title: Universal order parameters and quantum phase transitions: a finite-size approach.
abstract: We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm.
authors.affiliation: 1] College of Materials Science and Engineering, Chongqing University, Chongqing 400044, The People's Republic of China [2] Centre for Modern Physics, Chongqing University, Chongqing 400044, The People's Republic of China.
authors.forename: Qian-Qian
authors.initials: QQ
authors.lastname: Shi
authors.affiliation: Centre for Modern Physics, Chongqing University, Chongqing 400044, The People's Republic of China.
authors.forename: Huan-Qiang
authors.initials: HQ
authors.lastname: Zhou
authors.affiliation: 1] Centre for Modern Physics, Chongqing University, Chongqing 400044, The People's Republic of China [2] Australian National University, Canberra ACT 0200, Australia.
authors.forename: Murray T
authors.initials: MT
authors.lastname: Batchelor