Session L28: Focus Session: Spin Liquids I

Thermodynamic properties of magnetic strings on a square lattice

In the last years, spin ice systems have increasingly attracted attention by the scientific community, mainly due to the appearance of collective excitations that behave as magnetic monopole like particles. In these systems, geometrical frustration induces the appearance of degenerated ground states characterized by a local energy minimization rule, the ice rule. Violations of this rule were shown to behave like magnetic monopoles connected by a string of dipoles that carries the magnetic flux from one monopole to the other. In order to obtain a deeper knowledge about the behavior of these excitations we study the thermodynamics of a kind of magnetic polymer formed by a chain of magnetic dipoles in a square lattice. This system is expected to capture the main properties of monopole-string excitations in the artificial square spin ice. It has been found recently that in this geometry the monopoles are confined, but the effective string tension is reduced by entropic effects. To obtain the thermodynamic properties of the strings we have exactly enumerated all possible string configurations of a given length and used standard statistical mechanics analysis to calculate thermodynamic quantities. We show that the low-temperature behavior is governed by strings that satisfy ice rules.   

Dimer liquid state in the quantum dimer-pentamer model on the square lattice

We study the ground state of the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square lattice quantum dimer model (QDM) as its configuration space comprises fully-packed hard-core dimer coverings as well as configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully-packed, hard-core constraint of the QDM is relaxed such that the local dimer number at each vertex is fixed modulo 3; correspondingly, the local $U(1)$ gauge symmetry of the QDM Hilbert space is reduced to a local $Z_3$ gauge symmetry in the QDPM. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) state (the equal superposition of all configurations in a topological sector) is the exact ground state and has a 9-fold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wavefunction and that its dimer-dimer correlation function decays exponentially. Additionally, we discuss the possibility of $Z_3$ topological order in the ground state of the QDPM.   

Breakdown of antiferromagnetism and the Coulomb phase for RVB states on anisotropic three-dimensional lattices

Nearest-neighbor (NN) resonating-valence-bond (RVB) wave functions often serve as prototype ground states for various frustrated models in two dimensions because of their lack of long-range magnetic correlations. In three dimensions, these states are generally not featureless, and their tendency is toward antiferromagnetic order. On the cubic and diamond lattices, for example, the NN RVB state exhibits both antiferromagnetism and power law dimer correlations characteristic of the ``Coulomb phase'' (in analogy with classical hardcore dimer models). The introduction of strong spatial anisotropy, however, leads to the destruction of these long-range and algebraic correlations, leaving behind an apparent short-range spin liquid state. We characterize the critical exponents at the phase boundaries for wave functions built from products of SU(2) singlets as well as their SU(N) generalizations and discuss attempts to construct a field theory that describes the transitions.   

Topological defects in quantum spin-nematics

Topological defects play an important role in the theory of nematic phases in liquid crystals. However, relatively little is known about their role in quantum spin nematic phases which have no long-range dipole order and break only spin-rotational symmetry [1-3]. Here, we consider the topological defects in these nontrivial states. The model is the spin-1 bilinear biquadratic model on the triangular lattice [4-6]. We classify the defects by homotopy theory and numerical optimization approach, simulated annealing. We also discuss new type defects at particular point, which has global SU(3) symmetry. \\[4pt] [1] B. A. Ivanov, R. S. Khymyn, and A. K. Kolezhuk, Phys. Rev. Lett. {\bf 100}, 047203 (2008).\\[0pt] [2] T. Grover and T. Senthil, Phys. Rev. Lett. {\bf 107}, 077203 (2011).\\[0pt] [3] C. Xu and A. W. W. Ludwig, Phys. Rev. Lett, {\bf 108}, 047202 (2012).\\[0pt] [4] A. Lauchil, F. Mila and K. Penc, Phys. Rev. Lett. {\bf 97}, 087205 (2006).\\[0pt] [5] H. Tsunetsugu and M. Arikawa, J. Phys. Soc. Jpn. {\bf 75}, 083701 (2006).\\[0pt] [6] A. Smerald and N. Shannon, Phys. Rev. B {\bf 88}, 184430 (2013).   

