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.
A frustrated spin-
1/2 XXZ chain model comprising a ferromagnetic nearest-neighbor coupling with the bond alternation, ${J}_{1}(1\ifmmode\pm\else\textpm\fi{}\ensuremath{\delta})<0$, and an antiferromagnetic second-neighbor exchange coupling
J2>0 is studied at zero and weak magnetic fields by means of density-matrix renormalization-group calculations of order parameters, correlation functions, and the entanglement entropy, as well as an Abelian bosonization analysis. At zero magnetic field, the bond alternation $\ensuremath{\delta}>0$ suppresses the gapless phase characterized by a vector-chiral (VC) long-range order (LRO) and a quasi-LRO of an incommensurate spin spiral, whereas this phase occupies a large region in the space of
J1/J2 and the easy-plane exchange anisotropy for $\ensuremath{\delta}=0$ [S. Furukawa et al., Phys. Rev. Lett. 105, 257205 (2010)]. Then, four gapped phases are found to appear as the exchange anisotropy varies from the SU(2)-symmetric case to the U(1)-symmetric case: the Haldane dimer (D
+) phase with the same sign of the
x,y- and
z-component dimer order parameters, two VC dimer (VCD
+/VCD${}_{\ensuremath{-}}$) phases with the sign of the
z-component dimer order parameter being unaltered/reversed, and the even-parity dimer (D${}_{\ensuremath{-}}$) phase. At small magnetic fields, a field-induced ring-exchange interaction, which is proportional to a staggered scalar chirality and a magnetic flux penetrating the associated triangle, drives a transition from the D${}_{\ensuremath{-}}$ phase into a VC-Neel-dimer (VCND) phase, but not from the D
+ phase. This VCND phase is stable up to the large magnetic field at which the Zeeman term closes the spin gap. A possible relevance to Rb
2Cu
2Mo
3O
12 is discussed.
We quantify the stability of the formation of multipolar states against always present interchain couplings in quasi-one-dimensional spin-
21 chain systems with a frustrating in-chain ${J}_{1}\ensuremath{-}{J}_{2}$ exchange, including parameter regimes that are of direct relevance to many edge-shared cuprate spin-chain compounds. Three representative types of antiferromagnetic interchain coupling and the presence of uniaxial exchange anisotropy are considered. The magnetic phase diagrams are determined by density matrix renormalization group calculations and completed by very accurate analytic and numerical results for the nematic and the dipolar phases employing the hard-core-boson approach. We establish that a sizable interchain coupling has a strong influence on the possible instability of multipolar phases at high magnetic fields in the vicinity of the saturation fields in favor of the usual dipolar one-magnon phase. Moreover, skew interchain couplings strongly affect the pitch of spiral states. Our theoretical results bring to the fore candidate materials close to quantum nematic/triatic ordering.
The frustrated isotropic
J1−J2 model with ferromagnetic
J1 and anti-ferromagnetic
J2 interactions in presence of an axial magnetic field shows many exotic phases, such as vector chiral and multipolar phases. The existing studies of the phase boundaries of these systems are based on the indirect evidences such as correlation functions {\it etc}. In this paper, the phase boundaries of these exotic phases are calculated based on order parameters and jumps in the magnetization. In the strong magnetic field,
Z2 symmetry is broken, therefore, order parameter of the vector chiral phase is calculated using the broken symmetry states. Our results obtained using the modified density matrix renormalization group and exact diagonalization methods, suggest that the vector chiral phase exist only in narrow range of parameter space
J2/J1.
The ordering of the frustrated S = 1/2 XY spin chain with the competing nearest- and next-nearest-neighbor anti-ferromagnetic couplings, J1 and J2, is studied by using the density-matrix renormalization-group method. It is found that besides the well-known spin-fluid and dimer phases the chain exhibits a gapless "chiral" phase characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κl =SxlSyl+1 Syl Sxl+1, whereas the spin correlation decays algebraically. The dimer phase is realized for 0.33 [Formula: see text] j = J2/J1 [Formula: see text] 1.26 while the chiral phase is realized for j [Formula: see text] 1.26. PACS No.: 75.25
We present the phase diagram of the frustrated ferromagnetic
S=21 Heisenberg ${J}_{1}\ensuremath{-}{J}_{2}$ chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states toward spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in two-dimensional
S=21 quantum magnets in a magnetic field.