Introduction to Quantum Spin Liquids

Abstract

In SU(2)-invariant spin models with frustrated interactions and low spin quantum number, long-ranged magnetic order and breaking of the SU(2) symmetry is not the most general situation, especially in low dimensions. Many such systems are, loosely speaking, "quantum paramagnets" down to zero temperature, states conveniently represented in terms of spins paired into rotationally invariant singlets, or "valence bonds" (VBs). In this large family of states, at least two very different physical phases should be distinguished, valence bond crystals (or solids) and resonating-valence-bond (RVB) liquids.This chapter provides a basic introduction to the concept of short-range resonating-valence-bond (srRVB) states, and emphasizes the qualitative differences between VB crystals and RVB liquids. We explain in simple terms why the former sustain only integer-spin excitations while the latter possess spin-1 2 excitations (the property of fractionalization). We then elaborate qualitatively on the notion of macroscopic quantum resonances, which are behind the 'R' of the RVB spin liquid, to motivate the idea that spin liquids are not disordered systems but possess instead hidden quantum order parameters. After giving a brief list of models and materials of current interest as candidate spin liquids, we conclude by mentioning the role of the parity of the net spin in the unit cell (half-odd-integer or integer) in spin-liquid formation, by recalling the contrasting results for kagomé and pyrochlore lattices. IntroductionIn isotropic (SU(2)-invariant) Heisenberg spin systems, frustration of individual bond energies, arising due to competing interactions and/or lattice topology, and extreme quantum fluctuations, due to low spin values and low coordination numbers, can prevent T D 0 magnetic ordering (defined as the existence of a non-zero on-site magnetization, hs i i > 0). These factors lead instead to a large variety of quantum phases, sometimes given the misleading name "spin liquids." We begin the task of categorizing this large zoo of phases by excluding those which do possess an order parameter, but merely one more complex than an on-site magnetization, 23 24 C. Lhuillier and G. Misguich such as a quadrupolar moment or a spin current [1][2][3]). These exotic forms of complex order break SU(2) symmetry and support Goldstone modes, and hence can be understood by semiclassical (spin-wave-like) approximations.However, quantum effects may generate more radical situations where SU(2) symmetry is not broken in the ground state. One of the most common ways of achieving this is that the spins are paired in rotationally invariant singlets, or valence bonds (VBs). Such states are by definition non-magnetic, and thus qualify as "quantum paramagnets".1 This requirement on the ground-state wave function is insufficient to characterize the physics of an extended system, its low-energy excitations and the long-distance behavior of its correlation functions. In this large family of quantum paramagnets, a crucial distinction should be i...

Quantum phase diagram of a frustrated antiferromagnet on the bilayer honeycomb lattice

“…Disordered phases in frustrated two-dimensional spin systems are a very active field of research which thrives both, on the synthesis of new materials as well as the development of new theoretical concepts [1][2][3][4] . In this context, Heisenberg antiferromagnets on the honeycomb lattice have attracted considerable interest recently.…”

Quantum phases in the frustrated Heisenberg model on the bilayer honeycomb lattice

“…The interest is focused mainly on the existence of quantum spin liquids in quantum antiferromagnets [1][2][3][4][5] . Recently, possible quantum disordered phases have been reported in the phase diagram corresponding to the single layer honeycomb Heisenberg model [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] .…”

Candidate Quantum Spin Liquid in theCe3+Pyrochlore StannateCe2Sibille1, Lhotel2, Pomjakushin3 et al. 2015Phys. Rev. Lett.1076780View full textAdd to dashboardCite

“…In higher dimensions two paradigms are employed, often simultaneously, to try to obtain a quantum spin liquid (QSL). Firstly, for Heisenberg spins with S=1/2, where quantum mechanical corrections are most significant compared to classical states, quantum melting of the Néel ground state may be possible when spins pair into valence bond singlets [13]. The result may be a valence bond crystal (translationally ordered valence bonds) [14], a resonating valence bond state (singlet configurations resonate around a plaquette) [15], or a true spin liquid when valence bonds can be formed at all lengthscales so that the ground state wavefunction has a genuine long-range entanglement [5,16].…”