Fidelity and entanglement entropy for infinite-order phase transitions

Abstract

We study the fidelity and the entanglement entropy for the ground states of quantum systems that have infinite-order quantum phase transitions. In particular, we consider the quantum O(2) model with a spin-$S$ truncation, where there is an infinite-order Gaussian (IOG) transition for $S=1$ and there are Berezinskii-Kosterlitz-Thouless (BKT) transitions for $S\ge 2$. We show that the height of the peak in the fidelity susceptibility (${\chi }_F$) converges to a finite thermodynamic value as a power law of $1/L$ for the IOG transition and as $1/\ln (L)$ for BKT transitions. The peak position of ${\chi }_F$ resides inside the gapped phase for both the IOG transition and BKT transitions. On the other hand, the derivative of the block entanglement entropy with respect to the coupling constant ($S_{vN}^{\prime }$) has a peak height that diverges as ${\ln }^2(L)$ [${\ln }^3(L)$] for $S=1$ ($S\ge 2$) and can be used to locate both kinds of transitions accurately. We include higher-order corrections for finite-size scalings and crosscheck the results with the value of the central charge $c=1$. The crossing point of ${\chi }_F$ between different system sizes is at the IOG point for $S=1$ but is inside the gapped phase for $S\ge 2$, while those of $S_{vN}^{\prime }$ are at the phase-transition points for all $S$ truncations. Our work elaborates how to use the finite-size scaling of ${\chi }_F$ or $S_{vN}^{\prime }$ to detect infinite-order quantum phase transitions and discusses the efficiency and accuracy of the two methods.

References in corpus (24)

• The density-matrix renormalization group in the age of matrix product states
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Quantum critical scaling of the geometric tensors
• Quantum Phase Transitions and Bipartite Entanglement
• Mixed-state fidelity and quantum criticality at finite temperature
• Intrinsic relation between ground-state fidelity and the characterization of a quantum phase transition
• Fidelity and Quantum phase transition for the Heisenberg chain with the next-nearest-neighbor interaction
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Scaling Properties of Fidelity in Spin-one Anisotropic Model
• Scaling of the gap, fidelity susceptibility, and Bloch oscillations across the superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model
• Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
• Single-Site Entanglement of Fermions at a Quantum Phase Transition
• Fidelity at Berezinskii-Kosterlitz-Thouless quantum phase transitions
• Finite temperature fidelity susceptibility for one-dimensional quantum systems
• Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions
• Fidelity approach to Gaussian transitions
• Progress towards quantum simulating the classical O(2) model
• Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
• Gap scaling at Berezinskii-Kosterlitz-Thouless quantum critical points in one-dimensional Hubbard and Heisenberg models
• Generalized fidelity susceptibility at phase transitions
• Fidelity Susceptibility in the Quantum Rabi Model
• Spectral function and fidelity susceptibility in quantum critical phenomena
• Fidelity and superconductivity in two-dimensional t-J models
• Critical Entanglement for the Half-Filled Extended Hubbard Model

Cited by in corpus (4)

• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice
• Dipolar Bose-Hubbard Model in finite-size real-space cylindrical lattices
• Quantum simulation of spin-1/2 XYZ model using solid-state spin centers