Dynamics of the Geometric Phase in Inhomogeneous Quantum Spin Chains

Abstract

The dynamics of the geometric phase are studied in inhomogeneous quantum spin chains after a quench. Analytic expressions of the Pancharatnam geometric phase (PGP) $\mathcal{G}(t)$ are derived, for both the period-two quantum Ising chain (QIC) and the disordered QIC. In the period-two QIC, due to the periodic modulation, the PGP changes with time at the boundary of the Brillouin zone, and consequently, the winding number ${\nu }_D(t)={\int }_0^{\pi }[\partial {\varphi }_k^G(t)/\partial k]dk/2\pi$ based on the PGP is not quantized and thus not topological anymore. Nevertheless, the PGP and its winding number show non-analytic singularities at the critical times of the dynamical quantum phase transitions (DQPTs). This relation between the PGP and the DQPT is further confirmed in the disordered QIC, where the winding number is not defined. It is found that the critical time of DQPT inherited from the homogeneous system and the additional one induced by the weak disorder are also accompanied by the non-analytic singularity of the PGP, by decomposing the PGP into each quasiparticle mode. The connection between the non-analytic behavior of the PGP at the critical time and the DQPT, regardless of whether the winding number is topological, can be explained by the fact that they both arise when the Loschmidt amplitude vanishes.

14 pages, 8 figures

References in corpus (14)

• Dynamical phase transition in correlated fermionic lattice systems
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Geometry of quantum phase transitions
• Quantum quenches and off-equilibrium dynamical transition in the infinite-dimensional Bose-Hubbard model
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Observation of Dynamical Quantum Phase Transition with Correspondence in Excited State Phase Diagram
• Dynamical Topological Quantum Phase Transitions at Criticality
• Dynamical quantum phase transitions in the quantum Potts chain
• Dynamical quantum phase transition from a critical quantum quench
• Dynamical quantum phase transition in a system of non-interacting bosons
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Anomaly in dynamical quantum phase transition in non-Hermitian system with extended gapless phases

Cited by in corpus (5)

• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Loschmidt echo zeros in finite-size quantum systems with linear quench
• Quantum coherence assisted dynamical phase transition
• Critical Exponent of Dynamical Quantum Phase Transition in One-Dimensional Bose-Hubbard Model in the Strong Interacting Limit
• Exploring dynamical quantum phase transition from pure states to mixed states through extended Su-Schrieffer-Heeger models