Singlet-triplet excitations and long range entanglement in the spin-orbital liquid candidate FeSc$_2$S$_4$

Theoretical models of the spin-orbital liquid (SOL) FeSc$_2$S$_4$ have predicted it to be in close proximity to a quantum critical point separating a spin-orbital liquid phase from a long-range ordered magnetic phase. Here, we examine the magnetic excitations of FeSc$_2$S$_4$ through time-domain terahertz spectroscopy under an applied magnetic field. At low temperatures an excitation emerges that we attribute to a singlet-triplet excitation from the SOL ground state. A three-fold splitting of this excitation is observed as a function of applied magnetic field. Using experimentally obtained parameters we compare to existing theoretical models to determine FeSc$_2$S$_4$'s proximity to the quantum critical point and establish FeSc$_2$S$_4$ as a SOL with long-range entanglement.   

Probing hidden orders in frustrated magnets

We propose a new direct way to experimentally probe some hidden orders, in particular, spin nematic order in magnets. Both the general formulation and particular applications to possible materials with specific hidden orders will be discussed.   

A continuous Mott transition between a metal and a quantum spin liquid

More than half a century after first being proposed by Sir Nevill Mott, the deceptively simple question of whether the interaction-driven electronic metal-insulator transition may be continuous remains enigmatic. Recent experiments on two-dimensional materials suggest that when the insulator is a quantum spin liquid, lack of magnetic long-range order on the insulating side may cause the transition to be continuous, or only very weakly first order. Motivated by this, we study a half-filled extended Hubbard model on a triangular lattice strip geometry. We argue, through use of large-scale numerical simulations and analytical bosonization, that this model harbors a continuous (Kosterlitz-Thouless-like) quantum phase transition between a metal and a gapless spin liquid characterized by a spinon Fermi sea, i.e., a ``spin Bose metal''. These results may provide a rare insight into the development of Mott criticality in strongly interacting two-dimensional materials and elucidate a mechanism by which spin-liquid phases are stabilized in the vicinity of such transitions.   

The phase diagram of the XXZ model and the extended Hubbard model on the triangular lattice

The Heisenberg model on the triangular lattice was proposed as the first example of a spin-liquid by Anderson in the early 70's. Even though the isotropic Heisenberg model is by now well understood and known {\it not} to be a spin-liquid in the modern sense, so far the full phase diagram of the xxz model on the triangular lattice has received little attention. We now present DMRG calculations on order parameters and entanglement measures in order to establish the quantitative phase diagram as a function of both field and Ising anisotropy. We then also discuss the effect of introducing spin and charge degrees of freedom by considering the extended Hubbard model on the triangular lattice as a function of filling. In this case there is a very rich phase diagram with several different phases, where a stable charge order coexists with conducting behavior.   

Possible spin liquid phase of the S = 1/2 J1-J2 triangular Heisenberg model

We study the $S=1/2$ Heisenberg model on the triangular lattice with nearest neighbor interaction $J_1$ and next nearest neighbor interaction $J_2$ with the density matrix renormalization group. We are able to study long open cylinders with width up to 9 lattice spacings. At $J_2/J_1=0.1$, we find a possible spin liquid (SL) state with short range spin-spin, bond-bond and chiral correlation lengths, bordered by a classical $120^\circ$ Need order pattern at small $J_2$ and a two sub-lattice collinear magnetic ordered state at $J_2 > 0.17$. We identify two quasi-degenerate ground states in the SL phase on long even cylinders, with an energy gap that decreases exponentially with the cylinder width. We also observe a dimerization effect on odd cylinders. We further find a large spin triplet gap. Our evidence supports a fully gapped SL state for the intermediate phase.   

Quantum spin liquid in a $\pi$ flux triangular lattice Hubbard model

We propose the $\pi$ flux triangular lattice Hubbard model ($\pi$-THM) as a prototypical setup to stabilize magnetically disordered quantum states of matter in the presence of charge fluctuations. The quantum paramagnetic domain of the $\pi$-THM which we identify for intermediate Hubbard $U$ is framed by a Dirac semi-metal for weak coupling and by 120${}^{\circ}$ Neel order for strong coupling. Generalizing the Klein duality from spin Hamiltonians to tight-binding models, the $\pi$-THM maps to a Hubbard model which corresponds to the $(J_{\mathrm{H}},J_{\mathrm{K}})=(-1,2)$ Heisenberg-Kitaev model in its strong coupling limit. The $\pi$-THM provides a promising microscopic testing ground for exotic finite-$U$ spin liquid ground states amenable to numerical investigation.   

