Chiral ordered phases in a frustrated S=1 chain with uniaxial single-ion-type anisotropy

The ground-state phase transitions of a frustrated S=1 Heisenberg chain with the uniaxial single-ion-type anisotropy and the frustrating next-nearest-neighbor coupling are studied. For the system, it has been shown that there are gapless and gapped chiral phases in which the chirality \kappa_l = S^x_l S^y_{l+1} - S^y_l S^x_{l+1} exhibits a finite long-range order (LRO) and the spin correlation decays either algebraically or exponentially. In this study, the transitions between the Haldane and chiral phase and between the large-D (LD) and chiral phase are investigated using the infinite-system density-matrix renormalization group method. It is found that there exist two types of gapped chiral phases, "chiral Haldane" and "chiral LD" phases, in which the string LRO coexists with the chiral LRO and the string correlation decays exponentially, respectively.Comment: 4 pages, 2 figures, submitted to Canadian Journal of Physics for the Proceedings of the Higly Frustrated Magnetism 2000 Conference, Waterloo, Ontario, Canada, June 11-15, 200

Sine-square deformation of free fermion systems in one and higher dimensions

We study free fermion systems with the sine-square deformation (SSD), in which the energy scale of local Hamiltonians is modified according to the scaling function f(x)=sin^2[\pi(x-1/2)/L], where x is the position of the local Hamiltonian and L is the length of the system in the x direction. It has been revealed that when applied to one-dimensional critical systems the SSD realizes the translationally-invariant ground state which is the same as that of the uniform periodic system. In this paper, we propose a simple theory to explain how the SSD maintains the translational invariance in the ground-state wave function. In particular, for a certain one-dimensional system with SSD, it is shown that the ground state is exactly identical with the Fermi sea of the uniform periodic chain. We also apply the SSD to two-dimensional systems and show that the SSD is able to suppress the boundary modulations from the open edges extremely well, demonstrating that the SSD works in any dimensions and in any directions.Comment: 9 pages, 6 figures. v2: accepted versio

Phase diagram of the frustrated spin ladder

We re-visit the phase diagram of the frustrated spin-1/2 ladder with two competing inter-chain antiferromagnetic exchanges, rung coupling J_\perp and diagonal coupling J_\times. We suggest, based on the accurate renormalization group analysis of the low-energy Hamiltonian of the ladder, that marginal inter-chain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line J_\perp = 2J_\times. Following this insight we then suggest that changing these competing inter-chain exchanges from the previously considered antiferromagnetic to the ferromagnetic ones eliminates the issue of the marginal interactions altogether and dramatically expands the region of stability of the columnar dimer phase. This analytical prediction is convincingly confirmed by the numerical density matrix renormalization group and exact diagonalization calculations as well as by the perturbative calculation in the strong rung-coupling limit. The phase diagram for ferromagnetic J_\perp and J_\times is determined.Comment: 12 pages, 12 figures, 1 Table. v2: version to appear in Phys. Rev.

Quantum phase transitions beyond Landau-Ginzburg theory in one-dimensional space revisited

The phase diagram of the quantum spin-1/2 antiferromagnetic $J^{\,}_{1}$-$J^{\,}_{2}$ XXZ chain was obtained by Haldane using bosonization techniques. It supports three distinct phases for $0\leq J^{\,}_{2}/J^{\,}_{1}<1/2$, i.e., a gapless algebraic spin liquid phase, a gapped long-range ordered Neel phase, and a gapped long-range ordered dimer phase. Even though the Neel and dimer phases are not related hierarchically by a pattern of symmetry breaking, it was shown that they meet along a line of quantum critical points with a U(1) symmetry and central charge $c=1$. Here, we extend the analysis made by Haldane on the quantum spin-1/2 antiferromagnetic $J^{\,}_{1}$-$J^{\,}_{2}$ XYZ chain using both bosonization and numerical techniques. We show that there are three Neel phases and the dimer phase that are separated from each other by six planes of phase boundaries realizing U(1) criticality when $0\leq J^{\,}_{2}/J^{\,}_{1}<1/2$. We also show that each long-range ordered phase harbors topological point defects (domain walls) that are dual to those across the phase boundary in that a defect in one ordered phase locally binds the other type of order around its core. By using the bosonization approach, we identify the critical theory that describes simultaneous proliferation of these dual point defects, and show that it supports an emergent U(1) symmetry that originates from the discrete symmetries of the XYZ model. To confirm this numerically, we perform DMRG calculation and show that the critical theory is characterized by the central charge $c=1$ with critical exponents that are consistent with those obtained from the bosonization approach. Furthermore, we generalize the field theoretic description of direct continuous phase transition to higher dimensions, especially in $d=3$, by using a non-linear sigma model (NLSM) with a topological term.Comment: 25 pages with 14 figure

Connecting distant ends of one-dimensional critical systems by a sine-square deformation

We study the one-dimensional quantum critical spin systems with the sine-square deformation, in which the energy scale in the Hamiltonian at the position $x$ is modified by the function f_x = \sin^2\left[{\pi}{L}(x-1/2)], where $L$ is the length of the system. By investigating the entanglement entropy, spin correlation functions, and wave-function overlap, we show that the sine-square deformation changes the topology of the geometrical connection of the ground state drastically; Although the system apparently has open edges, the sine-square deformation links those ends and realizes the periodic ground state at the level of wave function. Our results propose a new method to control the topology of quantum states by energy-scale deformation.Comment: 5 pages, 4 figures. v2: accepted versio

Spin-Nematic and Spin-Density-Wave Orders in Spatially Anisotropic Frustrated Magnets in a Magnetic Field

We develop a microscopic theory of finite-temperature spin-nematic orderings in three-dimensional spatially anisotropic magnets consisting of weakly-coupled frustrated spin-1/2 chains with nearest-neighbor and next-nearest-neighbor couplings in a magnetic field. Combining a field theoretical technique with density-matrix renormalization group results, we complete finite-temperature phase diagrams in a wide magnetic-field range that possess spin-bond-nematic and incommensurate spin-density-wave ordered phases. The effects of a four-spin interaction are also studied. The relevance of our results to quasi-one-dimensional edge-shared cuprate magnets such as LiCuVO4 is discussed.Comment: 5 pages (2 column version), 4 figures, Revtex, published versio