Finite temperature quantum condensations in the space of states: General Proof

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 \textit{J. Phys. A: Math. Theor.} \textbf{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 $\mathcal{H}$ into two subspaces, ${\mathcal{H}}_{\mathrm{cond}}$ and ${\mathcal{H}}_{\mathrm{norm}}$, such that, in the thermodynamic limit, $\dim {\mathcal{H}}_{\mathrm{cond}}/\dim \mathcal{H}\to 0$ 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 temperature of the system. We also show that the critical surface has universal features at high and low temperatures.

arXiv comment18 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2203.05803

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Cited by in corpus (1)

• Finite temperature quantum condensations in the space of states: a new perspective for quantum annealing