Square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor regular bonds

TL;DR

This paper investigates the phase diagram of a square-lattice S=1/2 Heisenberg antiferromagnet with two types of exchange interactions, revealing critical points and phase transitions driven by frustration and quantum fluctuations.

Contribution

It introduces a detailed analysis of the zero-temperature phase diagram with two exchange constants, identifying quantum phase transitions and comparing spin-wave and exact diagonalization results.

Findings

Identification of critical points separating N{\'e}el, helicoidal, and quantum paramagnetic phases.

Quantum phase transition driven by zero-point spin fluctuations.

Agreement between spin-wave calculations and exact diagonalization away from phase boundaries.

Abstract

We study the zero-temperature phase diagram of a square-lattice $S=1/2$ Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbor exchange constants, $J_1>0$ (antiferromagnetic) and $-\infty < J_2 < \infty $, using spin-wave series based on appropriate mean-field Hamiltonian and exact-diagonalization data for small clusters. At a quasiclassical level, the model displays two critical points separating the N\'eel state from (i) a helicoidal magnetic phase for relatively small frustrating ferromagnetic couplings $J_2<0$ ($J_2/J_1<-1/3$ for classical spins), and (ii) a finite-gap quantum paramagnetic phase for large enough antiferromagnetic exchange constants $J_2>0$. The quantum order-disorder transition (ii) is similar to the one recently studied in two-layer Heisenberg antiferromagnets and is a pure result of the zero-point spin fluctuations. On the other hand, the melting of the N\'eel state in the ferromagnetic region, $J_2<0$, is a combined effect of the frustration and quantum spin fluctuations. The second-order spin-wave calculations of the ground-state energy and on-site magnetization are in accord with our exact diagonalization data in a range away from the quantum paramagnetic phase. In approaching the phase boundary, the theory fails due to the enhanced longitudinal spin fluctuations, as it has recently been argued by Chubukov and Morr.