Year: 2026
Type: article
Abstract: For a many-body system in equilibrium, described by a thermodynamically stable Hamiltonian, quantum criticality is associated with structural changes of the many-body ground state. However, there exist physically relevant models, notably, certain quadratic bosonic Hamiltonians (QBHs), which fail to have a ground state. From a dynamical system-theory standpoint, QBHs can be either 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 for such QBHs is a naturally and unambiguously defined quasiparticle vacuum (QPV). 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 QPV is unique when the Krein gap is positive. In addition, we 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 (physically, a free-particle-like collective mode) or a Krein collision (often a bosonic zero mode). As a consequence, long-range correlations can ensue in the QPV. We conclude that (i) the Krein gap takes the role of the spectral gap for dynamically stable QBHs, and (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 equilibrium criticality from information geometry. Hence, 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.
Source: New Journal of Physics
Institutions: Dartmouth College, Boston College, SUNY Polytechnic Institute
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,610
OpenAlex ID: W7160521221