Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems

Abstract

We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-$\frac{1}{2}$ one-dimensional spin-chain models, viz., the Ising and anisotropic $XY$ models in a transverse field, and the $XXZ$ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system's single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in witnessing and characterizing first-, second- and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method's ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function's utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be intuitively analyzed.

20 pages, 8 figures

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Quantum computing with trapped ions
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Quantum coherence and uncertainty in the anisotropic XY chain
• The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
• Theory of ground state factorization in quantum cooperative systems
• Chiral Spin Liquids in Arrays of Spin Chains
• Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
• The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue
• Entanglement of finite cyclic chains at factorizing fields
• Going Beyond Bell's Theorem
• Magnetic quantum correlation in the 1D transverse-field XXZ model
• The Ising phase in the J1-J2 Heisenberg Model

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