Spin Liquid Research Articles

Magnetocaloric effect of topological excitations in Kitaev magnets

Traditional magnetic sub-Kelvin cooling relies on the nearly free local moments in hydrate paramagnetic salts, whose utility is hampered by the dilute magnetic ions and low thermal conductivity. Here we propose to use instead fractional excitations inherent to quantum spin liquids (QSLs) as an alternative, which are sensitive to external fields and can induce a very distinctive magnetocaloric effect. With state-of-the-art tensor-network approach, we compute low-temperature properties of Kitaev honeycomb model. For the ferromagnetic case, strong demagnetization cooling effect is observed due to the nearly free Z2 vortices via spin fractionalization, described by a paramagnetic equation of state with a renormalized Curie constant. For the antiferromagnetic Kitaev case, we uncover an intermediate-field gapless QSL phase with very large spin entropy, possibly due to the emergence of spinon Fermi surface and gauge field. Potential realization of topological excitation magnetocalorics in Kitaev materials is also discussed, which may offer a promising pathway to circumvent existing limitations in the paramagnetic hydrates.

Triplon analysis of magnetic disorder and order in maple-leaf Heisenberg magnet

The nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice formed by hexagons (couplingJh), triangles (couplingJt), and dimers (couplingJd), is investigated in a parameter regime whereJh>0andJt,Jd<0. This investigation aims to identify regions hosting exotic valence-bond solid states. Two potential magnetically disordered ground states are identified, and their stability is assessed through plaquette-triplon mean-field analyses. The resulting quantum phase diagram reveals that at large|Jt|and|Jd|, the system adopts a magnetically disordered dimerized VBS state, while for small|Jd|, it stabilizes a Néel state. A second-order phase transition from the dimerized phase to a Néel phase is observed, which, being Landau-forbidden, suggests the potential presence of exotic phenomena such as a deconfined quantum critical point or the appearance of a quantum spin liquid. This work provides insights into the phase diagram of the nearest-neighbor spin-1/2 Heisenberg model on the maple-leaf lattice and lays the groundwork for further investigations into its intriguing physics.

Emergence of vortex state in the S=1 Kitaev-Heisenberg model with single-ion anisotropy

The search for Kitaev spin liquid states has recently broadened to include a number of honeycomb materials with integer spin moments. The qualitative difference with their spin-1/2 counterparts is the presence of single-ion anisotropy (SIA). This motivates our investigation of the effects of SIA on the ground state of the spin-1 Kitaev-Heisenberg (KH) model using the density-matrix renormalization group which allows construction of detailed phase diagrams around the Kitaev points. We demonstrate that positive out-of-plane SIA induces an in-plane vortex state without the need for off-diagonal interactions. Conversely, negative SIA facilitates the emergence of a state in the presence of antiferromagnetic Heisenberg interactions, whereas a state can emerge for ferromagnetic Heisenberg coupling. These findings, pertinent even for weak SIA, not only enhance our theoretical understanding of the spin-1 KH model but also suggest experimental prospects for observing these novel magnetic states in material realizations. Published by the American Physical Society 2024

Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model

Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model

Simulating chiral spin liquids with fermionic projected entangled pair states

Simulating chiral spin liquids with fermionic projected entangled pair states

Symmetry, superposition, and fragmentation in classical spin liquids: A general framework and applications to square kagome magnets

Symmetry, superposition, and fragmentation in classical spin liquids: A general framework and applications to square kagome magnets

Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating.

We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3K and 1-500bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25bar does not freeze down to 0.1K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3K at 40-50bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.

Large oscillatory thermal hall effect in kagome metals

The thermal Hall effect recently provided intriguing probes to the ground state of exotic quantum matters. These observations of transverse thermal Hall signals lead to the debate on the fermionic versus bosonic origins of these phenomena. The recent report of quantum oscillations (QOs) in Kitaev spin liquid points to a possible resolution. The Landau level quantization would most likely capture only the fermionic thermal transport effect. However, the QOs in the thermal Hall effect are generally hard to detect. In this work, we report the observation of a large oscillatory thermal Hall effect of correlated Kagome metals. We detect a 180-degree phase change of the oscillation and demonstrate the phase flip as an essential feature for QOs in the thermal transport properties. More importantly, the QOs in the thermal Hall channel are more profound than those in the electrical Hall channel, which strongly violates the Wiedemann–Franz (WF) law for QOs. This result presents the oscillatory thermal Hall effect as a powerful probe to the correlated quantum materials.

