Quantum criticality beyond thermodynamic stability
- 1Dartmouth College
- 2Boston College
- 3SUNY Polytechnic Institute
Abstract
For a many-body system in equilibrium, described by a thermodynamically stable Hamiltonian, quantum criticality is associated with changes of the ground state. However, there exist relevant models, notably, certain quadratic bosonic Hamiltonians (QBHs), which fail to have a ground state. From a dynamical system-theory standpoint, QBHs can be dynamically stable or unstable. We show that criticality is a meaningful concept for the entire class of QBHs that are dynamically stable or at the boundary of instability - regardless of thermodynamic stability - and that the key state is a naturally defined quasiparticle vacuum. This state is Gaussian, and coincides with the ground state if the QBH is thermodynamically stable. We identify a relevant spectral gap, the Krein gap, associated to the minimal spectral separation between creation and annihilation operators, and show that the quasiparticle vacuum is unique if and only if the Krein gap is positive. We further prove that, for dynamically stable QBHs with finite-range couplings, correlations are exponentially bounded unless the Krein gap closes - which is associated with one of two kinds of spectral degeneracies: an exceptional point (a free-particle-like collective mode) or a Krein collision (often a bosonic zero mode). Accordingly, long-range correlations can ensue in the quasiparticle vacuum. We conclude that (i) the Krein gap takes the role of the spectral gap for dynamically stable QBHs; (ii) the boundary of dynamical stability and criticality (associated to exceptional points) or multicriticality (associated to Krein collisions) are one and the same. Alongside long-range correlations, we find that bosonic critical behavior beyond thermodynamic stability is witnessed by the scaling of the entanglement entropy and other indicators of criticality from information geometry. Our framework opens the door to investigating all dynamically stable QBHs through the lens of critical phenomena, including thermodynamically unstable models from photonics, opto-mechanics, cavity-QED, and magnonics.
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BibTeX
@article{ughrelidze2026quantum,
title = {{Quantum criticality beyond thermodynamic stability}},
author = {Mariam Ughrelidze and Vincent Flynn and Emilio Cobanera and Lorenza Viola},
journal = {New Journal of Physics},
year = {2026},
month = oct,
doi = {10.1088/1367-2630/aeb687},
url = {https://iopscience.iop.org/article/10.1088/1367-2630/aeb687},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Quantum criticality beyond thermodynamic stability
AU - Mariam Ughrelidze
AU - Vincent Flynn
AU - Emilio Cobanera
AU - Lorenza Viola
PY - 2026
DA - 2026/10/20
JO - New Journal of Physics
DO - 10.1088/1367-2630/aeb687
UR - https://iopscience.iop.org/article/10.1088/1367-2630/aeb687
AB - For a many-body system in equilibrium, described by a thermodynamically stable Hamiltonian, quantum criticality is associated with changes of the ground state. However, there exist relevant models, notably, certain quadratic bosonic Hamiltonians (QBHs), which fail to have a ground state. From a dynamical system-theory standpoint, QBHs can be dynamically stable or unstable. We show that criticality is a meaningful concept for the entire class of QBHs that are dynamically stable or at the boundary of instability - regardless of thermodynamic stability - and that the key state is a naturally defined quasiparticle vacuum. This state is Gaussian, and coincides with the ground state if the QBH is thermodynamically stable. We identify a relevant spectral gap, the Krein gap, associated to the minimal spectral separation between creation and annihilation operators, and show that the quasiparticle vacuum is unique if and only if the Krein gap is positive. We further prove that, for dynamically stable QBHs with finite-range couplings, correlations are exponentially bounded unless the Krein gap closes - which is associated with one of two kinds of spectral degeneracies: an exceptional point (a free-particle-like collective mode) or a Krein collision (often a bosonic zero mode). Accordingly, long-range correlations can ensue in the quasiparticle vacuum. We conclude that (i) the Krein gap takes the role of the spectral gap for dynamically stable QBHs; (ii) the boundary of dynamical stability and criticality (associated to exceptional points) or multicriticality (associated to Krein collisions) are one and the same. Alongside long-range correlations, we find that bosonic critical behavior beyond thermodynamic stability is witnessed by the scaling of the entanglement entropy and other indicators of criticality from information geometry. Our framework opens the door to investigating all dynamically stable QBHs through the lens of critical phenomena, including thermodynamically unstable models from photonics, opto-mechanics, cavity-QED, and magnonics.
SN - 1367-2630
ER -