The ground state phase diagram of a general isotropic spin-3/2 system with nearest-neighbor exchange is shown to contain unconventionally ordered spin nematic and antinematic states, as well as usual ferro- and antiferromagnetic phases. The two nematic phases have spontaneously broken rotational symmetry characterized by the long-range order of the nematic director u, as well as the broken time-reversal symmetry described by the pseudospin vector σ. Nematic phase differs from antinematic one by the type of ordering in σ vectors (uniform versus staggered). The ferromagnet-nematic and antiferromagnet-antinematic phase boundaries exhibit enhanced Sp(4) symmetry and correspond to the recently studied effective theory for spin-3/2 cold gases. We discuss optical properties and topological defects in the nematic phases.
The ground state phase diagram of a general isotropic spin-3/2 system with nearest-neighbor exchange is shown to contain unconventionally ordered spin nematic and antinematic states, as well as usual ferro- and antiferromagnetic phases. The two nematic phases have spontaneously broken rotational symmetry characterized by the long-range order of the nematic director u, as well as the broken time-reversal symmetry described by the pseudospin vector σ. Nematic phase differs from antinematic one by the type of ordering in σ vectors (uniform versus staggered). The ferromagnet-nematic and antiferromagnet-antinematic phase boundaries exhibit enhanced Sp(4) symmetry and correspond to the recently studied effective theory for spin-3/2 cold gases. We discuss optical properties and topological defects in the nematic phases.
Large spin systems can exhibit unconventional types of magnetic ordering, different from the ferromagnetic or N\'eel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invariance, and their magnetic order parameter is characterized by a second-rank tensor with the symmetry of an ellipsoid. Here we show direct experimental evidence of spin-nematic ordering in a spin 1 Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions. In a mean field description this order is enforced by locking the relative phase between spin components. We reveal this mechanism by studying the spin noise after a spin rotation, which is shown to contain information hidden when looking only at averages. The method should be applicable to high-spin systems in order to reveal complex magnetic phases.
The phase diagram of the XXZ spin-1 quantum magnet on the kagome lattice is studied for all cases where the z-component nearest-neighbor spin interaction Jz is antiferromagnetic. Besides Jz and the nearest-neighbor in-plane spin interaction Jxy, the system is also parametrized by an on-site anisotropic term D(Sz)2. In the zero magnetic field case, the six previously introduced phases, found using various methods, are the nondegenerate gapped photon phase, which breaks no space symmetry or spin symmetry; the sixfold degenerate phase with plaquette order, which breaks both time-reversal symmetry and translational symmetry; the ``superfluid'' (ferromagnetic) phase with an in-plane global U(1) symmetry broken when Jxy<0; the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ order when Jxy>0; the nematic phase when D<0 and large; and a phase with resonating dimers on each hexagon. We obtain all of these phases and partial information about their quantum phase transitions in a single framework by studying condensation of defects in the sixfold plaquette phases. The transition between nematic phase and the sixfold degenerate plaquette phase is potentially an unconventional second-order critical point. In the case of a nonzero magnetic field along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$, another ordered phase with translation symmetry broken is opened up in the nematic phase. Due to the breaking of time-reversal symmetry by the field, a supersolid phase emerges between the sixfold plaquette order and the superfluid phase. This phase diagram might be accessible in nickel compounds, organic compound $m\text{\ensuremath{-}}\mathrm{MPYNN}∙\mathrm{B}{\mathrm{F}}_{4}$, or optical lattices of atoms with three degenerate states on every site.
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J_1 and antiferromagnetic next-nearest-neighbor J_2 exchange couplings in the presence of magnetic field. We use both numerical approaches (the density matrix renormalization group method and exact diagonalization) and effective field-theory approach, and obtain the ground-state phase diagram for wide parameter range of the coupling ratio J_1/J_2. The phase diagram is rich and has a variety of phases, including the vector chiral phase, the nematic phase, and other multipolar phases. In the vector chiral phase, which appears in relatively weak magnetic field, the ground state exhibits long-range order (LRO) of vector chirality which spontaneously breaks a parity symmetry. The nematic phase shows a quasi-LRO of antiferro-nematic spin correlation, and arises as a result of formation of two-magnon bound states in high magnetic fields. Similarly, the higher multipolar phases, such as triatic (p=3) and quartic (p=4) phases, are formed through binding of p magnons near the saturation fields, showing quasi-LRO of antiferro-multipolar spin correlations. The multipolar phases cross over to spin density wave phases as the magnetic field is decreased, before encountering a phase transition to the vector chiral phase at a lower field. The implications of our results to quasi-one-dimensional frustrated magnets (e.g., LiCuVO_4) are discussed.
Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-1/2 Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons Jh and ferromagnetic couplings on triangles Jt and dimer Jd bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around Jd=Jt=0, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c120∘ antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.
The Heisenberg chain with alternating site spins ( S ,σ) = (1, 1/2) defines a realistic prototype model admitting extra isotropic three-body exchange terms which drive the chain into exotic quantum phases. In this paper, we focus on the non-magnetic part of the phase diagram. Based on numerical density-matrix renormalization group and exact-diagonalization calculations, we demonstrate that the nearest-neighbor three-body interaction stabilizes (i) a critical spin liquid phase described by two Gaussian conformal theories as well as (ii) a critical nematic-like phase characterized by dominant quadrupolar S-spin fluctuations. The emergence of these phases reflects some specific features of the three-body terms such as the promotion of local collinear spin configurations and the enhanced tendency towards nearest- neighbor clustering of the spins.
In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.