Electronic frustration with quantum dissipation: Entropy, coherence, sign problem, and time evolution
Phys. Rev. B 113, 085126 – Published 13 February, 2026
DOI: https://doi.org/10.1103/xtdp-yvhr
Abstract
We investigate the interplay between frustration and quantum dissipation in cyclic tight-binding Hamiltonians with three, four or five sites, which form the basic blocks of common frustrated lattices. The system-bath coupling is representative of interaction between excited electronic states and phonons, thus the models are relevant to exciton transfer. Four of the five model systems are electronically frustrated when the exciton coupling parameter is positive. We show analytically and numerically that the frustrated systems have positive and negative Boltzmann elements, which lead to destructive interference and give rise to a severe sign problem in the Monte Carlo evaluation of the imaginary-time path integral. We use quadrature-based, real- and imaginary-time small matrix path integral (SMatPI) methods, which circumvent the sign problem, to obtain the time evolution of the reduced density matrix and calculate thermodynamic properties. Coupling to dissipative baths dramatically slows down the relaxation of the frustrated systems. Our calculations show that the von Neumann entropy of frustrated Hamiltonians is minimally affected by the strength of system-bath coupling, in sharp contrast to systems that do not exhibit frustration. We find that the severity of the sign problem, the dynamical slowdown, and the phonon bath effects on the evolution of the purity and the equilibrium entropy correlate perfectly with a simple measure of frustration. We discuss the dynamical consequences of electronic frustration in terms of geometric phases associated with conical intersections in the multidimensional system-bath space and also through the sign flipping of coherences, which are severely quenched in frustrated systems, and present coherence maps that illustrate the dynamical bottlenecks to relaxation. These intriguing behaviors are absent in frustrated systems that lack dissipative environments and in conventional quantum dissipative systems that do not exhibit frustration.
