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arXiv:1112.5720 · Physical Review B

Frustrated spin chains in strong magnetic field: Dilute two-component Bose gas regime

Alexei K. Kolezhuk, Fabian Heidrich‐Meisner, Sebastian Greschner, T. Vekua

Published Feb 28, 2012• 44 citations
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Abstract

We study the ground state of frustrated spin-$S$ chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta $\ifmmode\pm\else\textpm\fi{}Q$, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around $\ifmmode\pm\else\textpm\fi{}Q$. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the help of this method, we are able to establish the magnetic phase diagram of frustrated chains close to saturation and study phase transitions between several nontrivial states, including a two-component Luttinger liquid, a vector chiral phase, and phases with bound magnons. We study those phase transitions numerically and find a good agreement with our analytical predictions.

DOI
10.1103/physrevb.85.064420

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We study the ground state of frustrated spin-SSS chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta \ifmmode±\else\textpm\fiQ\ifmmode\pm\else\textpm\fi{}Q\ifmmode±\else\textpm\fiQ, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around \ifmmode±\else\textpm\fiQ\ifmmode\pm\else\textpm\fi{}Q\ifmmode±\else\textpm\fiQ. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the help of this method, we are able to establish the magnetic phase diagram of frustrated chains close to saturation and study phase transitions between several nontrivial states, including a two-component Luttinger liquid, a vector chiral phase, and phases with bound magnons. We study those phase transitions numerically and find a good agreement with our analytical predictions.
We study the ground state phase diagram of a frustrated spin tube in a strong external magnetic field. This model can be viewed as two coupled zigzag spin chains, or as a two-leg spin ladder with frustrating next-nearest-neighbor couplings along the legs, and its study is motivated by the physics of such materials as sulfolane-Cu2Cl4{\mathrm{Cu}}_{2}{\mathrm{Cl}}_{4}Cu2​Cl4​ and BiCu2PO6{\mathrm{BiCu}}_{2}{\mathrm{PO}}_{6}BiCu2​PO6​. In magnetic fields right below the saturation, the system can be effectively represented as a dilute gas of two species of bosonic quasiparticles that correspond to magnons with inequivalent incommensurate momenta at two degenerate minima of the magnon dispersion. Using the method previously proposed and tested for frustrated spin chains, we calculate effective interactions in this two-component Bose gas. On this basis, we establish the phase diagram of nearly saturated frustrated spin tube, which is shown to include the two-component Luttinger liquid, two types of vector chiral phases, and phases whose physics is determined by the presence of bound magnons. We study the phase diagram of the model numerically by means of the density matrix renormalization group technique, and find a good agreement with our analytical predictions.
Quantum phase transition at the saturation field is studied for a class of frustrated quantum antiferromagnets. The considered models include (i) the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}$ frustrated square-lattice antiferromagnet with J2=12J1{J}_{2}=\frac{1}{2}{J}_{1}J2​=21​J1​ and (ii) the nearest-neighbor Heisenberg antiferromagnet on a face centered cubic lattice. In the fully saturated phase the magnon spectra for the two models have lines of degenerate minima. Transition into a partially magnetized state is treated via a mapping to a dilute gas of hard-core bosons and by complementary spin-wave calculations. Momentum dependence of the exact four-point boson vertex removes the degeneracy of the single-particle excitation spectra and selects the ordering wave vectors at $(\ensuremath{\pi},\ensuremath{\pi})$ and $(\ensuremath{\pi},0,0)$ for the two models. We predict a unique form for the magnetization curve $\ensuremath{\Delta}M=S\ensuremath{-}M\ensuremath{\simeq}{\ensuremath{\mu}}^{(d\ensuremath{-}1)/2}(\mathrm{log}\ensuremath{\mu}{)}^{(d\ensuremath{-}1)}$, where $\ensuremath{\mu}$ is a distance from the quantum critical point.
We investigate the ground-state phase diagram of frustrated mixed-spin (1, 1/2) chains with three-site four-spin interactions employing different approaches, such as cluster mean field theory, cluster variational method, and spin-wave theory. The interplay of next-nearest-neighbor and three-site interactions leads to a plethora of magnetic and nonmagnetic phases in the ground-state phase diagram. We show that aside from the ferromagnetic and Neel orders, the ground state possesses a magnetic phase in which magnon excitations are dispersionless. The emergence of flat-band magnons is a consequence of the inhomogeneity of our frustrated mixed-spin chains and does not occur in similar uniform spin chains. We also demonstrate that the presence of three-site interaction gives rise to various nonmagnetic phases, such as antiferroquadrupole order and quantum spin-liquid phase.
We show that spin-SSS chains with SU(2)-symmetric, ferromagnetic nearest-neighbor and frustrating antiferromagnetic next-nearest-neighbor exchange interactions exhibit metamagnetic behavior under the influence of an external magnetic field for small SSS, in the form of a first-order transition to the fully polarized state. The corresponding magnetization jump increases gradually starting from an SSS-dependent critical value of exchange couplings and takes a maximum in the vicinity of a ferromagnetic Lifshitz point. The metamagnetism results from resonances in the dilute magnon gas caused by an interplay between quantum fluctuations and frustration.
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 density matrix renormalization group and quantum Monte Carlo methods are used to describe coupled trimer chains in a magnetic field hhh. The Hamiltonian contains exchange terms involving the intratrimer coupling J1{J}_{1}J1​ (taken as the unit of energy) and the intertrimer coupling J2{J}_{2}J2​, plus the Zeeman interaction for a magnetic field hhh along the zzz direction. Results for the magnetization per trimer mmm are calculated in regimes of positive and negative values of the ratio J=J2/J1J={J}_{2}/{J}_{1}J=J2​/J1​, from which the rich field-induced ground state phase diagram hhh versus JJJ is derived, with the presence of a Luttinger liquid, the 1/3 plateau (m=1/2m=1/2m=1/2), and the one of fully polarized magnetization (m=3/2m=3/2m=3/2). Also, zero-field Lanczos calculation of the spin-wave dispersion from the 1/3 plateau for Sz=1{S}^{z}=1Sz=1 is shown at the previous regimes of JJJ values. In addition, we also report on the decay of correlation functions of trimers along open chains, as well as the average two-magnon distribution. The ground state is ferrimagnetic for $0<J\ensuremath{\le}1$, and is a singlet for $\ensuremath{-}1\ensuremath{\le}J<0$. In the singlet phase, the spin correlation functions along the legs present an antiferromagnetic power-law decay, similar to the spin-1/2 linear chain, thus suggesting that the ground state is made of three coupled antiferromagnetically oriented chains. In the singlet phase, the dimensionless thermal magnetic susceptibility per site normalized by 1/∣J∣1/|J|1/∣J∣ gets closer to $1/{\ensuremath{\pi}}^{2}$ as the temperature $T\ensuremath{\rightarrow}0$. For the ferrimagnetic phase, we fit the susceptibility to the experimental data for the compound Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ and estimate the model exchange couplings: J1=74.8K{J}_{1}=74.8\phantom{\rule{4pt}{0ex}}\text{K}J1​=74.8K and J=0.4J=0.4J=0.4. These values imply a range of energies for the magnon excitations that are in accord with the data from neutron scattering experiments on Pb3Cu3(PO4)4{\mathrm{Pb}}_{3}{\mathrm{Cu}}_{3}{({\mathrm{PO}}_{4})}_{4}Pb3​Cu3​(PO4​)4​ for two excitation modes. The 1/3 plateau closes only at 1/∣J∣=01/|J|=01/∣J∣=0 with J<0J<0J<0.