Schwinger-Boson Approach to Quantum Spin Systems: Gaussian Fluctuations in the “Natural” Gauge

Abstract

We compute the Gaussian-fluctuation corrections to the saddle-point Schwinger-boson results using collective coordinate methods. Concrete application to investigate the frustrated J1 −J2 antiferromagnet on the square lattice shows that, unlike the saddle-point predictions, there is a quantum nonmagnetic phase for 0.53 < ∼ J2/J1 < ∼ 0.64. This result is obtained by considering the corrections to the spin stiffness on large lattices and extrapolating to the thermodynamic limit, which avoids the infinite-lattice infrared divergencies associated to Bose condensation. The very good agreement of our results with exact numerical values on finite clusters lends support to the calculational scheme employed.In the last years there has been a lot of interest in the properties of quantum magnetic systems, [1] particularly frustrated quantum antiferromagnets. Although this interest was initially related to the possible connections between magnetism and superconductivity in the ceramic compounds, the current activity in the area is now well beyond this original motivation.Among the analytical methods used to study quantum spin systems, the Schwinger-boson approach [2] is one of the most elegant and successful techniques. Contrary to standard spin-wave theory, it does not rely on having a magnetized ground-state, which leads to nice rotational properties of the results and to the possibility of describing ordered and disordered phases in an unified treatment. However, this theory has the drawback of being defined in a constrained bosonic space, with unphysical configurations being allowed when this constraint is treated as a soft (average) restriction. This drawback can be in principle corrected by including local fluctuations of the boson chemical potential. [3] Despite the widespread use in the literature of the Schwinger-boson representation of quantum spin operators, we are not aware of a complete calculation of Gaussian corrections to saddle-point results. In particular, for frustrated quantum antiferromagnets such calculations have been sketched several times, [2,4,5] but never fully undertaken. In this work we fill up this gap by presenting the general calculation of Gaussian fluctuations in the Schwinger-boson approach. Since the theory presents a local U (1) symmetry, we use collective coordinate methods -as developed in the context of relativistic lattice gauge theories [6]-to handle the infinitely-many zero modes associated to the local symmetry breaking in the saddle-point expansion. As a concrete application, we study the existence and location of the nonmagnetic quantum phase predicted to occur as a consequence of quantum fluctuations and frustration in the J 1 −J 2 model. [7] We will consider a general Heisenberg Hamiltonian,where ij are links on a lattice. We write spin operators in terms of Schwinger bosons:is a bosonic spinor, σ is the vector of Pauli matrices, and there is a bosonnumber restriction σ a † iσ a iσ = 2S on each site. With this faithful representation of the spin algebra, the rotational invariant...

One dimensionalization in the spin-1 Heisenberg model on the anisotropic triangular lattice

“…On the other hand, the Gaussian corrected spin stiffness is obtained by deriving E F L once the twisted mean-field parameters are plugged in Eq. (22). Coming from the isotropic case J = 1 the Gaussian corrections for the spiral phases tend to weaken the spin stiffness until the ground state becomes unstable at J c = 0.43, in accordance with Fig.…”

“…To avoid them we introduce the Fadeev-Popov trick which restricts the integration to field fluctuations orthogonal to the gauge orbit 22 . This procedure gives the following Gaussian correction of the free energy:…”

Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

“…In fact, Gazza et al 11 performed a Schwinger boson mean field theory and found a continuous transition from collinear to spiral phases at η = 0.375 but with a nonvanishing magnetization m 0 ∼ 0.175. However, inclusion of gaussian fluctuations in this theory would tend to decrease the order, as it is known to occur in highly frustrated cases 12,3 , reaching probably more accord with our spin wave results. The same happens with both theories in the J 1 − J 2 model on a square lattice 13,14,12 .…”

Magnetic correlation in the square-lattice spin system (CuBr)Sr2Nb3O10: A neutron diffraction study

“…In the literature a large number of theoretical studies on systems with antiferromagnetic (AFM) J 1 and J 2 exist. [3][4][5][6][7][8][9][10][11][12][13][14] Here the J 1 -J 2 model 3-14 reveals several interesting magnetic ground states involving quantum phase transitions, such as (i) for α (=|J 2 / J 1 |) 0.4, a Néel AFM state [Q = (π π)], (ii) for α∼0. 4-0.6, a quantum spin-liquid state, and (iii) for α 0.6, an ordered collinear AFM state [Q = (π 0) or (0 π )], i.e., AFM coupling of ferromagnetic (FM) chains in a given plane (by disorder stabilization).…”