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

• URL: http://arxiv.org/abs/2203.12320v1
• Date: Wed, 23 Mar 2022 10:46:00 GMT
• Title: Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
• Authors: N. M. Millen, R. P. Rundle, J. H. Samson, Todd Tilma, R. F. Bishop, and M. J. Everitt
• Abstract summary: We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions. We demonstrate the utility of phase-space techniques in witnessing and characterizing first-, second- and infinite-order quantum phase transitions. We also highlight the method's ability to capture other features of spin systems such as ground-state factorization and critical system scaling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Thermalization and Criticality on an Analog-Digital Quantum Simulator [133.58336306417294]
  We present a quantum simulator comprising 69 superconducting qubits which supports both universal quantum gates and high-fidelity analog evolution. We observe signatures of the classical Kosterlitz-Thouless phase transition, as well as strong deviations from Kibble-Zurek scaling predictions. We digitally prepare the system in pairwise-entangled dimer states and image the transport of energy and vorticity during thermalization.
  arXiv  Detail & Related papers  (2024-05-27T17:40:39Z)
• Quantum Fisher Information and multipartite entanglement in spin-1 chains [0.0]
  We study the ground state Quantum Fisher Information (QFI) in one-dimensional spin-1 models, as witness to Multipartite Entanglement. We show that the scaling of the QFI of strictly non-local observables can be used for characterizing the phase diagrams and, in particular, for studying topological phases.
  arXiv  Detail & Related papers  (2023-07-05T16:28:23Z)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• Finite-size criticality in fully connected spin models on superconducting quantum hardware [0.0]
  We exploit the new resources offered by quantum algorithms to detect the quantum critical behaviour of fully connected spin$-1/2$ models. We propose a method based on variational algorithms run on superconducting transmon qubits.
  arXiv  Detail & Related papers  (2022-08-04T16:00:34Z)
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions [0.0]
  We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model dependent multifractal scaling of the wave-functions at any non-zero measurement rate.
  arXiv  Detail & Related papers  (2021-09-14T18:00:01Z)
• Probing quantum information propagation with out-of-time-ordered correlators [41.12790913835594]
  Small-scale quantum information processors hold the promise to efficiently emulate many-body quantum systems. Here, we demonstrate the measurement of out-of-time-ordered correlators (OTOCs) A central requirement for our experiments is the ability to coherently reverse time evolution.
  arXiv  Detail & Related papers  (2021-02-23T15:29:08Z)
• Probing the topological Anderson transition with quantum walks [48.7576911714538]
  We consider one-dimensional quantum walks in optical linear networks with synthetically introduced disorder and tunable system parameters. The option to directly monitor the walker's probability distribution makes this optical platform ideally suited for the experimental observation of the unique signatures of the one-dimensional topological Anderson transition.
  arXiv  Detail & Related papers  (2021-02-01T21:19:15Z)
• Finite-component dynamical quantum phase transitions [0.0]
  We show two types of dynamical quantum phase transitions (DQPTs) in a quantum Rabi model. One refers to distinct phases according to long-time averaged order parameters, the other is focused on the non-analytical behavior emerging in the rate function of the Loschmidt echo. We find the critical times at which the rate function becomes non-analytical, showing its associated critical exponent as well as the corrections introduced by a finite frequency ratio.
  arXiv  Detail & Related papers  (2020-08-31T17:31:17Z)
• Detecting Topological Quantum Phase Transitions via the c-Function [0.0]
  We consider a holographic model which exhibits a topological quantum phase transition between a topologically trivial insulating phase and a gapless Weyl semimetal. The c-function robustly shows a global feature at the quantum criticality and distinguishes with great accuracy the two separate zero temperature phases.
  arXiv  Detail & Related papers  (2020-07-14T18:03:24Z)
• Universality of entanglement transitions from stroboscopic to continuous measurements [68.8204255655161]
  We show that the entanglement transition at finite coupling persists if the continuously measured system is randomly nonintegrable. This provides a bridge between a wide range of experimental settings and the wealth of knowledge accumulated for the latter systems.
  arXiv  Detail & Related papers  (2020-05-04T21:45:59Z)
• Quantum Statistical Complexity Measure as a Signalling of Correlation Transitions [55.41644538483948]
  We introduce a quantum version for the statistical complexity measure, in the context of quantum information theory, and use it as a signalling function of quantum order-disorder transitions. We apply our measure to two exactly solvable Hamiltonian models, namely: the $1D$-Quantum Ising Model and the Heisenberg XXZ spin-$1/2$ chain. We also compute this measure for one-qubit and two-qubit reduced states for the considered models, and analyse its behaviour across its quantum phase transitions for finite system sizes as well as in the thermodynamic limit by using Bethe ansatz.
  arXiv  Detail & Related papers  (2020-02-05T00:45:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.