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The European Physical Journal B

Analysis of the ground-state wave function of theJ 1-J 2 quantum Heisenberg antiferromagnet

K. Retzlaff, Johannes Richter, Nedko B. Ivanov

Published Mar 1, 1993• 16 citations
Publisher
DOI
10.1007/bf01308803

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We study the spin-(1/2 Heisenberg antiferromagnet on an infinite square lattice. The calculational scheme known as ``paired-phonon analysis'' developed for strongly correlated quantum fluids is extended to a ``paired-magnon analysis'' to study quantum antiferromagnets. We define a complete and orthonormal set of multimagnon states and calculate the matrix elements of the Hamiltonian using a separability approximation. Our results obtained by diagonalizing the Hamiltonian matrix analytically are very similar to those obtained in spin-wave theory. We obtain -0.3290, for the ground-state energy per bond in units of the antiferromagnetic coupling and 0.303 for the ground-state staggered magnetization. These results compare well with the best-known estimates -0.334\ifmmode\pm\else\textpm\fi{}0.001 and 0.313, respectively. We derive the analytic form of the ground-state wave function in this approximation and find it to be of the same form as that assumed by Marshall in his variational studies.. The zero-point motion of long-wavelength excitations (spin waves) in the model, however, reflects a long-range tail in our wave function. We discuss the separability approximation by giving quantitative arguments which justify its validity.
We investigate the critical parameters of an order-disorder quantum phase transition in the spin-½ J - J ' Heisenberg and XY antiferromagnets on a square lattice. Based on the excitation gaps calculated by the exact diagonalization technique for systems up to 32 spins and finite-size scaling analysis we estimate the critical couplings and exponents of the correlation length for both models. Our analysis confirms the universal critical behaviour of these quantum phase transitions: they belong to 3D O(3) and 3D O(2) universality classes, respectively.
The nature of the intermediate ground‐state phase in the spin‐1/2 frustrated square lattice model has long been debated. We investigate the phase diagram of this model using cluster density matrix embedding theory (CDMET). Two antiferromagnetic phases are directly identified from our analysis of the ground‐state wave function: the Néel antiferromagnetic phase for J 2 ≤ 0.45 and the stripe antiferromagnetic phase for J 2 ≥ 0.65. Although our analysis of the ground state finds no direct evidence of an internal phase transition within the intermediate phase, an examination of the first excited state reveals a continuous quantum phase transition therein, with a critical point at J 2 = 0.55 that separates the intermediate phase into a plaquette valence bond solid (PVBS) and a (P + C) valence bond solid (VBS).