Universal order parameters and quantum phase transitions: a finite-size approach.
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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.
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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.
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. No MeSH data available. Related in: MedlinePlus |
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Mentions: Fig. 2 shows this expected relation between dâˆž(Î») and Î¾âˆž(Î») for different values of Î». Here, the data are mainly obtained using the iTEBD algorithm for infinite-size systems. The results are consistent with the relation (14) holding throughout the SSB phase Î» < 1. At the critical point Î» = 1, the correlation length Î¾ and energy gap Î´L scale as Î¾ ~ 1/Î´L. With scale invariance at criticality, Î¾ ~ L, and thus Î´L ~ 1/L. Then with the expected relation between the fidelity per site of the H-orthogonality states and finite size L at criticality is ln dL ~ âˆ’ ln L/L. The results presented in Fig. 3 indicate that this relation is more precisely |
View Article: PubMed Central - PubMed
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.
No MeSH data available.