repulsive interactions. We show that, depending on the ratio of the near neighbor to contact interactions, this model exhibits charge density waves, superfluid, supersolid, and the recently identified Haldane insulating phases. We show that the Haldane insulating phase exists only at the tip of the unit-filling charge density wave lobe and that there is a stable supersolid phase over a very wide range of parameters.

Columnar antiferromagnetic order and spin supersolid phase on the extended Shastry-Sutherland lattice

We use large scale quantum Monte Carlo simulations to study an extended version of the canonical Shastry-Sutherland model--including additional interactions and exchange anisotropy--over a wide range of interaction parameters and an applied magnetic field. The model is appropriate for describing the low energy properties of some members of the rare earth tetraborides. Working in the limit of large Ising-like exchange anisotropy, we demonstrate the stabilization of columnar antiferromagnetic order in the ground state at zero field and an extended magnetization plateau at 1/2 the saturation magnetization in the presence of an applied longitudinal magnetic field--qualitatively similar to experimentally observed low-temperature phases in ErB(4). Our results show that for an optimal range of exchange parameters, a spin supersolid ground state is realized over a finite range of an applied field between the columnar antiferromagnetic phase and the magnetization plateau. The full momentum dependence of the longitudinal and transverse components of the static structure factor is calculated in the spin supersolid phase to demonstrate the simultaneous existence of diagonal and off-diagonal long-range order. Our results provide crucial guidance in designing further experiments to search for the interesting spin supersolid phase in ErB(4).

Multicritical points in the three-dimensional XXZ antiferromagnet with single-ion anisotropy

The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy, the XXZ model, and competing planar single-ion anisotropy in a magnetic field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. The biconical (supersolid) phase, bordering the antiferromagnetic and spin-flop phases, is found to become thermally unstable well below the onset of the disordered, paramagnetic phase, leading to interesting multicritical points.

Condensation of anyons in frustrated quantum magnets

We derive the exact ground space of a family of spin-1/2 Heisenberg chains with uniaxial exchange anisotropy (XXZ) and interactions between nearest and next-nearest-neighbor spins. The Hamiltonian family, H(eff)(Q), is parametrized by a single variable Q. By using a generalized Jordan-Wigner transformation that maps spins into anyons, we show that the exact ground states of H(eff)(Q) correspond to a condensation of anyons with a statistical phase φ=-4Q. We also provide matrix-product state representations of some ground states that allow for the efficient computation of spin-spin correlation functions.

Anisotropic cascade of field-induced phase transitions in the frustrated spin-ladder system BiCu2PO6

BiCu(2)PO(6) is a frustrated two-leg spin-ladder compound with a spin gap that can be closed with a magnetic field of approximately 20 T. This quantum phase transition and its related phase diagram as a function of magnetic field and temperature (H, T) are investigated up to 60 T by means of specific heat, magnetocaloric effect, magnetization, and magnetostriction measurements. In contrast to other gapped quantum magnets, BiCu(2)PO(6) undergoes a series of unexpected first- and second-order phase transitions when an external magnetic field is applied along the crystallographic c axis. The application of a magnetic field along the b axis induces two second-order phase transitions. We propose that the anisotropy and complex phase diagram result from the interplay between strong geometrical frustration and spin-orbit interaction necessary for the description of this fascinating magnetic system.

Bose-Einstein condensation of semi-hard bosons in the S = 1 dimerized organic compound F(2)PNNNO

An analysis of the energy spectrum and magnetization curve of the two-dimensional organic antiferromagnet F(2)PNNNO with a spin-one dimerized structure shows that the behavior of the compound in an external magnetic field can be explained within a lattice boson model with an extended Pauli exclusion principle, i.e. no more than two bosons per dimer. The unusual magnetization curve observed experimentally in the compound reflects a sequence of phase transitions intrinsic for a lattice boson system with strong on-site and inter-site repulsions due to a tuning of magnon density by the applied magnetic field.