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arXiv:1505.05751 · Physical Review B

Schwinger boson mean field perspective on emergent spins in diluted Heisenberg antiferromagnets

Shivam Ghosh, Hitesh J. Changlani, Christopher L. Henley

Published Aug 3, 2015• 7 citations
arXivHTMLPDF

Abstract

The authors study the diluted spin-half Heisenberg model near the percolation threshold using Schwinger boson mean field theory (SBMFT). They show how SBMFT predicts the emergence of effective local spin degrees of freedom. They demonstrate that SBMFT applied to dilute spin systems is qualitatively accurate by also performing DMRG computations.

DOI
10.1103/physrevb.92.064401

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The authors study the diluted spin-half Heisenberg model near the percolation threshold using Schwinger boson mean field theory (SBMFT). They show how SBMFT predicts the emergence of effective local spin degrees of freedom. They demonstrate that SBMFT applied to dilute spin systems is qualitatively accurate by also performing DMRG computations.
We find that the Schwinger boson mean field theory (SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1) spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2) There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3) There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-12TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.
Frustrated quantum magnets have received a lot of attention in the past decades for they are expected to host exotic magnetic states such as quantum spin liquids exhibiting fractionalized excitations and topological properties. One way to study these spin liquid phases is to perform a parton construction of the quantum Heisenberg Hamiltonian. This mean-field method has the valuable advantage of treating magnetically ordered states and spin-liquid states on an equal footing. In this thesis, we have employed such a method based on the Schwinger boson mean-field theory (SBMFT) to study two magnetically frustrated systems. After a brief introduction of the core concepts behind frustrated magnetic systems in chapter 1 we will introduce the Schwinger boson theory and the associated numerical tools in chapter 2. In chapter 3, we will present the full phase diagram of the J1-J2 Heisenberg model on the square-kagome lattice with a particurlarly interesting ground state in the form of a topological nematic spin liquid. We will then make connections with a recently synthesized compound exhibiting perfect square-kagome geometry. In the final chapter of this manuscript, we will turn to the J1-J2-J3 Heisenberg model on the kagome lattice in the case where J2=J3=J. Once again, a full phase diagram is obtained thanks to our SBMFT self-consistent procedure. It is composed of three distinct ground states: a chiral spin liquid for J<1/3, a chiral long-range order for J>1/2 and a symmetric spin liquid in between. Finally, we will make connections with previous quantum and classical works, especially by discussing the presence of half-moon patterns in the static structure factor of an excited state of the model for J>1/2. In conclusion, we have revealed both rich and complex phase diagrams presenting various exotic spin-liquid states on the two frustrated systems studied in this manuscript.
The Schwinger-boson mean-field theory is applied to the quantum ferrimagnetic Heisenberg chain. There is a ferrimagnetic long-range order in the ground state. We observe two branches of the low-lying excitation and calculate the spin reduction, the gap of the antiferromagnetic branch, and the spin fluctuation at T=0K.T=0 \mathrm{K}.T=0K. These results agree with the established numerical results quite well. At finite temperatures, the long-range order is destroyed because of the disappearance of the Bose condensation. The thermodynamic observables, such as the free energy, magnetic susceptibility, specific heat, and the spin correlation at T>0K,T>0 \mathrm{K},T>0K, are calculated. The $T{\ensuremath{\chi}}_{\mathrm{uni}}$ has a minimum at intermediate temperatures and the spin-correlation length behaves as ${T}^{\ensuremath{-}1}$ at low temperatures. These qualitatively agree with the numerical results and the difference is small at low temperatures.
The Schwinger-boson mean-field theory (SBMFT) and the linearized tensor renormalization group (LTRG) methods are complementarily applied to explore the thermodynamics of the quantum ferromagnetic mixed spin (S, σ) chains. It is found that the system has double excitations, i.e. a gapless and a gapped excitation; the low-lying spectrum can be approximated by ωk∼Sσ2(S+σ)Jk2 with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization mtotz=N(S+σ). At low temperature, the spin correlation length is inversely proportional to temperature (T), the susceptibility behaviors as χ=a1∗1T2+a2∗1T, and the specific heat has the form of C=c1∗T−c2∗T+c3∗T32, with ai (i = 1, 2) and ci (i = 1, 2, 3) the temperature independent constants. The SBMFT results are shown to be in qualitatively agreement with those by the LTRG numerical calculations for S = 1 and σ = 1/2. A comparison of the LTRG results with the experimental data of the model material MnIINiII(NO2)4(en)2(en = ethylenediamine), is made, in which the coupling parameters of the compound are obtained. This study provides useful information for deeply understanding the physical properties of quantum ferromagnetic mixed spin chain materials.
We present the first exact results for the T=0 dynamical structure factor of finite-sized two-dimensional square-lattice spin-(1/2 antiferromagnetic Heisenberg systems with up to 16 spins. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra at all allowed wave vectors and for all system sizes studied. We also determine the mean-field value for the T=0 staggered magnetization, mMF=0.306{m}^{\mathrm{MF}=0.306}mMF=0.306, to be in excellent agreement with published Monte Carlo results.
Motivated by recent experimental and numerical evidence of deconfined quantum critical points and quantum spin liquid states in the spin-1/21/21/2 Heisenberg model on the Shastry-Sutherland lattice, we studied possible symmetric spin liquid states and their proximate ordered states under Schwinger boson formalism. We found a symmetric gapped Z2{Z}_{2}Z2​ spin liquid state for intermediate model parameter 0.66<J1/J2<0.710.66<{J}_{1}/{J}_{2}<0.710.66<J1​/J2​<0.71 under the mean-field approximation. The Schwinger boson mean-field picture is partially supported by exact-diagonalization and self-consistent spin wave theory results.