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Register a new userQuantum spin liquid at finite temperature: proximate dynamics and persistent typicality
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Added by
Ioannis Rousochatzakis
Publication date
2018
fields
Physics
and research's language is
English
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Quantum spin liquids are long-range entangled states of matter with emergent gauge fields and fractionalized excitations. While candidate materials, such as the Kitaev honeycomb ruthenate $alpha$-RuCl$_3$, show magnetic order at low temperatures $T$, here we demonstrate numerically a dynamical crossover from magnon-like behavior at low $T$ and frequencies $omega$ to long-lived fractionalized fermionic quasiparticles at higher $T$ and $omega$. This crossover is akin to the presence of spinon continua in quasi-1D spin chains. It is further shown to go hand in hand with persistent typicality down to very low $T$. This aspect, which has also been observed in the spin-1/2 kagome Heisenberg antiferromagnet, is a signature of proximate spin liquidity and emergent gauge degrees of freedom more generally, and can be the basis for the numerical study of many finite-$T$ properties of putative spin liquids.
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Single-crystal x-ray diffraction, density-functional band-structure calculations, and muon spin relaxation ($mu$SR) are used to probe pressure evolution of the triangular spin-liquid candidate YbMgGaO$_4$. The rhombohedral crystal structure is retained up to at least 10 GPa and shows a nearly uniform compression along both in-plane and out-of-plane directions, whereas local distortions caused by the random distribution of Mg$^{2+}$ and Ga$^{3+}$ remain mostly unchanged. The $mu$SR data confirm persistent spin dynamics up to 2.6 GPa and down to 250 mK with no change in the muon relaxation rate. Longitudinal-field $mu$SR reveals power-law behavior of the spin-spin autocorrelation function, both at ambient pressure and upon compression.
The quasi two-dimensional Mott insulator $alpha$-RuCl$_3$ is proximate to the sought-after Kitaev quantum spin liquid (QSL). In a layer of $alpha$-RuCl$_3$ on graphene the dominant Kitaev exchange is further enhanced by strain. Recently, quantum oscillation (QO) measurements of such $alpha$-RuCl$_3$ / graphene heterostructures showed an anomalous temperature dependence beyond the standard Lifshitz-Kosevich (LK) description. Here, we develop a theory of anomalous QO in an effective Kitaev-Kondo lattice model in which the itinerant electrons of the graphene layer interact with the correlated magnetic layer via spin interactions. At low temperatures a heavy Fermi liquid emerges such that the neutral Majorana fermion excitations of the Kitaev QSL acquire charge by hybridising with the graphene Dirac band. Using ab-initio calculations to determine the parameters of our low energy model we provide a microscopic theory of anomalous QOs with a non-LK temperature dependence consistent with our measurements. We show how remnants of fractionalized spin excitations can give rise to characteristic signatures in QO experiments.
The Kitaev quantum spin liquid epitomizes an entangled topological state, for which two flavors of fractionalized low-energy excitations are predicted: the itinerant Majorana fermion and the Z2 gauge flux. Detection of these excitations remains challenging, because of their fractional quantum numbers and non-locality. It was proposed recently that fingerprints of fractional excitations are encoded in the phonon spectra of Kitaev quantum spin liquids through a novel fractional-excitation-phonon coupling. Here, we uncover this effect in $alpha$-RuCl3 using inelastic X-ray scattering with meV resolution. At high temperature, we discover interlaced optical phonons intercepting a transverse acoustic phonon between 3 and 7 meV. Upon decreasing temperature, the optical phonons display a large intensity enhancement near the Kitaev energy, JK~8 meV, that coincides with a giant acoustic phonon softening near the Z2 gauge flux energy scale. This fractional excitation induced phonon anomalies uncover the key ingredient of the quantum thermal Hall effect in $alpha$-RuCl3 and demonstrates a proof-of-principle method to detect fractional excitations in topological quantum materials.
Topological spin liquids in two spatial dimensions are stable phases in the presence of a small magnetic field, but may give way to field-induced phenomena at intermediate field strengths. Sandwiched between the low-field spin liquid physics and the high-field spin-polarized phase, the exploration of magnetic phenomena in this intermediate regime however often remains elusive to controlled analytical approaches. Here we numerically study such intermediate-field magnetic phenomena for two representative Kitaev models (on the square-octagon and decorated honeycomb lattice) that exhibit either Abelian or non-Abelian topological order in the low-field limit. Using a combination of exact diagonalization and density matrix renormalization group techniques, as well as linear spin-wave theory, we establish the generic features of Kitaev spin liquids in an external magnetic field. While ferromagnetic models typically exhibit a direct transition to the polarized state at a relatively low field strength, antiferromagnetic couplings not only substantially stabilizes the topological spin liquid phase, but generically lead to the emergence of a distinct field-induced intermediate regime, separated by a crossover from the high-field polarized regime. Our results suggest that, for most lattice geometries, this regime generically exhibits significant spin canting, antiferromagnetic spin-spin correlations, and an extended proximate spin liquid regime at finite temperatures. Notably, we identify a symmetry obstruction in the original honeycomb Kitaev model that prevents, at least for certain field directions, the formation of such canted magnetism without breaking symmetries -- consistent with the recent numerical observation of an extended gapless spin liquid in this case.
We study trace estimators for equilibrium thermodynamic observables that rely on the idea of typicality and derivatives thereof such as the finite-temperature Lanczos method (FTLM). As numerical examples quantum spin systems are studied. Our initial aim was to identify pathological examples or circumstances, such as strong frustration or unusual densities of states, where these methods could fail. Instead we failed with the attempt. All investigated systems allow such approximations, only at temperatures of the order of the lowest energy gap the convergence is somewhat slower in the number of random vectors over which observables are averaged.
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