Spin Liquid Ground State Research Articles

Coherent control of rare earth 4f shell wavefunctions in the quantum spin liquid Tb2Ti2O7

The resonant excitation of electronic transitions with coherent laser sources creates quantum coherent superpositions of the involved electronic states. Most time-resolved studies have focused on gases or isolated subsystems embedded in insulating solids, aiming for applications in quantum information. Here, we focus on the coherent control of orbital wavefunctions in the correlated quantum material Tb2Ti2O7, which forms an interacting spin liquid ground state. We show that resonant excitation with a strong THz pulse creates a coherent superposition of the lowest energy Tb 4f states. The coherence manifests itself as a macroscopic oscillating magnetic dipole, which is detected by ultrafast resonant x-ray diffraction. We envision the coherent control of orbital wavefunctions demonstrated here to become a new tool for the ultrafast manipulation and investigation of quantum materials.

Monte Carlo study of frustrated Ising model with nearest- and next-nearest-neighbor interactions in generalized triangular lattices

We investigate the frustrated J 1–J 2 Ising model with nearest-neighbor interaction J 1 and next-nearest-neighbor interaction J 2 in two kinds of generalized triangular lattices (GTLs) employing the Wang–Landau Monte Carlo method and finite-size scaling analysis. In the first GTL (GTL1), featuring anisotropic properties, we identify three kinds of super-antiferromagnetic ground states with stripe structures. Meanwhile, in the second GTL (GTL2), which is non-regular in next-nearest-neighbor interaction, the ferrimagnetic 3×3 and two kinds of partial spin liquid (PSL) ground states are observed. We confirm that residual entropy is proportional to the number of spins in the PSL ground states. Additionally, we construct finite-temperature phase diagrams for ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor interactions. In GTL1, the transition into the ferromagnetic phase is continuous, contrasting with the first-order transition into the stripe phase. In GTL2, the critical temperature into the ferromagnetic ground state decreases as antiferromagnetic next-nearest-neighbor interaction intensifies until it meets the 3×3 phase boundary. For intermediate values of the next-nearest-neighbor interaction, two successive transitions emerge: one from the paramagnetic phase to the ferromagnetic phase, followed by the other transition from the ferromagnetic phase to the 3×3 phase.

Pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets

Motivated by recent experiments on Ce2Zr2O7 that reveal a dynamic, liquidlike ground state, we study the nearest-neighbor XYZ Hamiltonian of dipolar-octupolar pyrochlore magnets with the pseudofermion functional renormalization group (PFFRG), which is numerically implemented by the software. Taking the interaction between the octupolar components to be dominant and antiferromagnetic, we map out the phase diagram demarcating the quantum disordered and magnetically ordered states. We identify four distinct phases, namely, the 0-flux and π-flux quantum spin ices and the all-in-all-out magnetic orders along the local z and x axes. We further use the static two-spin correlation output by the PFFRG algorithm to compute the polarized neutron scattering cross sections, which are able to capture several qualitative features observed experimentally, in the materially relevant parameter regime that stabilizes the π-flux quantum spin ice. Our results provide support for a quantum spin-liquid ground state in Ce2Zr2O7. Published by the American Physical Society 2024

Engineering the Kitaev Spin Liquid in a Quantum Dot System.

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin-liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of 12 quantum dots. Despite the small system size, there are clear signatures of the Kitaev spin-liquid ground state, and there is a range of parameters where these signatures are predicted, allowing a potential platform where Kitaev spin-liquid physics can be explored experimentally in quantum dot plaquettes.

