2017/11/28 by Huang, Zhoushen, Balatsky, Alexander V.
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.1711.10471
We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic dimensionality DP is much smaller than the full Hilbert space dimension, and is equivalent to a statistical complexity measure eS2, where S2 is the 2nd Renyi entropy of the manifold. In the thermodynamic limit, DP closely approximates the quantum geometric volume of the manifold under the Fubini-Study metric, revealing an intriguing connection between information and geometry. This connection persists in compact manifolds such as a twisted boundary phase, where the corresponding geometric circumference is lower bounded by a term proportional to its topological index, reminiscent of entanglement entropy.