Quantum Information Geometry Meets DMRG: Uhlmann Gauge Improvements in Computational Methods

Abstract: We introduce and systematically investigate a novel approach combining the Uhlmann gauge bundle with Density Matrix Renormalization Group (DMRG) and Matrix Product State (MPS) techniques to enhance the representation and preservation of quantum coherence in strongly correlated many-body systems. Conventional DMRG and MPS methods frequently encounter limitations when dealing with subtle quantum correlations and entanglement structures near critical points, avoided crossings, and topologically ordered phases. By integrating the dynamical Uhlmann gauge potential and its categorical extensions into the numerical optimization and truncation procedures, our approach substantially improves coherence stability and accuracy. Through illustrative applications in quantum chemistry, condensed matter physics, and quantum dynamics, we demonstrate significant enhancements in precision and reliability, underscoring the broad potential of Uhlmann gauge-enhanced computational methods.