Abstract
I studied the non-equilibrium response of an initial Néel state under time evolution with the Kitaev honeycomb model. With isotropic interactions (J_x = J_y = J_zJx=Jy=Jz) the system quickly loses its antiferromagnetic order and crosses over into a steady state valence bond solid, which can be inferred from the long-range dimer correlations. There is no signature of a dynamical phase transition. Upon including anisotropy (J_x = J_y \neq J_zJx=Jy≠Jz), an exponentially long prethermal regime appears with persistent magnetization oscillations whose period derives from an effective toric code.
Highlights
Quantum spin liquids [1] are intriguing forms of matter characterized by the absence of magnetic order and the presence of long-range entanglement
One might wonder whether these opposite extremes can be connected under a rapid change of external parameters. Such a rapid change is known as a quench [2,3], and this set-up has lead to the prediction and observation of dynamical phase transitions. [4,5,6] For example, in the transverse field Ising model, time evolution of an initial magnetic state under a Hamiltonian with a trivial paramagnetic ground state leads to nonanalytic behavior in the return amplitude at certain times after the quench
The dynamics studied here can be viewed as a quench through a quantum critical point separating an antiferromagnetic phase and a paramagnetic spin liquid phase
Summary
Quantum spin liquids [1] are intriguing forms of matter characterized by the absence of magnetic order and the presence of long-range entanglement. In order to time evolve with the Kitaev model I first express the Néel state as a superposition of different gauge fields configurations. Starting from this initial state I will compute the time evolution using the Kitaev honeycomb model The spin liquid ground state of the Kitaev honeycomb model is in the zero-flux sector, meaning all gauge fields ujα are the same. In the extreme case that one has an initial state that lies purely within one flux sector, the corresponding quench dynamics is that of a non-interacting fermion model This is done in, for example, Refs. Much of our results deviate from this precisely because we intertwined various flux sectors by choosing an initial Néel state
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