Dynamics of a Quantum Phase Transition

2005/03/31 by Wojciech H. Zurek, U. Dorner, Uwe Dorner +2 · 821 citations
Physics and Astronomy · #Condensed matter physics #Ising model #Opinion Dynamics and Social Influence #Phase transition #Physics #Quantum #Quantum critical point #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Quantum phases #Statistical physics #Superfluid film #Theoretical and Computational Physics #Zener diode #cond-mat.stat-mech #hep-ph #quant-ph

paper · pdf · doi:10.1103/physrevlett.95.105701

published in Physical Review Letters 95(10), 105701 (American Physical Society) · 4 pages, 3 figures. Replaced by revised version

openalex publication_date 2005/09/01 · arxiv created 2006/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.

Citations

• Defect formation and critical dynamics in the early Universe
• Observation of Magnetic Flux Generated Spontaneously During a Rapid Quench of Superconducting Films
• Defect Formation and Local Gauge Invariance
• Vortex String Formation in a 3D U(1) Temperature Quench
• Nonappearance of Vortices in Fast Mechanical Expansions of Liquid4Hethrough the Lambda Transition
• Topology of cosmic domains and strings

Cited by

• Rapid passage to ordered states in Rydberg atom arrays
• Dynamical Phase Transitions in Periodically Driving 1D Ising Model
• Infinite temperature spin dynamics in the asymmetric Hatsugai-Kohmoto model
• Out-of-equilibrium dynamics across the first-order quantum transitions of one-dimensional quantum Ising models
• Quantum Phase Transitions from Topology in Momentum Space
• Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions
• Achieving continuously tunable critical exponents for long-range spin systems simulated with trapped ions
• Scaling regimes in slow quenches within a gapped phase