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arXiv · 1406.3588

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

Qian-Qian Shi·Huan-Qiang Zhou·Murray T. Batchelor
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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 (DMRG) algorithm.

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Qian-Qian Shi, Huan-Qiang Zhou, Murray T. Batchelor. 2014-06-13. Universal Order Parameters and Quantum Phase Transitions: A Finite-Size Approach. https://doi.org/10.1038/srep07673

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