Schwinger Bosons Approaches to Quantum Antiferromagnetism (original) (raw)
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Physical Review B, 2018
We compute the zero temperature dynamical structure factor S(q, ω) of the triangular lattice Heisenberg model (TLHM) using a Schwinger boson approach that includes the Gaussian fluctuations (1/N corrections) of the saddle point solution. While the ground state of this model exhibits a well-known 120 • magnetic ordering, experimental observations have revealed a strong quantum character of the excitation spectrum. We conjecture that this phenomenon arises from the proximity of the ground state of the TLHM to the quantum melting point separating the magnetically ordered and spin liquid states. Within this scenario, magnons are described as collective modes (two spinonbound states) of a spinon condensate (Higgs phase) that spontaneously breaks the SU(2) symmetry of the TLHM. Crucial to our results is the proper account of this spontaneous symmetry breaking. The main qualitative difference relative to semi-classical treatments (1/S expansion) is the presence of a high-energy spinon continuum extending up to about three times the single-magnon bandwidth. In addition, the magnitude of the ordered moment (m = 0.224) agrees very well with numerical results and the low energy part of the single-magnon dispersion is in very good agreement with series expansions. Our results indicate that the Schwinger boson approach is an adequate starting point for describing the excitation spectrum of some magnetically ordered compounds that are near the quantum melting point separating this Higgs phase from the deconfined spin liquid state.
Annals of Physics, 1999
We study the strong coupling limit of the 2-flavor massless Schwinger model on a lattice using staggered fermions and the Hamiltonian approach to lattice gauge theories. Using the correspondence between the low-lying states of the 2-flavor strongly coupled lattice Schwinger model and the antiferromagnetic Heisenberg chain established in a previous paper, we explicitly compute the mass spectrum of this lattice gauge model: we identify the low-lying excitations of the Schwinger model with those of the Heisenberg model and compute the mass gaps of other excitations in terms of vacuum expectation values (v.e.v.'s) of powers of the Heisenberg Hamiltonian and spin-spin correlation functions. We find a satisfactory agreement with the results of the continuum theory already at the second order in the strong coupling expansion. We show that the pattern of symmetry breaking of the continuum theory is well reproduced by the lattice theory; we see indeed that in the lattice theory the isoscalar ψ ψ and isovector ψ σ a ψ chiral condensates are zero to every order in the strong coupling expansion. In addition, we find that the chiral condensate < ψ (2) L ψ (1) L ψ (1) R ψ (2) R > is non zero also on the lattice; this is the relic in this lattice model of the axial anomaly in the continuum theory. We compute the v.e.v.'s of the spin-spin correlators of the Heisenberg model which are pertinent to the calculation of the mass spectrum and obtain an explicit construction of the lowest lying states for finite size Heisenberg antiferromagnetic chains.
Schwinger Boson Mean Field perspective on emergent spins in diluted Heisenberg antiferromagnets
Using an adaptation of Schwinger Boson Mean Field Theory (SBMFT) for non-uniform systems, we study the nature of low-energy spin excitations on the square and Bethe lattice at their percolation threshold. The optimal SBMFT parameters are interpreted as onsite potentials and pairing amplitudes, which enables an explanation of why emergent local moments develop in this system on dilution [Phys. Rev. Lett. 97, 117204 (2006); Phys. Rev. Lett. 111, 157201 (2013)] and why the corresponding single particle frequencies are driven to anomalously low values. We discuss how our mean field calculations suggest the strong link between the presence of sublattice imbalance and long range antiferromagnetic order, and why linear spin wave theory is inadequate for capturing this relation. Within the SBMFT framework, we also extract an energy scale for the interaction between emergent moments, which show qualitative agreement with many-body calculations.
Heisenberg model with Dzyaloshinskii-Moriya interaction: A mean-field Schwinger-boson study
Physical Review B, 1996
We present a Schwinger-boson approach to the Heisenberg model with Dzyaloshinskii-Moriya interaction. We write the anisotropic interactions in terms of Schwinger bosons keeping the correct symmetries present in the spin representation, which allows us to perform a conserving mean-field approximation. Unlike previous studies of this model by linear spin-wave theory, our approach takes into account magnon-magnon interactions and includes the effects of three-boson terms characteristic of noncollinear phases. The results reproduce the linear spin-wave predictions in the semiclassical large-S limit, and show a small renormalization in the strong quantum limit S = 1/2.
Schwinger boson theory of ordered magnets
Physical Review B
The Schwinger boson theory (SBT) provides a natural path for treating quantum spin systems with large quantum fluctuations. In contrast to semi-classical treatments, this theory allows us to describe a continuous transition between magnetically ordered and spin liquid states, as well as the continuous evolution of the corresponding excitation spectrum. The square lattice Heisenberg antiferromagnet is one of the first models that was approached with the Schwinger boson theory. Here we revisit this problem to reveal several subtle points that were omitted in previous treatments and that are crucial to further develop this formalism. These points include the freedom for the choice of the saddle point (Hubbard-Stratonovich decoupling and choice of the condensate) and the 1/N expansion in the presence of a condensate. A key observation is that the spinon condensate leads to Feynman diagrams that include contributions of different order in 1/N, which must be accounted to get a qualitatively correct excitation spectrum. We demonstrate that a proper treatment of these contributions leads to an exact cancellation of the single-spinon poles of the dynamical spin structure factor, as expected for a magnetically ordered state. The only surviving poles are the ones arising from the magnons (two-spinon bound states), which are the true collective modes of an ordered magnet.
Quantum antiferromagnet at finite temperature: A gauge-field approach
Physical review. B, Condensed matter, 1994
Starting from the CP N−1 model description of the thermally disordered phase of the D = 2 quantum antiferromagnet, we examine the interaction of the Schwinger-boson spin-1/2 mean-field excitations with the generated gauge (chirality) fluctuations in the framework of the 1/N expansion. This interaction dramatically supresses the one-particle motion, but enhances the staggered static susceptibility. This means that actual excitations in the system are represented by the collective spin-1 excitations , whereas one-particle excitations disappear from the problem. We also show that massive fluctuations of the constraint field are significant for the susceptibility calculations. A connection with the problem of a particle in random magnetic field is discussed.
Physical Review B, 2004
The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a twodimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Qi = 1 on each lattice site i , which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, ξ(T ) ∝ exp(a J/T ) , come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T . This drawback, which is caused by overdamping, is overcome in a 'minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths λ > ξ and in the short-range-order regime at λ < ξ . We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.
Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons
Physical Review B, 1996
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard model is derived in the framework of the slave-boson mean-field approximation. The expansion can be obtained in terms of moments of the density of states of freely hopping electrons on a lattice, which in turn are obtained for hypercubic lattices in arbitrary dimension. The expansion is given for the case of half-filling and for the energy up to fifth order in the ratio of hopping integral t over on-site interaction U , but can straightforwardly be generalized to the non-half-filled case and be extended to higher orders in t/U. For the energy the expansion is found to have an accuracy of better than 1% for U/t ≥ 8. A comparison is given with an earlier perturbation expansion based on the Linear Spin Wave approximation and with a similar expansion based on the Hartree-Fock approximation. The case of an infinite number of spatial dimensions is discussed.