Exactly solvable non-unitary time evolution in quantum critical systems I: Effect of complex spacetime metrics

Abstract

In this series of works, we study exactly solvable non-unitary time evolutions in one-dimensional quantum critical systems ranging from quantum quenches to time-dependent drivings. In this part I, we are motivated by the recent works of Kontsevich and Segal [1] and Witten [2] on allowable complex spacetime metrics in quantum field theories. In general, such complex spacetime metrics will lead to non-unitary time evolutions. In this work, we study the universal features of such non-unitary time evolutions based on exactly solvable setups. Various physical quantities including entanglement Hamiltonian and entanglement spectrum, entanglement entropy, and energy density at an arbitrary time can be exactly solved. Due to the damping effect introduced by the complex time, the excitations in the initial state are gradually damped out in time. The non-equilibrium dynamics exhibits universal features that are qualitatively different from the case of real-time evolutions. For instance, for an infinite system after a global quench, the entanglement entropy of the semi-infinite subsystem will grow logarithmically in time, in contrast to the linear growth in a real-time evolution. Moreover, we study numerically the time-dependent driven quantum critical systems with allowable complex spacetime metrics. It is found that the competition between driving and damping leads to a steady state with an interesting entanglement structure.

40 pages, many figures; v2: refs added

References in corpus (15)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Deriving covariant holographic entanglement
• Entanglement hamiltonians in two-dimensional conformal field theory
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Floquet conformal field theories with generally deformed Hamiltonians
• The fine structure of heating in a quasiperiodically driven critical quantum system
• Modular Hamiltonians for the massless Dirac field in the presence of a boundary
• The Real-Time Correlation Function of Floquet Conformal Fields
• Local operator quench induced by two-dimensional inhomogeneous and homogeneous CFT Hamiltonians
• Note on complex metrics, complex time and periodic universes
• Floquet's Refrigerator: Conformal Cooling in Driven Quantum Critical Systems
• Notes on heating phase dynamics in Floquet CFTs and Modular quantization
• New horizons for inhomogeneous quenches and Floquet CFT

Cited by in corpus (4)

• Gapless higher-order topology and corner states in Floquet systems
• Phase Transitions in Quasi-Periodically Driven Quantum Critical Systems: Analytical Results
• Driven Non-Unitary Dynamics of Quantum Critical Systems
• Universal time evolution of string order parameter in quantum critical systems with boundary invertible or non-invertible symmetry breaking