This is an introductory review of the physics of quantum spin liquid states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semiclassical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semiclassical approaches fail once quantum mechanics become important and then describe the alternative approaches for addressing the problem. Mainly spin-1/2 systems are discussed, and most of the time is spent in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called SU(2), U(1), or Z2 spin liquid states. A review is given of the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin (S>1/2) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular-lattice systems [κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2], kagome-lattice system [ZnCu3(OH)6Cl2], and hyperkagome lattice system (Na4Ir3O8), is reviewed and compared against the corresponding theories.

Quantum spin liquid states

We review ground states and excitations of a quantum antiferromagnet on triangular and other frustrated lattices. We pay special attention to the combined effects of magnetic field h, spatial anisotropy R and spin magnitude S. The focus of the review is on the novel collinear spin density wave and spin nematic states, which are characterized by fully gapped transverse spin excitations with Sz = ± 1. We discuss extensively the R − h phase diagram of the antiferromagnet, both in the large-S semiclassical limit and the quantum S = 1/2 limit. When possible, we point out connections with experimental findings.

https://iopscience.iop.org/article/10.1088/0034-4885/78/5/052502/pdf

Unusual ordered phases of highly frustrated magnets: a review

Motivated by experimental studies that have found signatures of a quantum spin liquid phase in organic crystals whose structure is well described by the two-dimensional triangular lattice, we study the Hubbard model on this lattice at half filling using the infinite-system density matrix renormalization group (iDMRG) method. On infinite cylinders with finite circumference, we identify an intermediate phase between observed metallic behavior at low interaction strength and Mott insulating spin-ordered behavior at strong interactions. Chiral ordering from spontaneous breaking of time-reversal symmetry, a fractionally quantized spin Hall response, and characteristic level statistics in the entanglement spectrum in the intermediate phase provide strong evidence for the existence of a chiral spin liquid in the full two-dimensional limit of the model.

Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study

Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts \kappa-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this observation, we propose as a minimal model of the observed quantum spin-liquid behavior the S=1/2 antiferromagnetic Heisenberg on the triangular lattice with a quenched randomness in the exchange interaction. We study both zero- and finite-temperature properties of the model by an exact diagonalization method, to find that when the randomness exceeds a critical value the model exhibits a quantum spin-liquid ground state. This randomness-induced quantum spin-liquid state exhibits gapless behaviors including the temperature-linear specific heat. The results provide a consistent explanation of the recent experimental observations on organic salts.

Quantum spin-liquid behavior in the spin-1/2 random Heisenberg antiferromagnet on the triangular lattice

This review article is devoted to the interplay between frustrated magnetism and quantum critical phenomena, covering both theoretical concepts and ideas as well as recent experimental developments in correlated-electron materials. The first part deals with local-moment magnetism in Mott insulators and the second part with frustration in metallic systems. In both cases, frustration can either induce exotic phases accompanied by exotic quantum critical points or lead to conventional ordering with unconventional crossover phenomena. In addition, the competition of multiple phases inherent to frustrated systems can lead to multi-criticality.

http://iopscience.iop.org/article/10.1088/1361-6633/aab6be/pdf

Frustration and quantum criticality.

We study the competition between magnetic and spin-liquid phases in the Hubbard model on the anisotropic triangular lattice, which is described by two hopping parameters $t$ and ${t}^{\ensuremath{'}}$ in different spatial directions and is relevant for layered organic charge-transfer salts. By using a variational approach that includes spiral magnetic order, we provide solid evidence that a spin-liquid phase is stabilized in the strongly correlated regime and close to the isotropic limit ${t}^{\ensuremath{'}}/t=1$. Otherwise, a magnetically ordered spiral state is found, connecting the (collinear) N\'eel and the (coplanar) ${120}^{\ensuremath{\circ}}$ phases. The pitch vector of the spiral phase obtained from the unrestricted Hartree-Fock approximation is substantially renormalized in the presence of electronic correlations, and the N\'eel phase is stabilized in a wide regime of the phase diagram, i.e., for ${t}^{\ensuremath{'}}/tl0.75$. We discuss these results in the context of organic charge-transfer salts.

Spin-liquid versus spiral-order phases in the anisotropic triangular lattice

Using density functional theory, we determine parameters of tight-binding Hamiltonians for a variety of Fabre charge transfer salts, focusing, in particular, on the effects of temperature and pressure. Besides relying on previously published crystal structures, we experimentally determine two new sets of structures: (TMTTF)2SbF6 at different temperatures and (TMTTF)2PF6 under various hydrostatic pressures. We find that a few trends in the electronic behavior can be connected to the complex phase diagram shown by these materials. Decreasing temperature and increasing pressure cause the systems to become more two dimensional. We analyze the importance of correlations by considering an extended Hubbard model parameterized using Wannier orbital overlaps and show that while charge order is strongly activated by the intersite Coulomb interaction, the magnetic order is only weakly enhanced. Both orders are suppressed when the effective pressure is increased.

/pdf/electronic-properties-of-fabre-charge-transfer-salts-under-32tqt8ta2h.pdf

Electronic properties of Fabre charge-transfer salts under various temperature and pressure conditions

A combination of density functional theory calculations, many-body model considerations, and magnetization and electron-spin-resonance measurements shows that the multiferroic FeTe2O5Br should be described as a system of alternating antiferromagnetic S = 5/2 chains with strong Fe-O-Te-O-Fe bridges weakly coupled by two-dimensional frustrated interactions, rather than the previously reported tetramer model. The peculiar temperature dependence of the incommensurate magnetic vector can be explained in terms of interchain exchange striction being responsible for the emergent net electric polarization.

/pdf/multiferroic-fete-2-o-5-br-alternating-spin-chains-with-4l6jfve3sz.pdf

Multiferroic FeTe 2 O 5 Br: Alternating spin chains with frustrated interchain interactions

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Papers

Spin-liquid versus spiral-order phases in the anisotropic triangular lattice

Electronic properties of Fabre charge-transfer salts under various temperature and pressure conditions

Multiferroic FeTe 2 O 5 Br: Alternating spin chains with frustrated interchain interactions