Dynamical Quantum Phase Transitions in Quantum Systems

Dynamical quantum phase transitions (DQPTs) extend the concept of equilibrium criticality into the time domain by identifying nonanalyticities in the return probability amplitude of a quantum system following a rapid change in its Hamiltonian. These singular points, termed critical times, manifest through cusps or kinks in the Loschmidt echo or related rate functions. In both isolated and open quantum systems, DQPTs have been observed across a spectrum of platforms including ultracold atoms, trapped ions and engineered spin systems. The phenomenology of DQPTs often parallels that of equilibrium phase transitions—exhibiting scaling laws, universality classes and order-parameter dynamics—yet encompasses genuinely nonequilibrium signatures such as entanglement-driven transitions and topological robustness. Theoretical frameworks range from exact solutions in integrable models to random-matrix and field-theoretical approaches for nonintegrable dynamics. Finite-size effects and bath coupling modify critical behaviours, revealing anomalous transitions beyond conventional two-level oscillations. Beyond their fundamental interest, DQPTs offer routes to probe coherence, correlations and thermalisation in many-body systems and hold promise for characterising quantum information protocols and nonequilibrium materials with tailored dynamical responses.

Research from Nature Portfolio

Recent studies have demonstrated critical scaling in time during the relaxation of an open quantum system, realised via individual atomic spins coupled dissipatively to an ultracold bath. Through finite-size scaling of entropy dynamics, a temporal critical point was identified at which a characteristic correlation length diverges, governed by universal exponents independent of microscopic details. Complementing this, investigations into low-dimensional disordered systems have uncovered anomalous dynamical quantum phase transitions induced by spatial correlations in disorder. Quenches between ordered and random Hamiltonians revealed nonanalytic return-rate behaviour driven by infinite-correlation lengths, along with signatures of delocalisation transitions, thereby establishing a new paradigm of correlation-induced nonequilibrium criticality. These findings extend DQPT methodologies to open and disordered settings, underscoring the universality and tunability of nonequilibrium critical phenomena.

Dynamical Quantum Phase Transitions in Quantum Systems publication trend

The graph below shows the total number of articles in dynamical quantum phase transitions in quantum systems across all publications each year (not limited to Nature Index journals).

Technical terms

Dynamical quantum phase transition: A sudden, nonanalytic change in the time evolution of a quantum system’s return amplitude following a rapid parameter quench.

Loschmidt echo: The overlap between an initial quantum state and its time-evolved counterpart, used to detect temporal singularities.

Quench: A rapid change of one or more parameters in a system’s Hamiltonian, driving it out of equilibrium.

Critical time: The moment at which a nonanalyticity appears in the Loschmidt echo or rate function, signalling a DQPT.

Order parameter: A measure that distinguishes different dynamical phases by adopting distinct values on either side of a transition.

Thermodynamic limit: The idealised regime of infinite system size, in which finite-size corrections to critical behaviour vanish.

References

1. Indication of critical scaling in time during the relaxation of an open quantum system. Nature Communications (2024).
2. Dynamical quantum phase transitions from random matrix theory. Quantum (2024).
3. Anomalous correlation-induced dynamical phase transitions. Scientific Reports (2023).