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Journal of Physics Conference Series

The frustrated ferromagnetic S = 1/2 Heisenberg chain in a magnetic field – How multipolar spin correlations emerge from magnetically ordered states

Andreas Martin Läuchli, Julien Sudan, Andreas Lüscher

Published Jan 1, 2009• 10 citations
Publisher

Abstract

We present the phase diagram of the frustrated ferromagnetic S = 1/2 Heisenberg J 1 - J 2 chain in a magnetic field, obtained by large scale exact diagonalizations and densitymatrix-renormalization-group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin multipolar Luttinger liquid phases up to hexadecupolar order are found. Starting from classical considerations, we point out that various multipolar correlations are imprinted in a magnetic state and that they can survive the onset of frustration and quantum fluctuations which destroy the conventional magnetic order. Our results also shed new light on previously discovered spin multipolar phases in two-dimensional S = 1/2 quantum magnets in a magnetic field.

DOI
10.1088/1742-6596/145/1/012057

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We present the phase diagram of the frustrated ferromagnetic S = 1/2 Heisenberg J 1 - J 2 chain in a magnetic field, obtained by large scale exact diagonalizations and densitymatrix-renormalization-group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin multipolar Luttinger liquid phases up to hexadecupolar order are found. Starting from classical considerations, we point out that various multipolar correlations are imprinted in a magnetic state and that they can survive the onset of frustration and quantum fluctuations which destroy the conventional magnetic order. Our results also shed new light on previously discovered spin multipolar phases in two-dimensional S = 1/2 quantum magnets in a magnetic field.
We present the phase diagram of the frustrated ferromagnetic S=12S=\frac{1}{2}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=12S=\frac{1}{2}S=21​ quantum magnets in a magnetic field.
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.
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The frustrated ferromagnetic spin-1∕21∕21∕2 Heisenberg chain is studied by means of a low-energy field theory as well as the density-matrix renormalization group and exact diagonalization methods. First, we study the ground-state phase diagram in a magnetic field and find an ``even-odd'' (EO) phase characterized by bound pairs of magnons in the region of two weakly coupled antiferromagnetic chains. A jump in the magnetization curves signals a first-order transition at the boundary of the EO phase, but otherwise the curves are smooth. Second, we discuss thermodynamic properties at zero field, where we confirm a double-peak structure in the specific heat for moderate frustrating next-nearest-neighbor interactions.
The frustrated isotropic J1−J2J_1-J_2J1​−J2​ model with ferromagnetic J1J_1J1​ and anti-ferromagnetic J2J_2J2​ 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, Z2Z_2Z2​ 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/J1J_2/J_1J2​/J1​.