Quantum Antiferromagnents and Emergent Orders on Spatial Anisotropic Triangular Lattices

Schwinger boson representation and large $N$ expansion technique is applied to the quantum antiferromagnetic Heisenberg model on triangular lattices with spatial anisotropic nearest-neighbor and next-nearest-neighbor coupling. In the large N limit, we found several degenerate ground states with different magnetic ordering on sub-lattices,where the non-zero bonds form honeycomb lattice or dice lattice. Large $\kappa\left(=\frac{n_{b}}{N}\right)$ expansion is used to lift the degeneracy and to obtain the phase diagram. Possible applications to recent discovered compound $LiZnMo_{3}O_{8}$ are discussed.   

Magnetism in $S=1/2$ Double Perovskites with Strong Spin-Orbit Interactions

Motivated by recent studies on heavy-element double-perovskite (DP) compounds, we theoretically studied spin models on a FCC lattice with anisotropic interactions. In these systems, competition/cooperation of spin, orbital, and the lattice degrees of freedoms in the presence of the strong-spin orbit coupling is of particular interest. In a previous theoretical study, the magnetic phase diagrams of DP compounds with 5$d_1$ electron configuration was studied using a model with four-fold degenerated single-ion state. On the other hand, a recent experiment on a DP material, Ba$_2$Na$_2$OsO$_6$, reported that the compound is likely to be an effective $S=1/2$ magnet. Inspired by the experimental observation, we considered spin models with symmetry-allowed anisotropic nearest-neighbor interactions. By a combination of various analytical and numerical techniques, we present the magnetic phase diagram of the model and the effect of thermal and quantum fluctuations. In particular, we show that fluctuations induce $\langle110\rangle$ anisotropy of magnetic moments. We also discuss a possible ``nematic'' phase driven by spin-phonon couplings.\\[4pt] [1] H. Ishizuka and L. Balents, accepted for publication in PRB.   

A liquid-gas transition in a 3D Kitaev model

Quantum spin liquid (QSL) is an exotic quantum state of matter in insulating magnets, where long-range ordering is suppressed down to the lowest temperature. Several experimental candidates of QSL have been recently nominated thus far. In their characterization, the absence of thermodynamic anomalies, namely, adiabatic connection from the high-temperature paramagnet (spin gas), is regarded as a hallmark of QSL. Although adiabatic connection between liquid and gas is allowed by bypassing the critical end point in conventional fluids, it is highly nontrivial whether a thermodynamic transition between QSL and paramagnet exists or not in quantum spin systems. The issue is crucial not only for theoretical understanding of QSLs but also for the interpretation of existing and forthcoming experiments. To clarify this problem, we investigate a three-dimensional extension of the Kitaev model [1,2,3]. This model is relevant to the recently found Ir oxides Li$_{\mathrm{2}}$IrO$_{\mathrm{3}}$. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless QSLs, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with Z$_{\mathrm{2}}$ variables. Using this representation, we perform the Monte Carlo simulation and analyze the thermodynamic properties. We find that the model exhibits a finite-temperature phase transition between the QSLs and paramagnet in the whole parameter range. This result indicates that both gapless and gapped QSL phases at low temperatures are always distinguished from the high-temperature paramagnet by a phase transition. We also find that the difference between QSL and paramagnet comes from the topological nature of the excitations. This work has been done in collaboration with Y. Motome and M. Udagawa in Univ. of Tokyo. [1] J. Nasu, M. Udagawa, and Y. Motome, Phys. Rev. Lett. \textbf{113} 197205 (2014). [2] J. Nasu \textit{et al.}, Phys. Rev. B \textbf{89} 115125 (2014). [3] J. Nasu, M. Udagawa, and Y. Motome, preprint (arXiv:1409.4865).