Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach

作者：Shi Qian Qian^*; Zhou Huan Qiang; Batchelor Murray T

来源：Scientific Reports, 2015, 5(1): 7673.

DOI：10.1038/srep07673

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.

• 出版日期2015-1-8
• 单位重庆大学