Quantum criticality beyond thermodynamic stability

TL;DR

This paper extends the concept of quantum criticality to quadratic bosonic Hamiltonians that lack a ground state, linking stability, spectral properties, and entanglement behavior.

Contribution

It introduces a framework for understanding criticality in dynamically stable QBHs beyond thermodynamic stability, emphasizing the role of the Krein gap and quasiparticle vacuum.

Findings

Quantum criticality applies to stable or boundary QBHs regardless of thermodynamic stability.

The Krein gap determines the uniqueness of the quasiparticle vacuum and the nature of correlations.

Long-range correlations occur when the Krein gap closes, indicating criticality or multicriticality.

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. QBHs can be dynamically stable or unstable. We show the notion of criticality is meaningful 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. 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 spectral degeneracies: an exceptional point or a Krein collision. Consequently, long-range QPV correlations can ensue. Thus, the Krein gap takes the role of the spectral gap for dynamically stable QBHs, and the boundary of dynamical stability and criticality (associated to exceptional points) or multicriticality (associated to Krein collisions) are the same. We also 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. Our framework opens the door to investigating all dynamically stable QBHs through the lens of critical phenomena, including thermodynamically unstable ones from photonics, cavity-QED, and magnonics.