Candidate spin-liquid ground state in CsNdSe2 with an effective spin-1/2 triangular lattice

Rare-earth-based triangular lattice materials are extremely attractive for studying unconventional magnetism. Here, we report the magnetic properties of layered CsNdSe2 based on direct current (DC) and alternating current (AC) susceptibility measurements down to 0.04 K. While the AC susceptibility at the zero DC field shows a broad hump below 0.5 K, there is no sign of any long-range magnetic ordering. Quantitative analysis of the DC magnetic susceptibility gives the negative Curie-Weiss (CW) temperature θCW < 0 in all directions, indicating antiferromagnetic interaction between Nd ions. Of particular interest is the low temperature magnetic susceptibility, which reflects the effective spin-1/2 state with θcwa/θcwc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\ heta }_{{{{{{{{\\rm{cw}}}}}}}}}^{a}/{\ heta }_{{{{{{{{\\rm{cw}}}}}}}}}^{c}$$\\end{document} > 3. The estimated exchange interactions are Ja/kB= 1.42 K (in-plane) and Jc/kB= 0.44 K (out-of-plane), pointing to the anisotropic magnetism. First-principles calculations that include spin-orbit coupling and Coulomb correlations reveal multiple states with zero net magnetization for CsNdSe2. Both experiment and simulation strongly suggest CsNdSe2 has the spin liquid ground state with effective spin-1/2. Application of a magnetic field can induce long-range antiferromagnetic ordering with the maximum transition temperature around 0.3 K, in further support of the zero-field spin liquid state.

Single-hole spectra of Kitaev spin liquids: from dynamical Nagaoka ferromagnetism to spin-hole fractionalization

The dynamical response of a quantum spin liquid upon injecting a hole is a pertinent open question. In experiments, the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy (ARPES) or locally in scanning tunneling microscopy (STM), can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Focusing on the gapped spin liquid phase, we reveal two fundamentally different scenarios. For ferromagnetic spin couplings, the spin liquid is highly susceptible to hole doping: a Nagaoka ferromagnet forms dynamically around the doped hole, even at weak coupling. By contrast, in the case of antiferromagnetic spin couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the analytically solvable case of slow holes. Our results demonstrate that dynamical hole spectral functions provide rich information on the structure of fractionalized quantum spin liquids.

Trimer quantum spin liquid in a honeycomb array of Rydberg atoms

Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.

Physics-Inspired Quantum Simulation of Resonating Valence Bond States─A Prototypical Template for a Spin-Liquid Ground State.

Spin liquids─an emergent, exotic collective phase of matter─have garnered enormous attention in recent years. While experimentally many prospective candidates have been proposed and realized, theoretically modeling real materials that display such behavior may pose serious challenges due to the inherently high correlation content of such phases. Over the last few decades, the second-quantum revolution has been the harbinger of a novel computational paradigm capable of initiating a foundational evolution in computational physics. In this report, we strive to use the power of the latter to study a prototypical model, a spin-1/2-unit cell of a Kagome antiferromagnet. Extended lattices of such unit cells are known to possess a magnetically disordered spin-liquid ground state. We employ robust classical numerical techniques such as the density-matrix renormalization group (DMRG) to identify the nature of the ground state through a matrix-product state (MPS) formulation. We subsequently use the gained insight to construct an auxiliary Hamiltonian with reduced measurables and also design an ansatz that is modular and gate-efficient. With robust error-mitigation strategies, we are able to demonstrate that the said ansatz is capable of accurately representing the target ground state even on a real IBMQ backend within 1% accuracy in energy. Since the protocol is linearly scaling O(n) in the number of unit cells, gate requirements, and the number of measurements, it is straightforwardly extendable to larger Kagome lattices that can pave the way for efficient construction of spin-liquid ground states on a quantum device.

NaRuO2: Kitaev-Heisenberg exchange in triangular-lattice setting

Kitaev exchange, a new paradigm in quantum magnetism research, occurs for 90° metal-ligand-metal links, {t}_{2g}^{5} transition ions, and sizable spin-orbit coupling. It is being studied in honeycomb compounds but also on triangular lattices. While for the former it is known by now that the Kitaev intersite couplings are ferromagnetic, for the latter the situation is unclear. Here we pin down the exchange mechanisms and determine the effective coupling constants in the {t}_{2g}^{5} triangular-lattice material NaRuO2, recently found to host a quantum spin liquid ground state. We show that, compared to honeycomb compounds, the characteristic triangular-lattice cation surroundings dramatically affect exchange paths and effective coupling parameters, changing the Kitaev interactions to antiferromagnetic. Quantum chemical analysis combined with subsequent effective spin model simulations provide perspective onto the nature of the experimentally observed quantum spin liquid—it seemingly implies fairly large antiferromagnetic second-neighbor isotropic exchange, and the atypical proximity to ferromagnetic order is related to ferromagnetic nearest-neighbor Heisenberg coupling.

