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arXiv:2410.17720

Fragile spin liquid in three dimensions

Anna Fancelli, R. Flores-Calderón, Owen Benton, B. Lake, Roderich Moessner, Johannes Reuther

Published Oct 23, 2024• 0 citations
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Abstract

Motivated by the recent appearance of the trillium lattice in the search for materials hosting spin liquids, we study the ground state of the classical Heisenberg model on its linegraph, the trilline lattice. We find that this network realises the recently proposed notion of a fragile spin liquid in three dimensions. Additionally, we analyze the Ising case and argue for a possible $\mathbb{Z}_2$ quantum spin liquid phase in the corresponding quantum dimer model. Like the well-known $U(1)$ spin liquids, the classical phase hosts moment fractionalisation evidenced in the diluted lattice, but unlike these, it exhibits exponential decay both in spin correlations and interactions between fractionalised moments. This provides the first instance of a purely short-range correlated classical Heisenberg spin liquid in three dimensions.

DOI
10.48550/arxiv.2410.17720

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Motivated by the recent appearance of the trillium lattice in the search for materials hosting spin liquids, we study the ground state of the classical Heisenberg model on its linegraph, the trilline lattice. We find that this network realises the recently proposed notion of a fragile spin liquid in three dimensions. Additionally, we analyze the Ising case and argue for a possible Z2\mathbb{Z}_2Z2​ quantum spin liquid phase in the corresponding quantum dimer model. Like the well-known U(1)U(1)U(1) spin liquids, the classical phase hosts moment fractionalisation evidenced in the diluted lattice, but unlike these, it exhibits exponential decay both in spin correlations and interactions between fractionalised moments. This provides the first instance of a purely short-range correlated classical Heisenberg spin liquid in three dimensions.
Motivated by the recent appearance of the trillium lattice in the search for materials hosting spin liquids, we study the ground state of the classical Heisenberg model on its line graph, the trilline lattice. We find that this network realizes the recently proposed notion of a fragile spin liquid in three dimensions. Additionally, we analyze the Ising case and argue for a possible Z 2 quantum spin liquid phase in the corresponding quantum dimer model. Like the well-known U ( 1 ) spin liquids, the classical phase hosts moment fractionalization evidenced by the diluted lattice, but unlike those, it exhibits exponential decay in both spin correlations and interactions between fractionalized moments. This provides an instance of a purely short-range correlated classical Heisenberg spin liquid in three dimensions.
Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalized spin liquid phase, the so-called Coulomb or U(1) spin liquid, has until recently been identified: This exhibits algebraic spin correlations and impurity moments, "orphan spins," whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalization in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z_{2} spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavor.
We study fermionic quantum spin liquids (QSLs) on the three-dimensional trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frustration. Using the framework of projective symmetry groups (PSG), we obtain a classification of all symmetric Z 2 and U ( 1 ) QSLs on the trillium lattice. We find two Z 2 spin-liquids, and a single U ( 1 ) spin-liquid that is proximate to one of the Z 2 states. The small number of solutions reflects the constraints imposed by the nonsymmorphic symmetries in the space group of the trillium lattice. Using self-consistency conditions of the mean-field equations, we obtain the spinon band-structure and spin structure factors corresponding to these states. All three of our spin liquids are gapless at their saddle points: one of the two Z 2 QSLs is nodal, while the U ( 1 ) case hosts a spinon Fermi surface. One of our Z 2 spin liquids hosts a stable gapless nodal star that is protected by projective symmetries against additions of further neighbor terms in the mean-field ansatz. We comment on directions for further work.
We study quantum disordered ground states of the two-dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg and Kitaev couplings and sufficiently small spin SSS, we find three different symmetric Z2{Z}_{2}Z2​ spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well-known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops ${120}^{\ensuremath{\circ}}$ order in the semiclassical limit at large SSS. In the opposite Kitaev limit, we find a different spin liquid ground state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings, we find a spin liquid state with unusual spin correlations. Upon spinon condensation, this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.
The tetratrillium lattice has recently been proposed as being responsible for the dynamical properties observed in the S = 1 langbeinite compound K 2 Ni 2 ( SO 4 ) 3 . Here, we study in detail the classical spin liquid properties of this lattice of tricoordinated tetrahedra using classical Monte Carlo and large- N theory calculations. In the large- N limit, we find that the system presents a gapped spectrum with flat bottom bands, giving rise to a fragile spin liquid with exponentially decaying correlations according to the classification of classical spin liquids. We confirm that this scenario also holds in the more realistic Ising and Heisenberg cases, for which the system does not exhibit any finite-temperature phase transition, and the low-temperature spin structure factors exhibit excellent quantitative agreement with the large- N theory. We also provide insight into the quantum S = 1 / 2 limit by performing pseudo-Majorana functional renormalization-group calculations at finite temperatures, and we discuss the possible phases that can arise in the ground state due to quantum fluctuations.
We study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-1/21/21/2 antiferromagnetic Heisenberg model on the triangular lattice with nearest- (J1)({J}_{1})(J1​), next-nearest- (J2)({J}_{2})(J2​), and third-neighbor (J3)({J}_{3})(J3​) interactions by using the density-matrix renormalization group (DMRG) method. By combining parallel DMRG with SU(2)\mathrm{SU}(2)SU(2) spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to Lx=48{L}_{x}=48Lx​=48 and circumference Ly=6−−12{L}_{y}=6--12Ly​=6−−12. Our results suggest that the QSL phase of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model is gapped, which is characterized by the absence of a gapless mode and by short-range spin-spin and dimer-dimer correlations. In the presence of J3{J}_{3}J3​ interaction, we find that a critical QSL with a single gapless mode emerges. While both spin-spin and scalar chiral-chiral correlations are short ranged, dimer-dimer correlations are quasi long ranged and decay as a power law at long distances.