Rigorous existence and location of quantum phase transitions in lattice Hamiltonian systems

• URL: http://arxiv.org/abs/2608.20209v1
• Date: Thu, 20 Aug 2026 16:09:27 GMT
• Title: Rigorous existence and location of quantum phase transitions in lattice Hamiltonian systems
• Abstract summary: We extend the analysis of the class of quantum phase transitions (QPTs) that can be interpreted as condensations in state space.<n>Our analysis suggests that, under conditions typically satisfied in physical contexts, any QPT taking place in lattice systems can be interpreted as a condensation in state space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We extend the analysis of the class of quantum phase transitions (QPTs) that can be interpreted as condensations in state space, first introduced in [M. Ostilli and C. Presilla, J. Phys. A 54, 055005 (2021)], by generalizing the arguments of [M. Ostilli and C. Presilla, Phys. Rev. Lett. 127, 040601 (2021)] to prove the existence and determine the location (via simple bounds) of QPTs in general one-parameter lattice Hamiltonians. Unlike our original formulation, this extension also encompasses second-order QPTs, for which we provide the explicit example of the transverse-field Ising model. Our analysis suggests that, under conditions typically satisfied in physical contexts, any QPT taking place in lattice systems can be interpreted as a condensation in state space.

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