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We study spin-phonon interactions in quantum spin liquid candidate RuCl3 under magnetic fields of up to 6T and mK temperatures with polarization-resolved Raman spectroscopy.
Here we study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-1/2 antiferromagnetic Heisenberg model on the triangular lattice with nearest- (J 1 ), next-nearest- (J 2 ), and third-neighbor (J 3 ) interactions by using density-matrix renormalization group (DMRG) method. By combining parallel DMRG with SU(2) spin rotational symmetry, we are able to obtain accurate results on large cylinders with length up to L x =48 and circumference L y =6–12. Our results suggest that the QSL phase of the J 1 -J 2 Heisenberg model is gapped which is characterized by the absence of gapless mode, short-range spin-spin and dimer-dimer correlations. In the presence of J 3 interaction, we find that a new 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 which decays as a power-law at long distances.
The barlowite [Cu 4 (OD) 6 FBr] family of materials is characterized by antiferromagnetic spin-1/2 kagome layers and are believed to host interesting ground states of quantum magnetism. Substituting the interlayer sites with zinc ions yields Zn-barlowite (Zn 𝑥 Cu 4−𝑥 (OD) 6 FBr, 𝑥 ≈ 0.80) which is a strong candidate to have a quantum spin liquid (QSL) state. Experimentally distinguishing between valence bond crystal (VBC) and QSL states in the absence of magnetic ordering can prove challenging as both states exhibit similar average spin-spin correlations. Using high-resolution inelastic x-ray scattering with 1.4 meV energy resolution, we probe acoustic phonons in these structurally similar materials at various temperatures. Our measurements uncover robust differences possibly driven by different spin-phonon physics in VBC and QSL states, particularly at the 𝑀-point Brillouin zone boundary. Over a large 𝑇=[15,200] K temperature range, where neither material undergoes magnetic ordering nor a structural transition, we observe phonon softening in Zn-barlowite in contrast to a hardening of the same phonon in barlowite. Further, these results indicate that acoustic phonons in the barlowite system can be used to study and possibly distinguish between QSL and disordered VBC states in quantum magnets.
Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model—albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z 2 spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing Floquet-mediated chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state “Kitaev materials” and, more generally, it spotlights a different angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.
The interplay between spin frustration and charge fluctuation gives rise to an exotic quantum state in the intermediate-interaction regime of the half-filled triangular-lattice Hubbard model, while the nature of the state is under debate. Using the density matrix renormalization group with SU(2) spin ⓍU(1) charge symmetries implemented, we study the triangular-lattice Hubbard model defined on the long cylinder geometry up to circumference W=6. A gapped quantum spin liquid, with on-site interaction 9≲U/t≲10.75, is identified between the metallic and the antiferromagnetic Mott insulating phases. In particular, we find that this spin liquid develops a robust long-range spin scalar-chiral correlation as the system length L increases, which unambiguously unveils the spontaneous time-reversal symmetry breaking. In addition, the degeneracy of the entanglement spectrum supports symmetry fractionalization and spinon edge modes in the obtained ground state. The possible origin of chiral order in this intermediate spin liquid and its relation to the rotonlike excitations have also been discussed.
In this work, we introduce the notion of combinatorial gauge symmetry—a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states)—that preserve the commutation and anticommutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.
The 3d 7 Co 2+ -based insulating magnet Na 2 Co 2 TeO 6 has recently been reported to have strong Kitaev interactions on a honeycomb lattice and is thus being considered as a Kitaev quandum spin liquid candidate. However, due to the existence of other types of interactions, a spontaneous long-range magnetic order occurs. This order is suppressed by applied magnetic fields leading to a succession of phases and ultimately saturation of the magnetic moments. The precise phase diagram, the nature of the phases, and the possibility that one of the field-induced phases is a Kitaev quantum spin liquid phase are still a matter of debate. Here, in this study, we measured an extensive set of physical properties to build the complete temperature-field phase diagrams to magnetic saturation at 10 T for magnetic fields along the a and a* axes, and a partial phase diagram up to 60 T along c. We probe the phases using magnetization, specific heat, magnetocaloric effect, magnetostriction, dielectric constant, and electric polarization, which is a symmetry-sensitive probe. With these measurements, we identify all the previously incomplete phase boundaries and find additional high-field phase boundaries. We find strong magnetoelectric coupling in the dielectric constant and moderate magnetostrictive coupling at several phase boundaries. Furthermore, we detect the symmetry of the magnetic order using electrical polarization measurements under magnetic fields. Based on our analysis, the absence of electric polarization under zero or finite magnetic field in any of the phases or after any combination of magnetic/electric field cooling suggests that a zigzag spin structure is more likely than a triple-Q spin structure at zero field. Finally, we investigate the hysteresis and first- or second-order nature of each phase transition and its entropy changes. With this information, we establish a map of the magnetic phases of this compound and its magnetic, thermodynamic, and magnetoelectric properties, and discuss where spin liquid or other phases may be sought in future studies.
A geometrically frustrated (GF) magnet consists of localised magnetic moments, spins, whose orientation cannot be arranged to simultaneously minimise their interaction energies. Such materials may host novel fascinating phases of matter, such as fluid-like states called quantum spin-liquids. GF magnets have, like all solid-state systems, randomly located impurities whose magnetic moments may “freeze” at low temperatures, making the system enter a spin-glass state. We analyse the available data for spin-glass transitions in GF materials and find a surprising trend: the glass-transition temperature grows with decreasing impurity concentration and reaches a finite value in the impurity-free limit at a previously unidentified, “hidden”, energy scale. We propose a scenario in which the interplay of interactions and entropy leads to a crossover in the permeability of the medium that assists glass freezing at low temperatures. This low-temperature, “eminuscent”, phase may obscure or even destroy the widely-sought spin-liquid states in rather clean systems.
We present the first circularly polarized non-resonant pump time-resolved resonant inelastic X-ray scattering (tr-RIXS) experiment in H 3 LiIr 2 O 6 , an iridium-based Kitaev system. Our calculations and experimental results are consistent with the modification of the low-energy magnetic excitations in H 3 LiIr 2 O 6 only during illumination by the laser pulse. We discuss these results in a cooperative framework between the Floquet engineering of the exchange interactions and the dynamic renormalization of electron-electron correlations. However, the penetration length mismatch between the X-ray probe and laser pump and the intrinsic complexity of Kitaev magnets prevents us from unequivocally extracting towards which ground state H 3 LiIr 2 O 6 is driven. We outline possible solutions to these challenges for light-driven stabilization and observation of the Kitaev quantum spin liquid limit by RIXS.
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We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.
We construct Hamiltonians with only 1- and 2-body interactions that exhibit an exact non-Abelian gauge symmetry (specifically, combinatiorial gauge symmetry). Our spin Hamiltonian realizes the quantum double associated to the group of quaternions. It contains only ferromagnetic and anti-ferromagnetic ZZ Z Z interactions, plus longitudinal and transverse fields, and therefore is an explicit example of a spin Hamiltonian with no sign problem that realizes a non-Abelian topological phase. In addition to the spin model, we propose a superconducting quantum circuit version with the same symmetry.
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