A Complexity for Quantum Field Theory States and Application in Thermofield Double States

Abstract

This paper defines a complexity between states in quantum field theory by introducing a Finsler structure based on ladder operators (the generalization of creation and annihilation operators). Two simple models are shown as examples to clarify the differences between complexity and other conceptions such as complexity of formation and entanglement entropy. When it is applied into thermofield double (TFD) states in $d$-dimensional conformal field theory, results show that the complexity density between them and corresponding vacuum states are finite and proportional to $T^{d-1}$, where $T$ is the temperature of TFD state. Especially, a proof is given to show that fidelity susceptibility of a TFD state is equivalent to the complexity between it and corresponding vacuum state, which gives an explanation why they may share the same object in holographic duality. Some enlightenments to holographic conjectures of complexity are also discussed.

Improved the language and presentation, adjusted the structure of the paper, modified some errors and typos, added some appendices to give out more details

References in corpus (7)

• The Unruh effect and its applications
• Complexity and Shock Wave Geometries
• Quantum Computation as Geometry
• Gravitational action with null boundaries
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• On Volumes of Subregions in Holography and Complexity
• On complexity growth in massive gravity theories, the effects of chirality and more

Cited by in corpus (62)

• Circuit Complexity in Fermionic Field Theory
• Complexity and entanglement for thermofield double states
• Quantum Computation as Gravity
• Circuit complexity in interacting QFTs and RG flows
• Holographic Complexity in Vaidya Spacetimes II
• Quantum Computational Complexity -- From Quantum Information to Black Holes and Back
• Circuit Complexity for Coherent States
• Subsystem Complexity and Holography
• Time Evolution of Complexity: A Critique of Three Methods
• Black holes, complexity and quantum chaos
• Chaos and Complexity in Quantum Mechanics
• Quantum Dynamics in Krylov Space: Methods and Applications
• The Complexity Geometry of a Single Qubit
• Krylov Complexity in Open Quantum Systems
• Holographic Subregion Complexity from Kinematic Space
• The effect of Dilaton on the holographic complexity growth
• Renormalized Circuit Complexity
• Complexity Growth Rate in Lovelock Gravity
• Holographic Complexity for Defects Distinguishes Action from Volume
• Principles and symmetries of complexity in quantum field theory
• Subregion Action and Complexity
• Complexity change under conformal transformations in AdS${}_3$/CFT${}_2$
• Evolution of complexity following a quantum quench in free field theory
• Circuit Complexity across a Topological Phase Transition
• Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity
• Aspects of The First Law of Complexity
• Complexity of Holographic Superconductors
• Thermofield Theory for Finite-Temperature Quantum Chemistry
• WdW-patches in AdS${}_3$ and complexity change under conformal transformations II
• Circuit Complexity for Fermionic Thermofield Double states
• Circuit Complexity and 2D Bosonisation
• Time evolution of the complexity in chaotic systems: concrete examples
• Circuit complexity for generalised coherent states in thermal field dynamics
• Binding Complexity and Multiparty Entanglement
• Circuit complexity for free Fermion with a mass quench
• Holographic Subregion Complexity in Einstein-Born-Infeld theory
• Complexity growth of rotating black holes with a probe string
• Modified "complexity equals action" conjecture
• Null boundary terms for Lanczos-Lovelock gravity
• Complexity of operators generated by quantum mechanical Hamiltonians
• Holographic complexity of charged Taub-NUT-AdS black holes
• Bulk reconstruction of metrics inside black holes by complexity
• Universal Hypothesis of Autocorrelation Function from Krylov Complexity
• Holographic complexity of the electromagnetic black hole
• Decomposable coherence and quantum fluctuation relations
• Stringy Effects and the Role of the Singularity in Holographic Complexity
• Complexity measures in QFT and constrained geometric actions
• Reparameterization Dependence is Useful for Holographic Complexity
• Nielsen complexity of coherent spin state operators
• Holographic Complexity in a Charged Supersymmetric Black Holes
• Complexity growth for topological black holes by holographic method
• Holographic Complexity of Subregions in the Hyperscaling Violating Theories
• New Topological Gauss-Bonnet Black Holes in Five Dimensions
• Weighting gates in circuit complexity and holography
• Real space circuit complexity as a probe of phase diagrams
• Circuit Complexity From Supersymmetric Quantum Field Theory With Morse Function
• Reduced Density Matrices and Phase-Space Distributions in Thermofield Dynamics
• What kind of "complexity" is dual to holographic complexity?
• Reparameterization Dependence and Holographic Complexity of Black Holes
• Holographic complexity of rotating black holes
• Switchback effect of holographic complexity in multiple-horizon black holes
• D5-brane on topological black holes