Abstract
We study the ground-state phases of the S=1/2 Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice (SATL) and on the square lattice with up to next-next-nearest-neighbor coupling (the J1J2J3 model), making use of Takahashi's modified spin-wave (MSW) theory supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that the MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular, collinear magnetic order is promoted at the expense of non-collinear (spiral) order, and several spiral states that are stable at the classical level disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which the MSW theory breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the SATL, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains. This shows that the MSW theory is—despite its apparent simplicity—a versatile tool for finding candidate regions in the case of spin-liquid phases, which are among prime targets for relevant quantum simulations.
Highlights
Low-dimensional frustrated quantum spin systems can display an intriguing interplay between order and disorder: classical order has been shown to be quite resilient in two or three dimensions [1,2,3,4]; frustration, can lead to the melting of magnetic long-range order (LRO) and the emergence of quantum disordered states like valence-bond solids or resonating valence bond states [5, 6]
We find that modified spin-wave (MSW) theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram
The optimization of the ordering vector shows dramatic quantum corrections to the ordering vector for spiraling states present in both models: such corrections show the general trend of promoting collinearly ordered states against spiraling ones. Both for the triangular and the J1J2J3 lattice, MSW theory breaks down over a sizable region of parameter space, showing a dramatic suppression of the order parameter and of the spin stiffness as the breakdown region is approached: this finding is strongly suggestive of the appearance of quantum-disordered regions in the phase diagram of the models under investigation, an issue which is still under intense debate
Summary
Low-dimensional frustrated quantum spin systems can display an intriguing interplay between order and disorder: classical order has been shown to be quite resilient in two or three dimensions [1,2,3,4]; frustration, can lead to the melting of magnetic long-range order (LRO) and the emergence of quantum disordered states like valence-bond solids or resonating valence bond states [5, 6]. The phase diagram of the spatially anisotropic triangular lattice (SATL) up to values of α ≡ t2/t1 = 1 has been studied by Yunoki and Sorella using variational quantum Monte Carlo methods [16] They find that the gapless spin-liquid phase of the isolated chains (t2 = 0) persists at finite coupling up to a critical value α ≈ 0.65, followed by a gapped spin liquid; for α ≈ 0.8 the gap closes and the system undergoes an ordering transition to spiral order, continuously connected with the 3-sublattice order of the isotropic Heisenberg antiferromagnet (α = 1). This further reinforces the idea of a quasi one-dimensional behavior up to relatively high inter-chain interactions mentioned in the previous paragraph
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