Generalized Phase-Space Techniques to Explore Quantum Phase Transitions in Critical Quantum Spin Systems
arXiv:2203.12320 · doi:10.1016/j.aop.2023.169459
Abstract
We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin- one-dimensional spin-chain models, viz., the Ising and anisotropic models in a transverse field, and the 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.
arXiv comment20 pages, 8 figures
References in corpus (48)
- Quantum entanglement
- Many-Body Physics with Ultracold Gases
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Entanglement in quantum critical phenomena
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Scaling of Entanglement close to a Quantum Phase Transitions
- Entanglement in a simple quantum phase transition
- Entanglement spectrum of a topological phase in one dimension
- Quantum computing with trapped ions
- Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
- Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
- Classifying quantum phases using Matrix Product States and PEPS
- Classical Correlation and Quantum Discord in Critical Systems
- Localization protected quantum order
- Quantum correlations in spin chains at finite temperatures and quantum phase transitions
- Discrete phase space based on finite fields
- Quantum coherence and uncertainty in the anisotropic XY chain
- Quantifying entanglement resources
- Genuine quantum correlations in quantum many-body systems: a review of recent progress
- Wigner Functions for Arbitrary Quantum Systems
- The renormalization of entanglement in the anisotropic Heisenberg (XXZ) model
- Theory of ground state factorization in quantum cooperative systems
- Quantum discord in finite XY chains
- Scaling of genuine multiparticle entanglement at a quantum phase transition
- Exact results for quantum phase transitions in random XY spin chains
- 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
- Criticality, factorization and long-range correlations in the anisotropic XY-model
- Genuine Multipartite Entanglement in the Model
- A general approach to quantum mechanics as a statistical theory
- Going Beyond Bell's Theorem
- Entanglement in spin-one Heisenberg chains
- Quantum spin systems on infinite lattices
- Discrete truncated Wigner approach to dynamical phase transitions in Ising models after a quantum quench
- Magnetic quantum correlation in the 1D transverse-field XXZ model
- Global Quantum Correlation in the Ising model
- The Ising phase in the J1-J2 Heisenberg Model
- Entanglement and local extremes at an infinite-order quantum phase transition
- Revealing quantum correlation by negativity of the Wigner function
- Discrete Wigner distribution for two qubits: a characterization of entanglement properties
- Compressed Simulation of evolutions of the XY-model
- Visualizing entanglement in atoms and molecules
- Path dependent scaling of geometric phase near a quantum multi-critical point
- Discrete and generalized phase space techniques in critical quantum spin chains
- Non-Coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method
- Quantum Entanglement and Geometry