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 intro- duced 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 H into two subspaces, Hcond and Hnorm, such that, in the thermodynamic limit, dimHcond/dimH → 0 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 temper- ature of the system. We also show that the critical surface has universal features at high and low temperatures.

Finite temperature quantum condensations in the space of states: general proof / Ostilli, Massimo; Presilla, Carlo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:50(2022), p. 505004. [10.1088/1751-8121/acad49]

Finite temperature quantum condensations in the space of states: general proof

Carlo Presilla
2022

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 intro- duced 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 H into two subspaces, Hcond and Hnorm, such that, in the thermodynamic limit, dimHcond/dimH → 0 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 temper- ature of the system. We also show that the critical surface has universal features at high and low temperatures.
2022
quantum phase transitions; finite temperature; condensation in the space of states; general proof; Grover model
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Finite temperature quantum condensations in the space of states: general proof / Ostilli, Massimo; Presilla, Carlo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 55:50(2022), p. 505004. [10.1088/1751-8121/acad49]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1665029
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