Krylov Complexity and Dynamical Phase Transition in the quenched LMG model
arXiv:2312.05321 · doi:10.1103/PhysRevB.109.224304
Abstract
Investigating the time evolution of complexity in quantum systems entails evaluating the spreading of the system's state across a defined basis in its corresponding Hilbert space. Recently, the Krylov basis has been identified as the one that minimizes this spreading. In this study, we develop a numerical exploration of the Krylov complexity in quantum states following a quench in the Lipkin-Meshkov-Glick model. Our results reveal that the long-term averaged Krylov complexity acts as an order parameter for this model. It effectively discriminates between the two dynamic phases induced by the quench, sharing a critical point with the conventional order parameter. Additionally, we examine the inverse participation ratio and the Shannon entropy in both the Krylov basis and the energy basis. A matching dynamic behavior is observed in both bases when the initial state possesses a specific symmetry. This behavior is analytically explained by establishing the equivalence between the Krylov basis and the pre-quench energy eigenbasis.
12 pages, 7 figures, comments are welcome
References in corpus (53)
- A bound on chaos
- Quantum many-body systems out of equilibrium
- Dynamical Quantum Phase Transitions in the Transverse Field Ising Model
- Dynamical quantum phase transitions: a review
- Thermalization and prethermalization in isolated quantum systems: a theoretical overview
- A Universal Operator Growth Hypothesis
- Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
- Quantum chaos and the complexity of spread of states
- Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
- Exact spectrum of the Lipkin-Meshkov-Glick model in the thermodynamic limit and finite-size corrections
- Dynamical phase transitions after quenches in non-integrable models
- Dynamical quantum phase transitions and the Loschmidt echo: A transfer matrix approach
- Dynamical quantum phase transitions in systems with broken-symmetry phases
- Operator complexity: a journey to the edge of Krylov space
- Microscopic diagonal entropy and its connection to basic thermodynamic relations
- On The Evolution Of Operator Complexity Beyond Scrambling
- Krylov complexity from integrability to chaos
- Dynamical Quantum Phase Transitions in the Kitaev Honeycomb Model
- Toda chain flow in Krylov space
- Krylov Localization and suppression of complexity
- Operator growth and Krylov construction in dissipative open quantum systems
- Dynamical transitions and quantum quenches in mean-field models
- Quantum quenches, dynamical transitions and off-equilibrium quantum criticality
- Operator growth in open quantum systems: lessons from the dissipative SYK
- Quantum Kolmogorov Complexity
- Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
- Ultimate Speed Limits to the Growth of Operator Complexity
- Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model
- Quantum complexity and topological phases of matter
- Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
- Krylov Complexity in Open Quantum Systems
- Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
- Krylov complexity and orthogonal polynomials
- On Krylov complexity in open systems: an approach via bi-Lanczos algorithm
- Long-time behavior of many-particle quantum decay
- Krylov complexity and chaos in quantum mechanics
- Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
- Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Criticality revealed through quench dynamics the Lipkin-Meshkov-Glick model
- Dynamical phase transitions in the two-dimensional transverse-field Ising model
- Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
- Shortcuts to Adiabaticity in Krylov Space
- Finite-component dynamical quantum phase transitions
- Exact Quantum Decay of an Interacting Many-Particle System: the Calogero-Sutherland model
- Time evolution of spread complexity in quenched Lipkin-Meshkov-Glick model
- Dynamical and excited-state quantum phase transitions in collective systems
- Theory of dynamical phase transitions in quantum systems with symmetry-breaking eigenstates
- Geometric Operator Quantum Speed Limit, Wegner Hamiltonian Flow and Operator Growth
- Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions
- Analytical description of the survival probability of coherent states in regular regimes
- Wehrl entropy production rate across a dynamical quantum phase transition
- Gauge invariant quantum thermodynamics: consequences for the first law
Cited by in corpus (18)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Krylov fractality and complexity in generic random matrix ensembles
- Correlations and Krylov spread for a non-Hermitian Hamiltonian: Ising chain with a complex-valued transverse magnetic field
- Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
- Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
- Spread complexity and quantum chaos for periodically driven spin chains
- Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
- Properties of Krylov state complexity in qubit dynamics
- Krylov Complexity in the Schrödinger Field Theory
- Dynamical quantum phase transition, metastable state, and dimensionality reduction: Krylov analysis of fully connected spin models
- Quantum speed limit for the OTOC from an open systems perspective
- Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
- Speedup of thermodynamic entropy production via quantum dynamical criticality
- Higher-Order Krylov State Complexity in Random Matrix Quenches
- Asymmetry and dynamical criticality
- Krylov Complexity Under Hamiltonian Deformations and Toda Flows
- Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory
- Spread complexity and localization in -symmetric systems