Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law

Abstract

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and non critical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.

to appear in PRB,8 pages, 2 figures, 3 tables

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Cited by in corpus (20)

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• Dynamics of entanglement entropy and entanglement spectrum crossing a quantum phase transition
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• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Critical points of the anyon-Hubbard model
• Anderson Topological Superconductor
• Confinement and bound states of bound states in a transverse-field two-leg Ising ladder
• Dynamics of the quantum search and quench-induced first-order phase transitions
• Entanglement Entropy of the Low-Lying Excited States and Critical Properties of an Exactly Solvable Two-Leg Spin Ladder with Three-Spin Interactions
• Tricritical Ising phase transition in two-ladder Majorana fermion lattice
• Universal behavior of the Shannon mutual information in non-integrable self-dual quantum chains
• Quench dynamics in the Aubry-André-Harper model with \textit{p}-wave superconductivity
• Universal Finite-Size Corrections of the Entanglement Entropy of Quantum Ladders and the Entropic Area Law
• Coexistence of spontaneous dimerization and magnetic order in a transverse-field Ising ladder with four-spin interactions
• Critical behavior of a quantum chain with four-spin interactions in the presence of longitudinal and transverse magnetic fields
• Study of the 1D anisotropic Kondo necklace model at criticality via an entanglement entropy estimator
• Spacetime Supersymmetry in the Truncated Lattice Schwinger Model
• The c-d conjecture
• Emergent spacetime supersymmetry in an interacting Kitaev chain with explicit supersymmetry