Experimental Evidences for Quantum Spin Liquid Ground State in Layered Hexagonal Y2CuTiO6

Experimental Evidences for Quantum Spin Liquid Ground State in Layered Hexagonal Y2CuTiO6

Structural and spin-glass properties of single crystal J eff = ½ pyrochlore antiferromagnet NaCdCo2F7: correlating T f with magnetic-bond-disorder

Weak bond disorder disrupts the expected spin-liquid ground-state of the ideal S = 1/2 Heisenberg pyrochlore antiferromagnet. Here we introduce a single crystal study of the structural and magnetic properties of the bond-disordered pyrochlore NaCdCo2F7. The magnetic susceptibility appears isotropic, with a large negative Curie-Weiss temperature (θCW = −108(1) K), however no magnetic order is observed on cooling until a spin-glass transition at T f = 4.0 K. AC-susceptibility measurements show a frequency-dependent shift of the associated cusp in χ’ at T f, that can be fitted well by the empirical Vogel-Fulcher law. The magnetic moment of μ eff = 5.4(1) μ B/Co2+ indicates a significant orbital contribution and heat capacity measurements show that down to 1.8 K, well below T f, only S mag ∼ Rln(2) of the magnetic entropy is recovered, suggestive of residual continued dynamics. Structural and magnetism comparisons are made with the other known members of the NaA’’Co2F7 family (A″ = Ca2+, Sr2+), confirming the expected relationship between spin-glass freezing temperature, and extent of magnetic bond disorder brought about by the size mismatch between A-site ions.

Combinatorial exploration of quantum spin liquid candidates in the herbertsmithite material family

Geometric frustration of magnetic ions can lead to a quantum spin liquid ground state where long range magnetic order is avoided despite strong exchange interactions. The physical realization of quantum spin liquids comprises a major unresolved area of contemporary materials science. One prominent magnetically-frustrated structure is the kagome lattice. The naturally occurring minerals herbertsmithite [ZnCu$_3$(OH)$_6$Cl$_2$] and Zn-substituted barlowite [ZnCu$_3$(OH)$_6$BrF] both feature perfect kagome layers of spin-$1/2$ copper ions and display experimental signatures consistent with a quantum spin liquid state at low temperatures. To investigate other possible candidates within this material family, we perform a systematic first-principles combinatorial exploration of structurally related compounds [$A$Cu$_3$(OH)$_6B_2$ and $A$Cu$_3$(OH)$_6BC$] by substituting non-magnetic divalent cations ($A$) and halide anions ($B$, $C$). After optimizing such structures using density functional theory, we compare various structural and thermodynamic parameters to determine which compounds are most likely to favor a quantum spin liquid state. Convex hull calculations using binary compounds are performed to determine feasibility of synthesis. We also estimate the likelihood of interlayer substitutional disorder and spontaneous distortions of the kagome layers. After considering all of these factors as a whole, we select several promising candidate materials that we believe deserve further attention.

