Studies of competing orders in one-dimensional magnetic chains have attracted considerable attention in recent years, as the presence of distant-neighbor Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and noncollinear interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the noncollinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.
Studies of competing orders in one-dimensional magnetic chains have attracted considerable attention in recent years, as the presence of distant-neighbor Heisenberg interactions is found to allow interesting quantum phase transitions. We investigate here the role of spin-orbit effects by considering spin-1/2 chains in the presence of both collinear and noncollinear interactions. By employing exact diagonalization and density matrix renormalization group calculations we investigate the rich phase diagram of this system. We find transitions from collinear to transverse magnetic correlated order as the strength of the noncollinear coupling increases, accompanied by a jump in the vector spin chirality order parameter of the system. This shows that tuning interactions allows control of the onset of sizable vector spin chirality in a system, which may be used to transmit information down the chain. We investigate the characteristic structure of the distinct phases and explore their possible physical implementation in different materials systems.
We obtain the ground-state phase diagram of two spin chains consisting in a set of two-level systems asymmetrically coupled to an XX chain through a chiral interaction. The interaction is parametrized by its magnitude and an angle defined by the relative orientation of the spins in different chains. From the entanglement spectrum, we identify the critical lines separating distinct magnetically ordered phases, with the interaction angle able to shift or fully suppress the transition. By increasing the coupling strength, the system is driven through a quantum phase transition, leading to the formation of two types of in-plane antiferromagnetic stripes. The interaction strength sets stripe formation, while the angle controls the spins' orientations. The chiral interaction also induces a nontrivial finite vector spin chirality with opposite orientation on the chains. We show that the vector spin chirality emerges smoothly from the decoupled limit and occurs for angles different from zero and π / 2 , where collinear order is favored instead.
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.
We study the one-dimensional spin-1/2 Heisenberg chain with competing ferromagnetic nearest-neighbor J1 and antiferromagnetic next-nearest-neighbor J2 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 J1/J2. 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 antiferronematic 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 antiferromultipolar 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., LiCuVO4) are discussed.
Ordering of frustrated S=1/2 and 1 XY and Heisenberg spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied by exact diagonalization and density-matrix renormalization-group methods. It is found that the S=1 XY chain exhibits both gapless and gapped `chiral' phases characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κi=SixSi+1y−SiySi+1x, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor in the Heisenberg chains.
The spin-3/2 chain is a versatile prototypical platform for the study of competition between different kinds of magnetic orders, with the objective of obtaining a deeper understanding of the corresponding quantum phase transitions. In this work, we investigate the spin-3/2 chain with nearest-neighbor J1, next-nearest-neighbor J2, and uniaxial single-ion anisotropy D terms in the absence of a magnetic field. For positive values of J2/J1 and D/J1, we find seven different phases in a rich phase diagram. Without frustration J2=0, a gapless Luttinger liquid phase remains stable for all D>0. As J2 increases, we observe three phases with distinct dimerized valence bond orders, which show an intricate competition with vector chiral order and incommensurate correlations. For large J2, regions of phase coexistence between the dimerized and vector chiral orders emerge. We present large-scale numerical data for the determination of transition lines, order parameters, and the nature of the phase transitions.
We calculate the vector spin chirality for S=1/2 zigzag spin chains having U(1) symmetry, using the density matrix renormalization group combined with unitary transformation. We then demonstrate the occurrence of the chiral order for the zigzag XY chain and discuss the associated phase transition. The results are consistent with the analysis based on the bosonization and the long distance behaviour of the chirality correlation function. For the S=1/2 zigzag Heisenberg chain in a magnetic field, we also verify the chiral order that is predicted by the effective field theory and the chirality correlation function, and then determine its magnetic phase diagram.