Mixed-State Quantum Spin Liquids and Dynamical Anyon Condensations in Kitaev Lindbladians

Quantum spin liquids and anyons, used to be subjects of condensed matter physics, now are realized in various platforms of qubits, offering unprecedented opportunities to investigate fundamental physics of many-body quantum entangled states. Qubits are inevitably exposed to environment effects such as decoherence and dissipation, which are believed to be detrimental to many-body entanglement. Here, we argue that unlike the common belief decoherence and dissipation can give rise to novel topological phenomena in quantum spin liquids. We study open quantum systems of the Kitaev spin liquid and the toric code via the Lindblad master equation approach. By using exact solutions and numerical approaches, we show the dynamical occurrence of anyon condensation by decoherence and dissipation, which results in a topological transition from the initial state spin liquid to the steady state spin liquid. The mechanism of the anyon condensation transition by the Lindblad dynamics is elucidated. We also provide an insight into the relationship between the Kitaev spin liquid and the toric code in the picture of anyon condensation. Our work suggests open quantum systems to be a new venue for topological phenomena of quantum spin liquids and anyons.

Eight-color chiral spin liquid in the S=1 bilinear-biquadratic model with Kitaev interactions

Multipolar spin systems provide a rich ground for the emergence of unexpected states of matter due to their enlarged spin degree of freedom. In this study, with a specific emphasis on S=1 magnets, we explore the interplay between spin nematic states and spin liquids. Based on the foundations laid in the prior work [R. Pohle , ], we investigate the S=1 Kitaev model with bilinear-biquadratic interactions, which stabilizes, next to Kitaev spin liquid, spin nematic and triple-q phases, also an exotic chiral spin liquid. Through a systematic reduction of the spin degree of freedom—from CP2 to CP1 and ultimately to a discrete eight-color model—we provide an intuitive understanding of the nature and origin of this chiral spin liquid. We find that the chiral spin liquid is characterized by an extensive ground-state degeneracy, bound by a residual entropy, extremely short-ranged correlations, a nonzero scalar spin chirality marked by Z2 flux order, and a gapped continuum of excitations. Our work contributes not only to the specific exploration of S=1 Kitaev magnets but also to the broader understanding of the importance of multipolar spin degree of freedom on the ground state and excitation properties in quantum magnets. Published by the American Physical Society 2024

Inverse Hamiltonian design of highly entangled quantum systems

Solving inverse problems to identify Hamiltonians with desired properties holds promise for the discovery of fundamental principles. In quantum systems, quantum entanglement plays a pivotal role in not only characterizing the quantum nature but also developing quantum technology such as quantum computing. Nonetheless, the design principles of the quantum entanglement are yet to be clarified. Here we apply an inverse design framework using automatic differentiation to quantum spin systems, aiming to construct Hamiltonians with large quantum entanglement. We show that the method automatically finds the Kitaev model with bond-dependent anisotropic interactions, whose ground state is a quantum spin liquid, on both honeycomb and square-octagon lattices. On triangular and maple-leaf lattices with geometrical frustration, it generates numerous solutions with spatially inhomogeneous interactions rather than converging to a specific model, but it still helps to construct unprecedented models. The comparative study reveals that bond-dependent anisotropic interactions, rather than isotropic Heisenberg interactions, amplify quantum entanglement, even in the systems with geometrical frustration. The present study paves the way for the automatic design of new quantum systems with desired quantum nature and functionality. Published by the American Physical Society 2024

Non-Abelian Anyons in Periodically Driven Abelian Spin Liquids.

We show that non-Abelian anyons can emerge from an Abelian topologically ordered system subject to local time-periodic driving. This is illustrated with the toric-code model, as the canonical representative of a broad class of Abelian topological spin liquids. The Abelian anyons in the toric code include fermionic and bosonic quasiparticle excitations which see each other as π fluxes; namely, they result in the accumulation of a π phase if wound around each other. Non-Abelian behavior emerges because the Floquet modulation can engineer a nontrivial band topology for the fermions, inducing their fractionalization into Floquet-Majorana modes bound to the bosons. The latter then develop non-Abelian character akin to vortices in topological superconductors, realizing Ising topological order. Our findings shed light on the nonequilibrium physics of driven topologically ordered quantum matter and may facilitate the observation of non-Abelian behavior in engineered quantum systems.

Vison condensation and spinon confinement in a kagome-lattice Z2 spin liquid: A numerical study of a quantum dimer model

Quantum spin liquids are exotic many-body states featured with long-range entanglement and fractional anyon quasiparticles. Quantum phase transitions of spin liquids are particularly interesting problems related with novel phenomena of anyon condensation and anyon confinement. Here we study a quantum dimer model, which implements a transition between a Z2 spin liquid (Z2SL) and a valence bond solid (VBS) on the kagome lattice. The transition is driven by the condensation of vison excitation of the Z2 spin liquid, which impacts on other anyon excitations especially leading to the confinement of spinon excitations. By numerical exact diagonalization of the dimer model, we directly measure the vison condensation using vison string operators, and explicitly check a confining potential acting on spinon excitations in the VBS state. It is observed that topological degeneracy of the spin-liquid state is lifted concomitantly with the vison condensation. The dimer ordering pattern of the VBS state is identified by investigating dimer structure factor. Furthermore, we find an interesting state that exhibits features of spin liquid and VBS simultaneously. We discuss the origin of the mixed behaviors and possible scenarios expected in thermodynamic limit. This work complements the previous analytical studies on the dimer model [ and ] by providing numerical evidences on the vison condensation and the spinon confinement in the Z2SL-to-VBS transition. Published by the American Physical Society 2024