Chiral spin liquid state of strongly interacting bosons with a moat dispersion: A Monte Carlo simulation

We consider a system of strongly interacting bosons in two dimensions with moat band dispersion which supports an infinitely degenerate energy minimum along a closed contour in the Brillouin zone. The system has been theoretically predicted to stabilize a chiral spin liquid (CSL) ground state. In the thermodynamic limit and vanishing densities, n→0, chemical potential, μ, of the uniform CSL state was shown to scale with n as μ∼n2log2n. Here we perform a Monte Carlo simulation to find the parametric window for particle density, n≲k0282π, where k0 is the linear size of the moat (the radius for a circular moat), for which the scaling ∼n2log2n in the equation of state of the homogeneous CSL is preserved. We variationally show that the uniform CSL state is favorable in an interval beyond the obtained scale and present a schematic phase diagram for the system. Our results offer some density estimates for observing the low-density behavior of CSL in time-of-flight experiments with a recently Floquet-engineered moat band system of ultracold atoms in Bracamontes et al. (2022), and for the recent experiments on emergent excitonic topological order in imbalanced electron–hole bilayers.

Majorana lattice gauge theory: Symmetry breaking, topological order and intertwined orders all in one

The Majorana lattice gauge theory purely composed of Majorana fermions on square lattice is studied throughly. The ground state is obtained exactly and exhibits the coexistence of symmetry breaking and topological order. The Z_2Z2 symmetry breaking of matter fields leads to the intertwined antiferromagnetic spin order and \etaη-pairing order. The topological order is reflected in the Z_2Z2 quantum spin liquid ground state of gauge fields. The Majorana lattice gauge theory, alternatively can be viewed as interacting Majorana fermion model, is possibly realized on a Majorana-zero-mode lattice.

Ligand field luminescence in the honeycomb Mott insulator α-RuCl3

Novel electronic structure is central to Kitaev-like quantum spin liquid ground state in the van der Waals antiferromagnet α-RuCl3. In this octahedral low-spin system, the rich bandstructure includes Mott–Hubbard insulating bandgap of ∼1.1 eV and ligand field induced gap of ∼2 eV. Though the bandgap is extensively reported in previous optical and photoemission studies, the latter gap is less understood. In this regard, we probed the ligand field-induced electronic structure of bulk α-RuCl3 single crystals via unpolarized photoluminescence (PL) spectroscopy under linearly polarized excitation in the visible region. We observed the broad principal PL peak at E PL 1.87 eV, close to the energy required for the optical transition across the ligand field splitting gap (∼2 eV). This gap (E PL) monotonically increases with temperature, described by the thermal expansion of lattice parameters dominating the electron–phonon interaction in this Honeycomb Mott insulator. Moreover, we observed the multiplet structure of the PL spectra, which can be explained by parity-forbidden d–d transitions in the light of single ion ligand-field theory. We attribute the broad PL linewidths to strong vibronic coupling modeled by the Huang–Rhys parameter. Further we observed the signature of structural transitions, indicated by thermal hysteresis in normalized integrated PL intensity.

Z_{2} Spin Liquids in the Higher Spin-S Kitaev Honeycomb Model: An Exact Deconfined Z_{2} Gauge Structure in a Nonintegrable Model.

The higher spin Kitaev model prominently features the extensive locally conserved quantities the same as the spin-1/2 Kitaev honeycomb model, although it is not exactly solvable. It remains an open question regarding the physical meaning of these conserved quantities in the higher spin model. In this Letter, by introducing a Majorana parton construction for a general spin-S we uncover that these conserved quantities are exactly the Z_{2} gauge fluxes in the general spin-S model, including the case of spin-1/2. Particularly, we find an even-odd effect that the Z_{2} gauge charges are fermions in the half integer spin model, but are bosons in the integer spin model. We further prove that the fermionic Z_{2} gauge charges are always deconfined; hence, the half integer spin Kitaev model would have nontrivial spin liquid ground states regardless of interaction strengths in the Hamiltonian. The bosonic Z_{2} gauge charges of the integer spin model, on the other hand, could condense, leading to a trivial product state, and this is indeed the case at the anisotropic limit of the model.

Pinch-points to half-moons and up in the stars: The kagome skymap

Pinch point singularities, associated with flat band magnetic excitations, are tell-tale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features -- shaped as half-moons and stars -- arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns.

