When quantum criticality has no ground state

A broader way to think about criticality

In the familiar picture of quantum criticality, a system’s ground state changes sharply as conditions such as an interaction strength are varied. That framework assumes the system has a stable lowest-energy state. Some quadratic bosonic Hamiltonians do not: their energy can fail to have a minimum, even when their dynamics remain stable. The distinction matters because a system can have well-behaved motion without being thermodynamically stable in the usual sense.

In this theoretical work, Mariam Ughrelidze and colleagues ask whether critical behavior can still be defined for such systems. Their answer is yes for quadratic bosonic Hamiltonians that are dynamically stable, or sit at the boundary of dynamical instability. The paper is an arXiv preprint, and this account is based on its abstract rather than a full-text review.

A vacuum without a lowest energy

The authors identify a state they call the quasiparticle vacuum (QPV). In accessible terms, it is a state defined by the system’s quasiparticle modes—the effective excitations used to describe its behavior. The QPV is Gaussian, a broad class of states whose properties can be characterized through correlations. When the Hamiltonian is thermodynamically stable, this state coincides with the ordinary ground state. When it is not, the QPV provides a different reference state for examining the system.

The paper also introduces the Krein gap. Rather than measuring the energy difference above a ground state, this quantity tracks the minimum spectral separation between modes associated with creating and annihilating quasiparticles. According to the authors, a positive Krein gap makes the QPV unique.

When correlations can reach farther

The central result links the closing of this gap to changes in the system’s spectrum. For dynamically stable models with finite-range couplings, the authors prove that correlations in the QPV are exponentially bounded unless the Krein gap closes. When it does close, correlations can become long-ranged.

The abstract identifies two kinds of spectral degeneracy associated with gap closure: an exceptional point or a Krein collision. The authors connect these cases to different forms of critical behavior, describing the former as criticality and the latter as multicriticality. In this framework, the boundary of dynamical stability aligns with the onset of these behaviors.

The paper further reports that entanglement entropy and other measures from information geometry can reveal this bosonic critical behavior, including beyond thermodynamic stability. These measures describe features of a state’s information and correlations; the abstract does not provide numerical examples or enough detail to assess how they perform in particular models.

What the result does—and does not—establish

The proposed framework expands the mathematical reach of quantum criticality: a conventional ground state is not always necessary, provided the system meets the stated dynamical conditions. It offers researchers a way to investigate dynamically stable bosonic models that would not fit neatly into a ground-state-based account.

This is a theoretical result, not evidence that a specific experiment has observed these transitions. The abstract says the framework could open investigations of models in photonics, cavity quantum electrodynamics and magnonics; it does not report experimental tests. Because the available source here is only the abstract, details of the proofs, model assumptions and proposed information-geometric indicators cannot be independently examined in this account. The work is a preprint, so its claims should also be read with the usual caution that accompanies research not established here as peer reviewed.

Source: arXiv:2605.04153v2.