Symmetry Keeps Fermions Pure in a Noisy World
Quantumness is famously fragile. Decoherence, particle loss, and other dissipative processes typically destroy delicate quantum superpositions, causing open quantum systems to behave classically. This universal, inevitable fate suggests that, even when a system’s constituents are fully quantum, its nonequilibrium critical points could be described by classical universality classes. That is, the system could belong to a group whose behavior near a critical point is identical and scale invariant regardless of microscopic details. In a new theoretical study, Rohan Mittal and his collaborators at the University of Cologne in Germany have overturned this expectation for open systems of fermions [1]. They identified a particular symmetry, which, if present, blocks most of the noise channels that would ordinarily wash out quantum behavior at large scales. With this protection, the fermions remain fully coherent as the system is driven through a phase transition, and the large-scale physics remains governed by the fascinating laws of quantum mechanics. The conceptual impact of this work may extend well beyond quantum critical phenomena. If the protection can be generalized, it could serve as a design principle for robust quantum devices that must be continuously measured and controlled.
Universality is a central concept in modern physics, stating that microscopically distinct systems can display the same behavior at long distances and large time scales. Manifesting this principle are the scaling laws that govern continuous thermal phase transitions, such as the critical point at which water and vapor become indistinguishable. These universality classes are typically labelled by dimensionality, symmetry, and other simple properties. When we move from classical to quantum physics, the landscape expands. Quantum phase transitions in the system’s ground state are driven by tuning parameters in the system’s Hamiltonian rather than by raising or lowering the temperature [2]. Here, quantum ingredients take center stage. Particle statistics, geometric phases, and topology naturally extend the classification of matter, making way for phenomena that lack classical counterparts.
Thanks to the rapid development of quantum science and technology over the past decade, physicists can now drive, measure, and control many-body systems with exquisite precision. Unfortunately, wielding that ability typically introduces particle loss and dephasing. These “open” dynamics can nevertheless be captured by one of two theoretical frameworks: Lindblad master equations and Keldysh field theory [3]. Both track coherent evolution alongside dissipation on small length scales and timescales. However, trying to obtain an effective description that works on large scales can be discouraging. Environmental fluctuations usually wash out quantum correlations and steer systems toward classical behavior, frustrating attempts to explore nonequilibrium quantum universality classes. A dissipative Bose-Einstein condensate exemplifies the problem [4]. In equilibrium, the condensate supports dissipationless phonons. However, when it’s driven, its long-wavelength dynamics can be described by a classical universality class [5]. Nevertheless, theorists have suspected that, under the right conditions, coherence can be protected on large scales.
Mittal and his collaborators devised precisely such a scenario. By constructing a microscopic lattice model, they demonstrated that fermions remain “pure” across a dynamical transition between two topologically distinct steady states, despite the presence of a thermal bath. Here, fermion purity means that the fermions remain fully coherent and can be described by a quantum wave function. The key to the proposal is the use of what the researchers call structured dissipation. They formulated the system–bath interactions so that the resulting steady states correspond to filled, noninteracting fermion modes that are immune to decoherence. Such dissipationless states are usually known as dark states. Adjusting a single tuning parameter, they found that they could drive a transition between two topologically distinct dark states [6]. That theoretical move yielded a simple realization of fermionic quantum criticality that maintains full coherence.
Unfortunately, the purity of fermions in such constructions can vanish in the presence of interactions among fermions or between fermions and bosonic fields. Mittal and his collaborators provided a novel resolution to this issue based on a symmetry principle. They identified an emergent global symmetry and a novel antiunitary symmetry, which protect the purity of the state. Together, the two symmetries constitute the so-called fermionic dark-state symmetry. The antiunitary symmetry relies on the antisymmetry of fermions’ wave functions and has no direct analogue in bosonic systems. Imposing this symmetry on a generic system guarantees that the fermion state remains pure under arbitrary perturbations (Fig. 1). Moreover, it enabled the researchers to devise an effective field theory that contains all the important terms—those that dominate in the long-wavelength limit—compatible with the symmetry.
Having derived this effective field theory, Mittal and his collaborators went on to analyze it using a perturbative renormalization-group expansion. The analysis revealed several features that resemble certain thermal transitions in magnetic systems. Despite the similarities, the effective theory differs because it contains critical fermionic modes, and its coupling constants can become complex, clearly highlighting its quantum and nonequilibrium nature.
Relating this theoretical discovery to realistic experimental systems will pose a new challenge. Of particular interest is the identification of relevant setups that naturally satisfy the fermionic dark-state symmetry, as it could pave the way for the experimental study of nonequilibrium quantum criticality. Extending the current study to other symmetry classes and investigating the consequent nonequilibrium critical points is also an interesting direction. Lastly, it’s important to validate Mittal and his collaborators’ predictions by performing advanced numerical simulations of either the effective theory or the lattice model. Overall, the message of this work is optimistic. In theory, at least, a quantum system can be controlled and driven without decohering it.
References
- R. Mittal et al., “Fermion quantum criticality far from equilibrium,” Phys. Rev. X 16, 011069 (2026).
- S. Sachdev, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, 2011)[Amazon][WorldCat].
- A. Kamenev, Field Theory of Non-Equilibrium Systems, 2nd ed. (Cambridge University Press, Cambridge, 2023)[Amazon][WorldCat].
- L. M. Sieberer et al., “Keldysh field theory for driven open quantum systems,” Rep. Prog. Phys. 79, 096001 (2016).
- M. Kardar et al., “Dynamic scaling of growing interfaces,” Phys. Rev. Lett. 56, 889 (1986).
- C.-K. Chiu et al., “Classification of topological quantum matter with symmetries,” Rev. Mod. Phys. 88, 035005 (2016).