Complexity and information geometry in spin chains

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.

Scaling analysis of the complexity is added. Generic geodesic analysis added. Major additions and revisions

References in corpus (6)

• Quantum critical scaling of the geometric tensors
• Quenching Dynamics of a quantum XY spin-1/2 chain in presence of a transverse field
• Multicriticality and entanglement in the one-dimensional quantum compass model
• 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

Cited by in corpus (14)

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• Circuit Complexity in ${\mathcal{Z}}_2$ $\mathcal{EEF}\mathcal{T}$
• 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