Exploring quantum phase transitions by the cross derivative of the ground state energy

Abstract

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models [Phys. Rev. B 101, 165123 (2020)], is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.

7 pages, 7 figures

References in corpus (11)

• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The iTEBD algorithm beyond unitary evolution
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Quantum Phase Diagram and Excitations for the One-Dimensional S=1 Heisenberg Antiferromagnet with Single-Ion Anisotropy
• On $c=1$ critical phases in anisotropic spin-1 chains
• Fidelity approach to Gaussian transitions
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods
• Tunable Single-Ion Anisotropy in Spin-1 Models Realized with Ultracold Atoms
• Tangential finite-size scaling of the Gaussian topological transition in the quantum spin-1 anisotropic chain
• Variational corner transfer matrix renormalization group method for classical statistical models
• High-pressure inelastic neutron scattering study of the anisotropic $S=1$ spin chain [Ni(HF${}_2$)(3-Clpyradine)${}_4$]BF${}_4$

Cited by in corpus (4)

• Grüneisen parameter as an entanglement compass and the breakdown of the Hellmann-Feynman theorem
• Refined Phase Diagram for a Spin-1 System Exhibiting a Haldane Phase
• Determination of ground states of one-dimensional quantum systems using the cluster iTEBD method
• Topological materials with extensive flat-band surface states