2021/03/31 by Ning Wu, Pei Yang · 1 citation
Physics and Astronomy · #Condensed matter physics #Ising model #Mathematical physics #Operator (biology) #Opinion Dynamics and Social Influence #Physics #Quantum #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Sigma #Sigma model #Spin (aerodynamics) #Spins #Thermodynamics #Zero (linguistics) #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevb.103.174428
published as Phys. Rev. B 103, 174428 (2021) · 13 pages, 10 figures
arxiv created 2021/05/10 · openalex publication_date 2021/05/24 · arxiv updated 2021/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the nonequilibrium dynamics of a homogeneous quantum Ising ring after a quench, in which the transverse field g suddenly changes from zero to a nonzero value. The long-timescale reduced dynamics of a single spin and of two nearest-neighbor spins, which involves the evaluation of expectation values of odd operators that break the fermion parity, is exactly obtained for finite-size but large rings through the use of a recently developed Pfaffian method [N. Wu, Phys. Rev. E 101, 042108 (2020)]. Time dependence of the transverse and longitudinal magnetizations (\ensuremath⟨\ensuremathσjz\ensuremath⟩t and \ensuremath⟨\ensuremathσjx,y\ensuremath⟩t), single-spin purity, expectation value of the string operator Xj=\ensuremath∏l=1^j\ensuremath-1\ensuremathσlz\ensuremathσjx (\ensuremath⟨Xj\ensuremath⟩t), several equal-time two-site correlators (\ensuremath⟨\ensuremathσjx,z\ensuremathσj+1x,z\ensuremath⟩t, \ensuremath⟨\ensuremathσjx\ensuremathσj+1y\ensuremath⟩t, and \ensuremath⟨\ensuremathσjx\ensuremathσj+1z\ensuremath⟩t), and pairwise concurrence after quenches to different phases are numerically studied. Our main findings are that (i) The expectation value of a generic odd operator approaches zero in the long-time limit; (ii) \ensuremath⟨Xj\ensuremath⟩t exhibits j-independent exponential decay for a quench to g=1 and the time at which \ensuremath⟨Xj\ensuremath⟩t reaches its first maximum scales linearly with j; (iii) The single-spin purity dynamics is mainly controlled by \ensuremath⟨\ensuremathσjx\ensuremath⟩t (\ensuremath⟨\ensuremathσjz\ensuremath⟩t) for a quench to g<1 (g\ensuremath≥1). For quenches to the disordered phase with g\ensuremath≫1, the single-spin tends to be in the maximally mixed state and the transverse and longitudinal correlators \ensuremath⟨\ensuremathσjz\ensuremathσj+1z\ensuremath⟩t and \ensuremath⟨\ensuremathσjx\ensuremathσj+1x\ensuremath⟩t, respectively, approaches \ensuremath-0.25 and 0.5 in the thermodynamic limit; (iv) The nearest-neighbor entanglement acquires a finite plateau value that increases with increasing g, and approaches a saturated value \ensuremath∼0.125 for g\ensuremath≫1.