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

N. M. Millen, R. P. Rundle, J. H. Samson, Todd Tilma, R. F. Bishop, M. J. Everitt

Research output: Working paperPreprint

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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.
Original languageUndefined
Publication statusPublished - 23 Mar 2022


  • quant-ph
  • cond-mat.str-el

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