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

TL;DR

This paper investigates exactly solvable non-unitary time evolutions in quantum critical systems induced by complex spacetime metrics, revealing universal damping effects and distinct entanglement dynamics compared to real-time evolution.

Contribution

It introduces a framework for analyzing universal features of non-unitary quantum dynamics driven by complex spacetime metrics in critical systems, with exact solutions for key physical quantities.

Findings

Entanglement entropy grows logarithmically after a global quench.

Complex time induces damping, leading to different non-equilibrium behaviors.

Steady states with unique entanglement structures emerge under driven complex 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.