Quantum Phase Transitions in Many-Body Systems

Quantum phase transitions occur at zero temperature when a many-body system’s ground state changes its qualitative character as an external parameter is varied. Unlike classical phase transitions driven by thermal fluctuations, these transitions are governed by quantum fluctuations and entanglement. At a quantum critical point, long-range correlations diverge and the system exhibits universal scaling laws. Prototypical models include the transverse-field Ising chain, the Bose–Hubbard model and the Dicke and Lipkin–Meshkov–Glick spin models, which capture competing interactions and tunnelling effects. Theoretical approaches range from renormalisation-group analyses and conformal field theory to tensor-network algorithms and quantum Monte Carlo. Experimentally, ultracold atoms in optical lattices, trapped ions and superconducting circuits have realised tunable Hamiltonians that traverse quantum critical points, revealing critical exponents through measurements of order parameters, excitation gaps and out-of-time-ordered correlators. The study of quantum phase transitions underpins developments in quantum simulation, topological matter and materials with exotic magnetic or superconducting phases, offering routes to engineer robust quantum states and to explore nonequilibrium dynamics across criticality.

Research from Nature Portfolio

Recent studies have established a deep analogy between classical rigid-body dynamics and critical phenomena in a generalised Lipkin–Meshkov–Glick model. By mapping the motion of an asymmetric rotor to spin-squeezing Hamiltonians, researchers have expanded the catalogue of accessible quantum phase transitions, including one-axis and two-axis twisting schemes. This framework has further enabled the exploration of topological transitions in periodically driven systems, predicting the emergence of time-crystalline order in a Floquet-engineered spin ensemble. The classical perspective enriches our understanding of quantum criticality by linking macroscopic mechanical instabilities to many-body entanglement and by suggesting novel control protocols for quantum simulators.

Quantum Phase Transitions in Many-Body Systems publication trend

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

Technical terms

Quantum phase transition: A zero-temperature transition between distinct ground states driven by a non-thermal control parameter.

Order parameter: A measurable quantity that is zero in one phase and non-zero in another, indicating symmetry breaking.

Quantum critical point: The precise parameter value at which a quantum phase transition occurs, featuring divergent correlation length and vanishing energy gap.

Entanglement entropy: A measure of quantum correlations between subsystems, often used to characterise critical scaling.

Floquet engineering: The design of effective Hamiltonians via periodic driving to access novel phases and transition pathways.

References

1. Analogies of the classical Euler top with a rotor to spin squeezing and quantum phase transitions in a generalized Lipkin-Meshkov-Glick model. Scientific Reports (2018).
2. Excited-State Phase Diagram of a Ferromagnetic Quantum Gas. Physical Review Letters (2023).
3. Quantum Phase Transitions in periodically quenched systems. Quantum (2024).