A quantum spin liquid hosts massive quantum entanglement whose identification is one of the most significant problems in physics. Yet, its detection is known to be notoriously difficult because of featureless properties without a symmetry order parameter. Here, we demonstrate dynamic signatures of a quantum spin liquid state by investigating Kitaev's spin model on the hyper-honeycomb lattice, where a quantum spin liquid state is stabilized as a stable thermodynamic phase. The real-time dynamics of spin correlation function is obtained with the large-scale quantum Monte Carlo simulation. We find the onset of a characteristic oscillation in dynamic local spin correlation as entering the quantum spin liquid phase. Our results show that a quantum spin liquid may be characterized by a sharp growth of coherent spin dynamics of the system, which we name as a dynamic order. We further propose that a dynamic-order may naturally detect a featureless thermal phase transition, which has been reported in a class of strongly correlated materials.
Abstract Many-body entanglement properties of quantum spin liquids (QSLs), persisting at arbitrarily long distances, have been intensely explored over the past two decades, but mostly for QSLs viewed as closed quantum systems. However, in experiments and potential quantum computing applications, candidate materials for this exotic phase of quantum matter will always interact with a dissipative environment, such as the one generated by bosonic quasiparticles in solids at finite temperature. Here we investigate both the stability and spatial distribution of entanglement for the Kitaev model of QSL, which is made open by its sudden coupling to an infinite bosonic bath of Caldeira–Leggett type and then time-evolved in both Markovian and non-Markovian regimes. From the time-dependent density matrix of QSL subregions, we extract genuine multipartite negativity (GMN), quantum Fisher information, spin–spin correlators, and the expectation value (EV) of the Wilson loop operator. In particular, time dependence of GMN offers the most penetrating insights: ( i ) in the Markovian regime, it remains nonzero only in hexagonal loopy subregions of QSL (as also discovered very recently for closed QSLs), eventually vanishing on the same timescale on which the EV of the Wilson loop operator vanishes; ( ii ) in the non-Markovian regime with pronounced memory effects, surprisingly, GMN remains nonzero up to much higher temperatures. In addition, the non-Markovian dynamics generates emergent interactions between spins, thereby opening avenues for tailoring properties of QSL via engineering of dissipation.
The quantum spin liquid is an enigmatic entity that is often hard to characterize within the conventional framework of condensed matter physics. We here present theoretical and numerical evidence for the characterization of a quantum spin liquid phase extending from the exact ground state to a finite critical temperature. We investigate a three-dimensional variant of the Kitaev model on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables on a diamond lattice. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from the quantum spin liquid to a paramagnet at a finite critical temperature
Tc, accompanied by a divergent singularity of the specific heat. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above
Tc, while it obeys the Curie law at high temperature and approaches a nonzero Van Vleck--type constant at low temperature. Although the susceptibility changes continuously at
Tc, its temperature derivative shows a critical divergence at
Tc. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables or of the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition can be interpreted as one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. The correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently discovered hyperhoneycomb compound $\ensuremath{\beta}$-
Li2IrO3 is mentioned.