Complexity and entanglement for thermofield double states
Chapman S, Eisert J, Hackl L, Heller MR, Jefferson R, Marrochio H, Myers RC (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 6
Journal Issue: 3
DOI: 10.21468/SciPostPhys.6.3.034
Abstract
Motivated by holographic complexity proposals as novel probes of black hole spacetimes, we explore circuit complexity for thermofield double (TFD) states in free scalar quantum field theories using the Nielsen approach. For TFD states at t = 0, we show that the complexity of formation is proportional to the thermodynamic entropy, in qualitative agreement with holographic complexity proposals. For TFD states at t > 0, we demonstrate that the complexity evolves in time and saturates after a time of the order of the inverse temperature. The latter feature, which is in contrast with the results of holographic proposals, is due to the Gaussian nature of the TFD state of the free bosonic QFT. A novel technical aspect of our work is framing complexity calculations in the language of covariance matrices and the associated symplectic transformations, which provide a natural language for dealing with Gaussian states. Furthermore, for free QFTs in 1+1 dimension, we compare the dynamics of circuit complexity with the time dependence of the entanglement entropy for simple bipartitions of TFDs. We relate our results for the entanglement entropy to previous studies on non-equilibrium entanglement evolution following quenches. We also present a new analytic derivation of a logarithmic contribution due to the zero momentum mode in the limit of vanishing mass for a subsystem containing a single degree of freedom on each side of the TFD and argue why a similar logarithmic growth should be present for larger subsystems.
Involved external institutions
Max Planck Institute for Gravitational Physics / Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)
Germany (DE)
Perimeter Institute for Theoretical Physics
Canada (CA)
University of Amsterdam
Netherlands (NL)
Freie Universität Berlin
Germany (DE)
Germany (DE)
Perimeter Institute for Theoretical Physics
Canada (CA)
University of Amsterdam
Netherlands (NL)
Freie Universität Berlin
Germany (DE)
How to cite
APA:
Chapman, S., Eisert, J., Hackl, L., Heller, M.R., Jefferson, R., Marrochio, H., & Myers, R.C. (2019). Complexity and entanglement for thermofield double states. SciPost Physics, 6(3). https://dx.doi.org/10.21468/SciPostPhys.6.3.034
MLA:
Chapman, Shira, et al. "Complexity and entanglement for thermofield double states." SciPost Physics 6.3 (2019).
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