Zigzag magnetic order and possible Kitaev interactions in the spin-1 honeycomb lattice KNiAsO4

Despite the exciting implications of the Kitaev spin Hamiltonian, finding and confirming the quantum spin-liquid state have proven incredibly difficult. Recently, the applicability of the model has been expanded through the development of a microscopic description of a spin-1 Kitaev interaction. Here we explore a candidate spin-1 honeycomb system, ${\mathrm{KNiAsO}}_{4}$, which meets many of the proposed criteria to generate such an interaction. Bulk measurements reveal an antiferromagnetic transition at $\ensuremath{\sim}19$ K which is generally robust to applied magnetic fields. Neutron diffraction measurements show magnetic order with a $\mathbf{k}=(\frac{3}{2},0,0)$ ordering vector which results in the well-known ``zigzag'' magnetic structure thought to be adjacent to the spin-liquid ground state. Field-dependent diffraction shows that while the structure is robust, the field can tune the direction of the ordered moment. Inelastic neutron scattering experiments show a well-defined gapped spin-wave spectrum with no evidence of the continuum expected for fractionalized excitations. Modeling of the spin waves shows that the extended Kitaev spin Hamiltonian is are generally necessary to model the spectra and reproduce the observed magnetic order. First-principles calculations suggest that the substitution of Pd on the Ni sublattice may strengthen the Kitaev interactions while simultaneously weakening the exchange interactions thus pushing ${\mathrm{KNiAsO}}_{4}$ closer to the spin-liquid ground state.

Spin-wave dynamics in the KCeS2 delafossite: A theoretical description of powder inelastic neutron-scattering data

Layered rare-earth delafossites $ARX_2$ with $R$ = Yb(III) or Ce(III) have received a lot of interest as potential hosts for a quantum spin-liquid ground state. Some systems of this family that show no long-range order down to the lowest measured temperatures, such as NaYbO$_2$, NaYbS$_2$, and NaYbSe$_2$, are presumed to be in a quantum spin-liquid state. However, other isostructural compounds are known to order antiferromagnetically at subkelvin temperatures. Among them, KCeS$_2$ exhibits stripe-$yz$ magnetic order in the triangular-lattice planes that sets in below 400 mK. Here we investigate the spin-wave spectrum of this ordered phase with powder inelastic neutron scattering and describe it using a model Hamiltonian obtained from first-principles calculations based on the complete $|J,m_J\rangle$ multiplet description of the Ce sites with an anisotropic nearest-neighbor exchange interaction. Combing the current understanding of the exchange interaction in the systems with the effects of texturing in the powder, we have been able to model the inelastic neutron scattering spectrum with high fidelity.

Heat transport of the kagome Heisenberg quantum spin liquid candidate YCu3(OH)6.5Br2.5 : Localized magnetic excitations and a putative spin gap

The spin-1/2 kagom\'{e} Heisenberg antiferromagnet is generally accepted as one of the most promising two-dimensional models to realize a quantum spin liquid state. Previous experimental efforts were almost exclusively on only one archetypal material, the herbertsmithite ZnCu$_3$(OH)$_6$Cl$_2$, which unfortunately suffers from the notorious orphan spins problem caused by magnetic disorders. Here we turn to YCu$_3$(OH)$_{6.5}$Br$_{2.5}$, recently recognized as another host of a globally undistorted kagom\'{e} Cu$^{2+}$ lattice free from the orphan spins, thus a more feasible system for studying the intrinsic kagom\'{e} quantum spin liquid physics. Our high-resolution low-temperature thermal conductivity measurements yield a vanishing small residual linear term of $\kappa/T$ ($T\rightarrow 0$), and thus clearly rule out itinerant gapless fermionic excitations. Unusual scattering of phonons grows exponentially with temperature, suggesting thermally activated phonon-spin scattering and hence a gapped magnetic excitation, consistent with a $\mathbb{Z}_2$ quantum spin liquid ground state. Additionally, the analysis of magnetic field impact on the thermal conductivity reveals a field closing of the spin gap, while the excitations remain localized.