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Noise-driven quantum criticality · Around

2010

Noise-driven quantum criticality

Eisert, J., Prosen, T.

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We discuss a notion of quantum critical exponents in open quantum many-body systems driven by quantum noise.

We show that in translationally invariant quantum lattice models undergoing quasi-local Markovian dissipative processes, mixed states emerge as stationary points that show scaling laws for the divergence of correlation lengths giving rise to well-defined critical exponents.
The main new technical tool developed here is a complete description of steady states of free bosonic or fermionic translationally invariant systems driven by quantum noise: This approach allows to express all correlation properties in terms of a symbol, paralleling the Fisher-Hartwig theory used for ground state properties of free models.
We discuss critical exponents arising in bosonic and fermionic models.

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J. Eisert, PhD thesis (Potsdam, February 2001); G. Vidal and R. F. Werner, Phys. Rev. A 65
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J. Eisert, M. Cramer, and M. B. Plenio, Rev. Mod. Phys. 82
Original
2005
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To provide a complete classification of free dark states constitutes an interesting further perspective

Cited in the paper.

Only when viewed as a spin model, the noise becomes non-local as Jordan-Wigner strings arise

Cited in the paper.

This argument as such does not provide a bound to the spectral gap dictating the rate of convergence to this stationary point

Cited in the paper.