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Quantum Phase Transition of 1D Infinite Three-state Potts Model Based on iMPS Algorithm

Author: DaiYanWei
Tutor: HuBingQuan
School: Chongqing University
Course: Theoretical Physics
Keywords: bifurcation critical point quantum phase transition von Neumann entropy
CLC: O413
Type: Master's thesis
Year: 2009
Downloads: 18
Quote: 0
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Abstract


In this paper ,we will investigate that the ground-state fidelity per lattice site is computed for the quantum three-state Potts model in a transverse magnetic field on an infinite-size lattice in one spatial dimension in terms of the infinite matrix product state algorithm. It is found that, on the one hand, a pinch point is identified on the fidelity surface around the critical point, and on the other hand, the ground-state fidelity per lattice site exhibits bifurcations at pseudo critical points for different truncation dimensions, which in turn approach the critical point as the truncation dimension gets large. This implies that the ground-state fidelity per lattice site enables us to capture spontaneous symmetry breaking when the control parameter crosses the critical value. In addition, a finite-entanglement scaling of the von Neumann entropy is performed with respect to the truncation dimension, resulting in a precise determination of the central charge at the critical point. Finally, we compute both longitudinal and transverse magnetizations, from which critical exponents are extracted from the numerical data.

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CLC: > Mathematical sciences and chemical > Physics > Theoretical Physics > Quantum theory
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