Non-Hermitian terms in a quantum Hamiltonian model processes such as gain and loss, radiation decay, or engineered dissipation that break conventional Hermiticity. Pioneering theoretical work by Carl Bender at Washington University in St. Louis introduced PT symmetry as a way non-Hermitian Hamiltonians can nonetheless exhibit real spectra, while Nimrod Moiseyev at Technion developed foundational techniques for resonances and complex eigenvalues in open quantum systems. These ideas reframe quantum phase transitions: rather than occurring solely from competing Hermitian terms, criticality can emerge from the balance of coherent dynamics and non-conservative channels.
How non-Hermitian terms alter critical points
Adding complex potentials or asymmetric couplings produces exceptional points, parameter values where eigenvalues and eigenvectors coalesce. At an exceptional point the usual spectral decomposition fails and small perturbations produce large responses. This changes the causes of phase change: dissipation or amplification can drive transitions that have no Hermitian analogue. The universality of critical behavior can be modified because scaling laws and correlation functions depend on non-unitary dynamics. The non-Hermitian skin effect, analyzed by Zhong Wang at Peking University, further alters bulk-boundary correspondence by piling eigenmodes at system edges, so that thermodynamic-limit intuitions from Hermitian systems become unreliable. Consequences include shifted critical points, asymmetric response functions, and the emergence of complex-valued order parameters whose real and imaginary parts encode loss-driven phenomena.
Experimental platforms and observed modifications
Experiments in photonic lattices and coupled waveguides realize controlled gain and loss and have directly observed PT-symmetry breaking and exceptional-point physics. Stefano Longhi at Politecnico di Milano and collaborators used optical systems to demonstrate transitions where mode behavior changes qualitatively as loss and gain are tuned, confirming theoretical predictions about altered phase structure. Cold-atom setups with engineered dissipation and electronic circuits emulate non-Hermitian lattice models, allowing observation of modified spectral topology and non-equilibrium steady states. Practically, exceptional points enhance sensitivity in sensors but also introduce fragility to noise, creating trade-offs in device design.
Beyond fundamental physics, these modifications have cultural and territorial relevance: photonics groups in Europe and Asia are translating non-Hermitian principles into integrated devices, affecting regional research priorities and industrial applications. Nuanced understanding of how openness and non-Hermiticity reshape critical phenomena is therefore essential both for accurate theory and for engineering next-generation quantum technologies.