The geometric phase from imaginary time translations

A. Stanley

A new expression for the phase one-form is derived in terms of a derivative of the Kahler potential for the class of projective Hilbert spaces which are Kahler manifolds. The technique used is that of imaginary time-translation, previously introduced by the author.

Ravi Baijulal Bhandari

Jiao Zhi-Yong

By using the Lewis Riesenfeld invariant theory,we have studied the dynamical and the geometric phases in a generalized time-dependent Λ-type Jaynes-Cummings model with imaginary photon process.We find that the geometric phases in a cycle case have nothing to do with the frequency of the photon field,the coupling coefficient between photons and atoms,and the atom transition frequency.If we use the more accuracy device,the geometric phase in the imaginary photon process may be observed,and the geometric phases in this process have the observable physical effect.

Arno Böhm

Yu Zhai, Youhao Shang, Jian Liu

The geometric phase (GP) is a fundamental quantum effect arising from conical intersections (CIs), with profound consequences for vibronic energy levels. Standard imaginary-time path integral molecular dynamics (PIMD) based on the Born-Oppenheimer approximation does not account for the GP, potentially leading to significant errors in low-temperature thermodynamic properties. In this Perspective, we demonstrate that the multi-electronic-state path integral (MES-PI) formulation in imaginary time (developed in J. Chem. Phys. 2018, 148, 102319) naturally captures the GP effect through the electronic trace of the product of statistically weighted overlap matrices between successive imaginary-time slices. This crucial capability was already implicit in the benchmark MES-PIMD simulations in that foundational work. To isolate this topological effect from other nonadiabatic effects, we introduce a geometric signature matrix (for the CI) and a winding-number-induced phase factor, constructing an ad hoc GP-excluded MES-PI method. Comparing this ad hoc baseline against the rigorous MES-PI approach allows us to unambiguously quantify the impact of the GP on thermodynamic properties. While simpler approximations exist when only the ground electronic-state is considered, MES-PIMD is the most general and accurate approach applicable to real complex systems where the location and topology of CI seams are often not known a priori.

Arun Kumar Pati