Complexity and information geometry in spin chains
arXiv:2005.03532 · doi:10.1103/PhysRevE.104.024127
Abstract
We study Nielsen complexity and Fubini-Study complexity for a class of exactly solvable one dimensional spin systems. Our examples include the transverse XY spin chain and its natural extensions, the quantum compass model with and without an external magnetic field. We obtain the scaling behaviour of both complexities near quantum phase transitions in the thermodynamic limit, as a function of the system parameters. We provide analytical proofs of these, in an information geometric framework, which verify our numerical analysis. The scaling of the Nielsen complexity with the system size is also established, close to criticality. We also obtain analytic expressions for the Fubini-Study complexity in some special cases for all the models, while a numerical analysis in more generic situations is carried out. Our study clearly demonstrates the differences in the two notions of complexity in quasi-free fermionic systems.
arXiv commentScaling analysis of the complexity is added. Generic geodesic analysis added. Major additions and revisions
References in corpus (24)
- Fidelity approach to quantum phase transitions
- Quantum critical scaling of the geometric tensors
- Circuit complexity in quantum field theory
- Towards Complexity for Quantum Field Theory States
- Scaling of geometric phases close to quantum phase transition in the XY chain
- Circuit Complexity in Fermionic Field Theory
- Circuit complexity for free fermions
- Circuit complexity in interacting QFTs and RG flows
- Classifying and measuring the geometry of the quantum ground state manifold
- Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
- Circuit Complexity for Coherent States
- Complexity as a novel probe of quantum quenches: universal scalings and purifications
- Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
- Information geometry in vapour-liquid equilibrium
- Circuit Complexity across a Topological Phase Transition
- Multicriticality and entanglement in the one-dimensional quantum compass model
- Post-Quench Evolution of Complexity and Entanglement in a Topological System
- Information Geometry and Quantum Phase Transitions in the Dicke Model
- Geodesics in Information Geometry : Classical and Quantum Phase Transitions
- Circuit complexity for generalised coherent states in thermal field dynamics
- Geometric Critical Exponents in Classical and Quantum Phase Transitions
- Decoherence from spin environments: Loschmidt echo and quasiparticle excitations
- Nonanalyticity of circuit complexity across topological phase transitions
- Quantum Phase Transition in the One-Dimensional Extended Quantum Compass Model in a Transverse Field
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- Circuit Complexity in
- Circuit Complexity through phase transitions: consequences in quantum state preparation
- Nielsen complexity of coherent spin state operators
- Complexity and quenches in models with three and four spin interactions
- Real space circuit complexity as a probe of phase diagrams
- Quantum geometry in many-body systems with precursors of criticality
- Time-dependent Hamiltonians and Geometry of Operators Generated by Them
- Probing the self-coherence of primordial quantum fluctuations with complexity
- Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors
- Emergent Hawking Radiation and Quantum Sensing in a Quenched Chiral Spin Chain