Kolmogorov complexity as intrinsic entropy of a pure state: Perspective from entanglement in free fermion systems
arXiv:2202.02852 · doi:10.1103/PhysRevB.106.035143
Abstract
We consider free fermion systems in arbitrary dimensions and represent the occupation pattern of each eigenstate as a classical binary string. We find that the Kolmogorov complexity of the string correctly captures the scaling behavior of its entanglement entropy (EE). In particular, the logarithmically-enhanced area law for EE in the ground state and the volume law for EE in typical highly excited states are reproduced. Since our approach does not require bipartitioning the system, it allows us to distinguish typical and atypical eigenstates directly by their intrinsic complexity. We reveal that the fraction of atypical eigenstates which do not thermalize in the free fermion system vanishes exponentially in the thermodynamic limit. Our results illustrate explicitly the connection between complexity and EE of individual pure states in quantum systems.
arXiv commentAccepted version by PRB
References in corpus (47)
- Quantum entanglement
- Entanglement Entropy and Quantum Field Theory
- Chaos and Quantum Thermalization
- Thermalization and its mechanism for generic isolated quantum systems
- Area laws for the entanglement entropy - a review
- Nonequilibrium dynamics of closed interacting quantum systems
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Many body localization and thermalization in quantum statistical mechanics
- From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
- Detecting topological order in a ground state wave function
- Quantum many-body systems out of equilibrium
- An Area Law for One Dimensional Quantum Systems
- Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
- Quantum Many-Body Scars and Weak Breaking of Ergodicity
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Violation of the entropic area law for Fermions
- From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
- Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems
- Ultracold atoms out of equilibrium
- The Second Law of Quantum Complexity
- Does a single eigenstate encode the full Hamiltonian?
- Entanglement Entropy and the Fermi Surface
- Quantum Complexity and Negative Curvature
- The microscopic origin of thermodynamic entropy in isolated systems
- First and Second Law of Quantum Thermodynamics: A Consistent Derivation Based on a Microscopic Definition of Entropy
- Quantum Kolmogorov Complexity
- Thermodynamic entropy of a many body energy eigenstate
- Entanglement Entropy Scaling Laws and Eigenstate Typicality in Free Fermion Systems
- Quantum Kolmogorov Complexity Based on Classical Descriptions
- Towards measuring Entanglement Entropies in Many Body Systems
- Quantum Algorithmic Entropy
- Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization
- Algorithmic complexity and entanglement of quantum states
- Entangling power and quantum circuit complexity
- A brief introduction to observational entropy
- Entropy and Quantum Kolmogorov Complexity: A Quantum Brudno's Theorem
- Taking the temperature of a pure quantum state
- Entanglement Entropy and Mutual Information in Bose-Einstein Condensates
- Kolmogorov complexity of sequences of random numbers generated in Bell's experiments
- Entanglement Area Law in Disordered Free Fermion Anderson Model in One, Two, and Three Dimensions
- Block Entanglement Entropy of Ground States with Long-Range Magnetic Order
- Hidden thermal structure in Fock space
- Prefix-free quantum Kolmogorov complexity
- Breakdown of quantum-classical correspondence and dynamical generation of entanglement
- Kolmogorov complexity of unitary transformations in quantum computing
- Randomness of imperfectly entangled states