engleski

Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise

We investigated quantum critical behaviours in the non-equilibrium steady state of a XXZ spin chain with boundary Markovian noise using the Fisher information. The latter represents the distance between two infinitesimally close states, and its superextensive size scaling witnesses a critical behaviour due to a phase transition, since all the interaction terms are extensive. Perturbatively in the noise strength, we found superextensive Fisher information at anisotropy |Δ|⩽1 and irrational arccosΔπ irrespective of the order of two non- commuting limits, i.e. the thermodynamic limit and the limit of sending arccosΔπ to an irrational number via a sequence of rational approximants. From this result we argue the existence of a non- equilibrium quantum phase transition with a critical phase |Δ|⩽1. From the non- superextensivity of the Fisher information of reduced states, we infer that this non-equilibrium quantum phase transition does not have local order parameters but has non-local ones, at least at | Δ|=1. In the non-perturbative regime for the noise strength, we numerically computed the reduced Fisher information which lower bounds the full state Fisher information, and is superextensive only at |Δ|=1. Form the latter result, we derived local order parameters at |Δ|=1 in the non- perturbative case. The existence of critical behaviour witnessed by the Fisher information in the phase |Δ|<1 is still an open problem. The Fisher information also represents the best sensitivity for any estimation of the control parameter, in our case the anisotropy Δ, and its superextensivity implies enhanced estimation precision which is also highly robust in the presence of a critical phase.

non-equilibrium phase transitions ; non-equilibrium steady state ; open quantum systems ; Fisher information

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