Detecting quantum phase transitions in the quasistationary regime of Ising chains

Year: 2023

Authors: Dag CB., Uhrich P., Wang YD., McCulloch IP., Halimeh JC.

Autors Affiliation: Harvard Smithsonian Ctr Astrophys, ITAMP, Cambridge, MA 02138 USA; Harvard Univ, Dept Phys, 17 Oxford St, Cambridge, MA 02138 USA; Univ Michigan, Dept Phys, Ann Arbor, MI 48109 USA; Univ Trento, Pitaevskii BEC Ctr, CNR INO, I-38123 Trento, Italy; Univ Trento, Dipartimento Fis, I-38123 Trento, Italy; Univ Queensland, Sch Math & Phys, St Lucia, Qld 4072, Australia.

Abstract: Recently, single-site observables have been shown to be useful for probing critical slowing down in sudden quench dynamics [Dag et al., Phys. Rev. B 107, L121113 (2023)]. Here, we demonstrate the potential of single -site magnetization as a probe of quantum phase transitions in integrable and nonintegrable transverse-field Ising chains (TFIC). We analytically prove the requirement of zero modes for the quasistationary regime to emerge at a probe site near the edge, and show how this regime gives rise to a nonanalytic behavior in the dynamical order profiles. Our t-DMRG calculations verify the results of the quench mean-field theory for near-integrable TFIC both with finite-size and finite-time scaling analyses. We find that both finite-size and finite-time analyses suggest a dynamical critical point for a strongly nonintegrable and locally connected TFIC. We finally demonstrate the presence of a quasistationary regime in the power-law interacting TFIC, and extract local dynamical order profiles for TFIC in the long-range Ising universality class with algebraic light cones.

Journal/Review: PHYSICAL REVIEW B

Volume: 107 (9)      Pages from: 94432-1  to: 94432-20

KeyWords: Mean field theory; Phase transitions; Quantum theory; Critical slowing down; Finite size; Finite-time; Ising chains; Mean-field theories; Order profiles; Quantum-phase transition; Quasi-stationary regime; Single sites; Transverse field
DOI: 10.1103/PhysRevB.107.094432

Citations: 2
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