Evolution of entanglement entropy in one-dimensional systems

By Pasquale Calabrese, J. Cardy. 2005

1,268 citations recorded by the source corpus.

We study the unitary time evolution of the entropy of entanglement of a one-dimensional system between the degrees of freedom in an interval of length and its complement, starting from a pure state which is not an eigenstate of the Hamiltonian. We use path integral methods of quantum field theory as well as explicit computations for the transverse Ising spin chain. In both cases, there is a maximum speed v of propagation of signals. In general the entanglement entropy increases linearly with time t up to , after which it saturates at a value proportional to , the coefficient depending on the initial state. This behaviour may be understood as a consequence of causality.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/81a1e89eb949ae448dd0bc98e8c5583a5d9721f1

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Diffusive Hydrodynamics of Out-of-Time-Ordered Correlators with Charge Conservation (2017, background): “[4] Pasquale Calabrese and John Cardy, “Evolution of entanglement entropy in one-dimensional systems,” Journal of Statistical Mechanics: Theory and Experiment 2005, P04010 (2005).”
Many-body localization and delocalization in large quantum chains (2018, background): “[39] Pasquale Calabrese and John Cardy, “Evolution of entanglement entropy in one-dimensional systems,” J.”
Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions (2021, background): “[10] Pasquale Calabrese and John Cardy, “Evolution of entanglement entropy in one-dimensional systems,” Journal of Statistical Mechanics: Theory and Experiment 2005, P04010 (2005).”
Random Quantum Circuits (2022, background): “Physical Review B, 102(18):180302, 2020.”
Measurement-driven entanglement transition in hybrid quantum circuits (2019, background): “Quantum many-body systems under unitary dynamics will generally thermalize [1–7].”
Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, background): “As discussed, at small measurements rates p or strengths η, a volume-law phase manifests, and a ballistic growth in the entanglement entropy of a subsystem occurs before saturation in time [1, 2].”
On entanglement spreading in chaotic systems (2016, background): “We suggest that for chaotic systems with vB = vLC, this may be an appropriate replacement for the particle streaming picture of entropy dynamics in free field theories [1, 3, 6].”
Complexity and entanglement for thermofield double states (2018, neutral): “[92–94] and further developed in refs.”
Entanglement of local operators in large-N conformal field theories (2014, neutral): “here we deﬁned w1 = i(ǫ−it) − l, w2 = −i(ǫ+ it) −l, (7) w¯1 = −i(ǫ− it) − l, w¯2 = i(ǫ+ it) −l. (8) Throughout the computation we treat ǫ± itas purely real numbers until the end of calculations as in [16, 19, 9]. Now, if we deﬁne ∆S(n) A by subtracting the ground state result from S (n) A , then ∆S ”
Quantum thermalization through entanglement in an isolated many-body system (2016, background): “The approximately linear rise at early times (Figure 3 inset) is related to the spreading of entanglement in the system within an effective light cone [2, 31, 32].”
Probe branes, time-dependent couplings and thermalization in AdS/CFT (2010, background): “In the first limit, a parameter is changed quickly through a critical point (a quantum quench) and the subsequent time evolution is studied [32–38].”