Gapless dynamic magnetic ground state in the charge-gapped trimer iridate Ba4NbIr3O12

We present an experimental investigation of the magnetic ground state in Ba4NbIr3O12, a fractional valent trimer iridate. X-ray absorption and photoemission spectroscopy show that the Ir valence lies between 3+ and 4+ while Nb is pentavalent. Combined dc/ac magnetization, specific heat, and muon spin rotation/relaxation (µSR) measurements reveal no magnetic phase transition down to 0.05 K. Despite a significant Weiss temperature (ΘW∼−15 to −25 K) indicating antiferromagnetic correlations, a quantum spin-liquid (QSL) phase emerges and persists down to 0.1 K. This state likely arises from geometric frustration in the edge-sharing equilateral triangle Ir network. Our µSR analysis reveals a two-component depolarization, arising from the coexistence of rapidly (90%) and slowly (10%) fluctuating Ir moments. Powder x-ray diffraction and Ir-L3edge x-ray absorption fine structure spectroscopy identify 8–10% Nb/Ir site-exchange, reducing frustration within part of the Ir network, and likely leading to the faster muon spin relaxation, while the structurally ordered Ir ions remain highly geometrically frustrated, giving rise to the rapidly spin-fluctuating QSL ground state. At low temperatures, the magnetic specific heat varies as γT+αT2, indicating gapless spinon excitations, and possible Dirac QSL features with linear spinon dispersion, respectively. Published by the American Physical Society 2024

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.

Strain-tuned incompatible magnetic exchange-interaction in La2NiO4

Magnetic frustration is a route for novel ground states, including spin liquids and spin ices. Such frustration can be introduced through either lattice geometry or incompatible exchange interactions. Here, we find that epitaxial strain is an effective tool for tuning antiferromagnetic exchange interactions in a square-lattice system. By studying the magnon excitations in La2NiO4 films using resonant inelastic x-ray scattering, we show that the magnon displays substantial dispersion along the antiferromagnetic zone boundary, at energies that depend on the lattice of the film’s substrate. Using first principles simulations and an effective spin model, we demonstrate that the antiferromagnetic next-nearest neighbour coupling is a consequence of the two-orbital nature of La2NiO4. Altogether, we illustrate that compressive epitaxial strain enhances this coupling and, as a result, increases the level of incompatibility between exchange interactions within a model square-lattice system.

Quantum state preparation of topological chiral spin liquids via Floquet engineering

Quantum state preparation of topological chiral spin liquids via Floquet engineering

Candidate quantum spin liquids on the maple-leaf lattice

Candidate quantum spin liquids on the maple-leaf lattice

Time-Dependent Variational Principle with Controlled Bond Expansion for Matrix Product States.

We present a controlled bond expansion (CBE) approach to simulate quantum dynamics based on the time-dependent variational principle (TDVP) for matrix product states. Our method alleviates the numerical difficulties of the standard, fixed-rank one-site TDVP integrator by increasing bond dimensions on the fly to reduce the projection error. This is achieved in an economical, local fashion, requiring only minor modifications of standard one-site TDVP implementations. We illustrate the performance and accuracy of CBE-TDVP with several numerical examples on finite quantum lattices, including new results on bipolaron formation in the Peierls-Hubbard model and spin pumping via adiabatic flux insertion in a chiral spin liquid.

Twisted graphene superlattices: resonating valence bond states and magnetic properties

Resonating valence bond (RVB) states are fundamental for understanding quantum spin liquids in two-dimensional (2D) systems. The RVB state is a collective phenomenon in which spins are uncoupled. 2D lattices such as triangular, honeycomb, and dice lattices were investigated using the Hubbard model and exact diagonalization method. We analyzed the total spin, spin–spin correlation functions, local magnetic moments, and spin and charge gaps as a function of on-site Coulomb repulsion, electron concentration, and electronic hopping parameters. Phase diagrams showed that RVB states can live in half-filled and hole-doped anisotropic triangular lattices. We found two types of RVB states: one in the honeycomb sublattice and the other in the centered hexagons in the triangular lattices. Owing to the novel discovery of exotic magnetic ordering in triangular moiré patterns in twisted bilayer graphene and transition metal dichalcogenide systems, our results provide physical insights into the onset of magnetism and possible spin liquid states in these layered materials.