We study the classical and quantum phase transitions of Sp(4) spin systems on three-dimensional stacked square and triangular lattices. We present general Ginzburg-Landau field theories for various types of Sp(4) spin orders with different ground-state manifolds such as CP(3), ${S}^{7}/{Z}_{2}$, Grassmann manifold ${G}_{2,5}$, ${G}_{2,6}$, and so on, based on which the nature of the classical phase transitions are studied, and a global phase diagram is presented. The classical phase transitions close to quantum phase transitions toward spin-liquid states are also discussed based on renormalization group flow. Our results can be directly applied to the simplest Sp(4) and SU(4) Heisenberg models which can be realized using spin-3/2 atoms and alkaline-earth atoms trapped in optical lattice.
We study the classical and quantum phase transitions of Sp(4) spin systems on three-dimensional stacked square and triangular lattices. We present general Ginzburg-Landau field theories for various types of Sp(4) spin orders with different ground-state manifolds such as CP(3), S7/Z2, Grassmann manifold G2,5, G2,6, and so on, based on which the nature of the classical phase transitions are studied, and a global phase diagram is presented. The classical phase transitions close to quantum phase transitions toward spin-liquid states are also discussed based on renormalization group flow. Our results can be directly applied to the simplest Sp(4) and SU(4) Heisenberg models which can be realized using spin-3/2 atoms and alkaline-earth atoms trapped in optical lattice.
We propose quantum phase transitions beyond the Landau's paradigm of Sp(4) spin Heisenberg models on the triangular and square lattices motivated by the exact $\text{Sp}(4)\ensuremath{\simeq}\text{SO}(5)$ symmetry of spin-3/2 fermionic cold atomic system with only s-wave scattering. On the triangular lattice, we study a phase transition between the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ spin ordered phase and a Z2 spin liquid phase; this phase transition is described by an O(8) sigma model in terms of fractionalized spinon fields, with significant anomalous scaling dimensions of spin order parameters. On the square lattice, we propose a deconfined critical point between the Neel order and the valence bond solid (VBS) order, which is described by the CP(3) model, and the monopole effect of the compact U(1) gauge field is expected to be suppressed at the critical point.
Spin and charge are two fundamental degrees of freedom in strongly correlated electron systems. In this thesis we study low-energy effective theory and phase transitions of spin and charge in a variety of strongly correlated systems. First, we study effective theory of magnetic phase transition in Sp(4) spin system and iron-based superconductors. Quantum phase transitions beyond Landau paradigm has been proposed in SU(2) spill model. We generalize this paradigm to Sp(4) model, which can be realized using spin-[special characters omitted] cold atoms on optical lattice. In iron-based superconductors, we study low-energy effective theory for magnetic and structural phase transitions, and present a global phase diagram of the two phase transitions. Second, we study spin and charge fluctuations on triangular lattice, and compare our results with experiments on organic Mott insulator κ-(ET) 2(CN)2. We show that the spin liquid state observed in experiments can be explained by Z2 spin liquid theory which contains spin-½ spinon and Z2 vison excitations. We also argue that near the Mott-insulator-to-metal transition there are fractionalized spinless charge excitations, which form exciton bound states near the transition. At last, we study spin and charge excitations in high-T c cuprates. We describe fluctuating two-dimensional metallic antiferromagnets by a gauge-theoretic description of an 'algebraic charge liquid' involving spinless fermions and a spin S = 1/2 complex scalar. We propose a phenomenological effective lattice Hamiltonian which describes the binding of these particles into gauge-neutral, electron-like excitations, and describe its implications for the electron spectral function across the entire Brillouin zone. We discuss connections of our results to photoemission experiments in the pseudogap regime of the cuprate superconductors.
We study the quantum and thermal phase transition phenomena of the SU(3) Heisenberg model on triangular lattice in the presence of magnetic fields. Performing a scaling analysis on large-size cluster mean-field calculations endowed with a density-matrix renormalization-group solver, we reveal the quantum phases selected by quantum fluctuations from the massively degenerate classical ground-state manifold. The magnetization process up to saturation reflects three different magnetic phases. The low- and high-field phases have strong nematic nature, and especially the latter is found only via a nontrivial reconstruction of symmetry generators from the standard spin and quadrupolar description. We also perform a semiclassical Monte Carlo simulation to show that thermal fluctuations prefer the same three phases as well. Moreover, we find that exotic topological phase transitions driven by the binding-unbinding of fractional (half-)vortices take place, due to the nematicity of the low- and high-field phases. Possible experimental realization with alkaline-earth-like cold atoms is also discussed.
We study a large-N generalization of J1-J2 Heisenberg model on square lattice -- an Sp(2N) spin model. The possible quantum spin liquid phases of the Sp(2N) model are studied using the SU(2) projective construction. We find several spin liquid states at least in large N limit, which include SU(2) π-flux state, SU(2) chiral spin state and Z2 spin liquid states. All those spin liquid states have non-trivial quantum orders. We show how projective symmetry group, which characterizes quantum order, protects the stability of even gapless spin liquids. We also study the continuous quantum phase transition from the SU(2) π-flux state to the SU(2) chiral spin liquid state, and from the SU(2) π-flux state to the Z2 spin liquid state. We show that those phase transitions are beyond the paradigm of Landau symmetry-breaking theory. The first phase transition, although a Z2 symmetry breaking transition, contains critical exponents that are different from those obtained from the Ginzburg-Landau theory of Ising universality class. The second transition does not even involve a change of symmetry and has no symmetry breaking order parameter.
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.
The study of various types of orders and phases of matter in magnetic systems is extremely popular theme in condensed matter physics. Not only frequently applicable in real world, quantum magnetism provides a fruitful and at the same time frequently feasible framework to search for new phases of matter. In this work we study quantum and associated classical phase transitions of spin systems by combinations of numerical and analytical methods.In Chapter 1 we study quantum paramagnets that are a generalization of antiferromagnetic AKLT [2] construction for the spin group SU(N). We map the so called simplex solid state ansatz wavefunction into a partition function of the classical system on the same lattice using coherent state representation. Then we study phase transitions of that classical models via classical Monte Carlo methods to determine properties of the original quantum simplex solid state [3].In Chapter 2 we are interested in the O(2) model in (2+1)-dimensional system with the dilution, i.e. when some sites are removed from the system. This relativistic O(2) model originates from the description of a transition between superfluid and Mott insulator phases. We study critical properties of the transition using a recently invented [4] worm algorithm.In Chapter 3 we are studying large-N expansion for the symplectic spin group Sp(N). When the original SU(2) spin model proves to be too difficult to be solved, for example at low temperatures, one of the alternative ways is to consider a system based on a more general spin group, for example SU(N) or Sp(N). Results often remain relevant for the original SU(2) group. We are using the mean-field theory approach to find phase transitions associated with the cubic Sp(N) system at large N.Another fundamental question of interest is how different systems behave when they are periodically driven by some external field. Such systems are called Floquet systems, and we will study them in Chapter 4. We will consider interacting and non-interacting systems, that might have a non-conventional type of ordering, topological order.