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arXiv:cond-mat/9510151 · Europhysics Letters (EPL)

The Transition from an Ordered Antiferromagnet to a Quantum Disordered Spin Liquid in a Solvable Bilayer Model

Claudius Gros, Wolfgang Wenzel, Johannes Richter

Published Dec 20, 1995• 18 citations
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Abstract

We present a spin-(1/2) bilayer model for the quantum order-disorder transition which i) can be solved by mean-field theory for bulk quantities, ii) becomes critical at the transition, and iii) allows to include intra-layer frustration. We present numerical data (for systems with up to 240 sites) and analytical results for the critical coupling strength, ground-state energy, order parameter and for the gap. We show that the critical coupling decreases linearly with frustration.

DOI
10.1209/0295-5075/32/9/008

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We present a spin-(1/2) bilayer model for the quantum order-disorder transition which i) can be solved by mean-field theory for bulk quantities, ii) becomes critical at the transition, and iii) allows to include intra-layer frustration. We present numerical data (for systems with up to 240 sites) and analytical results for the critical coupling strength, ground-state energy, order parameter and for the gap. We show that the critical coupling decreases linearly with frustration.
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The two-layer square lattice quantum antiferromagnet with spins 12\frac{1}{2}21​ shows a magnetic order-disorder transition at a critical ratio of the interplane to intraplane couplings. We investigate the dynamics of a single hole in a bilayer antiferromagnet described by a $t\ensuremath{-}J$ Hamiltonian. To model the spin background we propose a ground-state wave function for the undoped system that covers both magnetic phases and includes transverse as well as longitudinal spin fluctuations. The photoemission spectrum is calculated using the spin-polaron picture for the whole range of the ratio of the magnetic couplings. This allows for the study of the hole dynamics on both sides of the magnetic order-disorder transition. For small interplane coupling we find a quasiparticle with properties known from the single-layer antiferromagnet, e.g., the dispersion minimum is at $(\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2).$ For large interplane coupling the hole dispersion is similar to that of a free fermion (with reduced bandwidth). The crossover between these two scenarios occurs inside the antiferromagnetic phase, which indicates that the hole dynamics is governed by the local environment of the hole.
The double-layer antiferromagnetic quantum XXZ model is studied by the bond-operator mean-field theory. The transverse and longitudinal modes in excited spectra, and the phase diagram for disorder–order phase transition about Δ and J/J⟂, which are the relative strength of spin anisotropy and the ratio of the intralayer coupling to the interlayer coupling, respectively, are obtained. It is found that the critical ratio of (J/J⟂)c is 0.174 for XY model (Δ = 0), and is 0.430 for isotropic model (Δ = 1). In the disordered phase and on the critical points, the excitation spectra are analyzed. The spin gap from the condensed spin singlets to the first excited states, the ground state energy and the spin wave velocities in the disordered state are calculated as functions of parameters Δ and J/J⟂.
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The frustrated spin-\textonehalf{} J1{J}_{1}J1​-J2{J}_{2}J2​ Heisenberg antiferromagnet on the 2D square lattice is a paradigmatic model of quantum magnetism. Despite extensive investigations over the last 30 years, no consensus has emerged for its zero-temperature quantum phase diagram. The authors explore its bilayer J1{J}_{1}J1​-J2{J}_{2}J2​-J1{J}_{1}J1​┴ counterpart by including an exchange coupling J1{J}_{1}J1​┴ between partner sites on the two layers. As well as being of great interest in its own right, the model provides considerable insight into the single-layer case by expanding to a two-parameter regime that includes the monolayer as a single slice.
We present three different methods of finding the critical spin value ScS_cSc​ of the quantum phase transition between the spin liquid and the Néel order phase on the mean field triangular Heisenberg antiferromagnet at T=0T=0T=0K. These methods are: using the sublattice magnetization as an order parameter, looking at the scaling of the energy difference of topologically degenerate states in different phases, and the quantum fidelity approach. All of these methods are able to pick up the signal of the phase transition, and their estimated numerical values of ScS_cSc​ agree for systems where the relative strength of next nearest neighbour interaction compared to the nearest neighbour interaction is small. For the relative interaction strength j=0j=0j=0 and j=0.1j=0.1j=0.1, all three methods predict Scapprox0.21S_c\\approx0.21Sc​approx0.21 and Scapprox0.25S_c\\approx0.25Sc​approx0.25 respectively, while j=0.2j=0.2j=0.2 gives deviating results. This deviation might be caused by the influence of other magnetically ordered states that we have not accounted for in our calculations, and so we restrict the validity of our results to j<0.125j<0.125j<0.125.