Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors

Abstract

This paper presents a geometrical analysis of finite length XY quantum chains. We begin by examining the ground state and the first excited state of the model, emphasizing the impact of finite size effects under two distinct choices of the Jordan Wigner transformation: the Neveu Schwartz (NS) and Ramond (R) sectors. We explore the geometric features of the system by analyzing the quantum (Berry) curvature derived from the Fubini Study metric, which is intimately connected to the quantum Fisher information. This approach uncovers a rich interplay between boundary conditions and quantum geometry. In the gamma h parameter space, we identify distinct sign changing arcs of the curvature, confined to some region. These arcs mark transitions between the NS and R sectors, indicating fundamental changes in the structure of the fermionic ground state. Remarkably, the number of such transition lines increases with system size, hinting at an emergent continuum of topological boundary effects in the thermodynamic limit. Our findings highlight a novel mechanism where boundary conditions shape quantum geometric properties, offering new insights into finite size topology and the structure of low dimensional quantum systems.

References in corpus (20)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Geometrothermodynamics
• Geometric phases and criticality in spin chain systems
• Geometry of quantum phase transitions
• Abelian and Non-Abelian Quantum Geometric Tensor
• Bures metric over thermal state manifolds and quantum criticality
• The quantum Ising chain for beginners
• Oscillating fidelity susceptibility near a quantum multicritical point
• Geometric phases and quantum phase transitions
• Even-odd parity transition in strongly correlated locally noncentrosymmetric superconductors : An application to CeRh${}_2$As${}_2$
• Formation probabilities and statistics of observables as defect problems in the free fermions and the quantum spin chains
• Complexity and information geometry in spin chains
• Unveiling the geometric meaning of quantum entanglement: discrete and continuous variable systems
• Quantum phases of spin-1/2 extended XY model in transverse magnetic field
• NSR Open Super-string in the proper-time gauge I: Free Field Theory
• The quantum XY chain with boundary fields: finite-size gap and phase behavior