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arXiv:1302.6349 · Physical Review Letters

Polar and Antiferromagnetic Order in f=1 Boson Systems

Hal Tasaki

Published Jun 4, 2013• 10 citations
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Abstract

In a system of interacting f=1 bosons (in the subspace where the total spin in the z direction is vanishing), we prove inequalities for the ground state expectation value of the density of spin-0 bosons. The inequalities imply that the ground state possesses "polar" or "antiferromagnetic" order when the quadratic Zeeman term q is large enough. In the low density limit, the inequalities establish the existence of a sharp transition at q=0 when q is varied.

DOI
10.1103/physrevlett.110.230402

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In a system of interacting f=1 bosons (in the subspace where the total spin in the z direction is vanishing), we prove inequalities for the ground state expectation value of the density of spin-0 bosons. The inequalities imply that the ground state possesses "polar" or "antiferromagnetic" order when the quadratic Zeeman term q is large enough. In the low density limit, the inequalities establish the existence of a sharp transition at q=0 when q is varied.
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This thesis investigates properties of classical and quantum spin systems on lattices. These models have been widely studied due to their relevance to condensed matter physics. We identify the ground states of an antiferromagnetic RP2 model, these ground states are very di�erent from the ferromagnetic model and there was some disagreement over their structure, we settle this disagreement. Correlation inequalities are proved for the spin- 1/2 XY model and the ground state of the spin-1 XY model. This provides fresh results in a topic that had been stagnant and allows the proof of some new results, for example existence of some correlation functions in the thermodynamic limit. The occurrence of nematic order at low temperature in a quantum nematic model is proved using the method of reflection positivity and infrared bounds. Previous results on this nematic order were achieved indirectly via a probabilistic representation. This result is maintained in the presence of a small antiferromagnetic interaction, this case was not previously covered. Probabilistic representations for quantum spin systems are introduced and some consequences are presented. In particular, N´eel order is proved in a bilinear-biquadratic spin-1 system at low temperature. This result extends the famous result of Dyson, Lieb and Simon [35]. Dilute spin systems are introduced and the occurrence of a phase transition at low temperature characterised by preferential occupation of the even or odd sublattice of a cubic box is proved. This result is the first of its type for such a mixed classical and quantum system. A probabilistic representation of the spin-1 Bose-Hubbard model is also presented and some consequences are proved.
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We derive the ground-state phase diagram of antiferromagnetic spin-1 bosons trapped in a square optical lattice in the limit of large negative quadratic Zeeman interaction, i.e., a limit where only two spin components σ=↑,↓\sigma=\uparrow, \downarrowσ=↑,↓ are involved. The system thus reduces to an interacting binary Bose gas. Our quantum Monte Carlo simulations reveal a phase transition from a x−yx-yx−y ferromagnetic-order to a spin insulator without symmetry breaking, inside the Mott insulating phase with two particles per site. This 3D-XY transition is characterized by the establishment of a finite local magnetic moment along the zzz-axis and by counterflow superfluidity inside the Mott phase. When increasing the spin-spin interaction amplitude U2U_2U2​, this transition merges with the Mott-superfluid transition and becomes first-order. We derive the phase diagram of the spin-charge separation with respect to U2U_2U2​ parameter.
We study the quadratic Zeeman effect (QZE) in a system of antiferromagnetic spin-1 bosons on a square lattice and derive the ground-state phase diagrams by means of quantum Monte Carlo simulations and mean-field treatment. The QZE imbalances the populations of the magnetic sublevels $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1$ and $\ensuremath{\sigma}=0$, and therefore affects the magnetic and mobility properties of the phases. Both methods show that the tip of the even Mott lobes, stabilized by singlet state, is destroyed when turning on the QZE, thus leaving the space to the superfluid phase. Contrariwise, the tips of odd Mott lobes remain unaffected. Therefore, the Mott-superfluid transition with even filling strongly depends on the strength of the QZE, and we show that the QZE can act as a control parameter for this transition at fixed hopping. Using quantum Monte Carlo simulations, we elucidate the nature of the phase transitions and examine in detail the nematic order: the first-order Mott-superfluid transition with even filling observed in the absence of QZE becomes second order for weak QZE, in contradistinction to our mean-field results which predict a first-order transition in a larger range of QZE. Furthermore, a spin nematic order with director along the zzz axis is found in the odd Mott lobes and in the superfluid phase for energetically favored $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1$ states. In the superfluid phase with even filling, the xyxyxy components of the nematic director remain finite only for moderate QZE.