Small matrix path integral (SMatPI) methods and the interplay between frustration and quantum dissipation in tight binding models

The small matrix decomposition of the path integral (SMatPI) allows stable, fully quantum mechanical calculations of equilibrium and dynamical properties in quantum dissipative systems, circumventing the sign problem of Monte Carlo methods and the large storage requirements of tensor-based algorithms. SMatPI calculations 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 calculations show that the von Neumann entropy of frustrated Hamiltonians is minimally affected by the strength of system-bath coupling, in sharp contrast to trends in systems that do not exhibit frustration, and that frustration significantly decreases transport and relaxation rates. The observed behaviors correlate perfectly with a simple measure of frustration and can be understood in terms of geometric phases associated with conical intersections, along with the sign flipping of coherences, which are severely quenched in frustrated systems. These intriguing equilibrium and dynamical phenomena are absent in frustrated systems that lack dissipative environments and in conventional quantum dissipative systems that do not exhibit frustration.