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- W4313452308 abstract "Abstract We formalize and prove the extension to finite temperature of a class of quantum phase transitions, acting as condensations in the space of states, recently introduced and discussed at zero temperature (Ostilli and Presilla 2021 J. Phys. A: Math. Theor. 54 055005). In details, we find that if, for a quantum system at canonical thermal equilibrium, one can find a partition of its Hilbert space <?CDATA $mathcal{H}$?> into two subspaces, <?CDATA $mathcal{H}_mathrm{cond}$?> and <?CDATA $mathcal{H}_mathrm{norm}$?> , such that, in the thermodynamic limit, <?CDATA $dim mathcal{H}_mathrm{cond}/ dim mathcal{H} to 0$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll><mml:mrow><mml:mi>dim</mml:mi><mml:msub><mml:mi>ℋ</mml:mi><mml:mrow><mml:mtext>cond</mml:mtext></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:mi>dim</mml:mi><mml:mi>ℋ</mml:mi><mml:mo>→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math> and the free energies of the system restricted to these subspaces cross each other for some value of the Hamiltonian parameters, then, the system undergoes a first-order quantum phase transition driven by those parameters. The proof is based on an exact probabilistic representation of quantum dynamics at an imaginary time identified with the inverse temperature of the system. We also show that the critical surface has universal features at high and low temperatures." @default.
- W4313452308 created "2023-01-06" @default.
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- W4313452308 date "2022-12-16" @default.
- W4313452308 modified "2023-10-16" @default.
- W4313452308 title "Finite temperature quantum condensations in the space of states: general proof" @default.
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- W4313452308 doi "https://doi.org/10.1088/1751-8121/acad49" @default.
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