Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E

Reply to “Comment on ‘Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field' ”

O. F. de Alcantara Bonfim, B. Boechat, J. Florencio

Published Jul 13, 2020• 0 citations
Publisher

Abstract

We disagree with the objections raised by Nemati et al. regarding the phase transitions reported in our paper, where we used the fidelity method. Contrary to their claims, our fidelity calculations do not depend on energy level crossing between excited states. We obtain the same results just by analyzing the second derivative of the ground-state energy with respect to the interaction energy coupling J_{2}.

DOI
10.1103/physreve.102.016102

Related papers

Comment on “Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field”

Somayyeh Nemati, F. Khastehdel Fumani, S. Mahdavifar

Here we show that, although quantum fidelity can truly identify two quantum phase transitions of a one-dimensional spin-1/2 quantum Ising model with competing nearest and next-nearest neighbor interactions in a transverse magnetic field, it may not be a suitable approach for analyzing its ground-state phase diagram.

Physical review. E•Jul 13, 2020•5 citations

Quantum fidelity approach to the ground-state properties of the one-dimensional axial next-nearest-neighbor Ising model in a transverse field

O. F. de Alcantara Bonfim, B. Boechat, J. Florencio

In this work we analyze the ground-state properties of the s=1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field B_{x} and the strength of the next-nearest-neighbor interaction J_{2}, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and 〈2,2〉 phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the 〈2,2〉 phases is possibly of first order.

arXiv:1705.09679•Physical review. E•Oct 17, 2017•10 citations

Fidelity approach: the misleading role of finite size level crossing of excited energies

Somayyeh Nemati, F. Khastehdel Fumani, S. Mahdavifar

Here, we show that, although quantum fidelity can truly identify two quantum phase transitions of a one-dimensional spin-1/2 quantum Ising model with competing nearest and next-nearest neighbour interactions in a transverse magnetic field, it may not be a suitable approach for analyzing its ground-state phase diagram.

arXiv:2007.01186•Jul 2, 2020•0 citations

Fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction

Shu Chen, Li Wang, Shi-Jian Gu +1 more

In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J1-J2 model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the J1-J2 model cannot be well characterized by the ground-state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.

arXiv:0706.0072•Physical Review E•Dec 7, 2007•139 citations

Ground-state properties of the one-dimensional transverse Ising model in a longitudinal magnetic field

O. F. de Alcantara Bonfim, B. Boechat, J. Florencio

The critical properties of the one-dimensional spin-1/2 transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J_{2}, we calculated the fidelity susceptibility as a function of the transverse field B_{x} and the longitudinal field B_{z}. The phase diagram in the (B_{x},B_{z})-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For B_{x}<1, we observed an antiferromagnetic phase for small values of B_{z} and a paramagnetic phase for large values of B_{z}. For B_{x}>1 and low B_{z}, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of B_{z}.

arXiv:1808.07591•Physical review. E•Jan 14, 2019•34 citations

Fidelity approach to quantum phase transitions: finite-size scaling for the quantum Ising model in a transverse field

Huan-Qiang Zhou, Jian-Hui Zhao, Bo Li

We analyze the fidelity per lattice site for two different ground states of the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the fidelity per lattice site is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite-size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.

arXiv:0704.2940•Journal of Physics A Mathematical and Theoretical•Oct 29, 2008•96 citations
We disagree with the objections raised by Nemati et al. regarding the phase transitions reported in our paper, where we used the fidelity method. Contrary to their claims, our fidelity calculations do not depend on energy level crossing between excited states. We obtain the same results just by analyzing the second derivative of the ground-state energy with respect to the interaction energy coupling J_{2}.
In this work we analyze the ground-state properties of the s=1/2 one-dimensional axial next-nearest-neighbor Ising model in a transverse field using the quantum fidelity approach. We numerically determined the fidelity susceptibility as a function of the transverse field B_{x} and the strength of the next-nearest-neighbor interaction J_{2}, for systems of up to 24 spins. We also examine the ground-state vector with respect to the spatial ordering of the spins. The ground-state phase diagram shows ferromagnetic, floating, and 〈2,2〉 phases, and we predict an infinite number of modulated phases in the thermodynamic limit (L→∞). Paramagnetism only occurs for larger magnetic fields. The transition lines separating the modulated phases seem to be of second order, whereas the line between the floating and the 〈2,2〉 phases is possibly of first order.
In this paper, we investigate the fidelity for the Heisenberg chain with the next-nearest-neighbor interaction (or the J1-J2 model) and analyze its connections with quantum phase transition. We compute the fidelity between the ground states and find that the phase transition point of the J1-J2 model cannot be well characterized by the ground-state fidelity for finite-size systems. Instead, we introduce and calculate the fidelity between the first excited states. Our results show that the quantum transition can be well characterized by the fidelity of the first excited state even for a small-size system.
The critical properties of the one-dimensional spin-1/2 transverse Ising model in the presence of a longitudinal magnetic field were studied by the quantum fidelity method. We used exact diagonalization to obtain the ground-state energies and corresponding eigenvectors for lattice sizes up to 24 spins. The maximum of the fidelity susceptibility was used to locate the various phase boundaries present in the system. The type of dominant spin ordering for each phase was identified by examining the corresponding ground-state eigenvector. For a given antiferromagnetic nearest-neighbor interaction J_{2}, we calculated the fidelity susceptibility as a function of the transverse field B_{x} and the longitudinal field B_{z}. The phase diagram in the (B_{x},B_{z})-plane shows three phases. These findings are in contrast with the published literature that claims that the system has only two phases. For B_{x}<1, we observed an antiferromagnetic phase for small values of B_{z} and a paramagnetic phase for large values of B_{z}. For B_{x}>1 and low B_{z}, we found a disordered phase that undergoes a second-order phase transition to a paramagnetic phase for large values of B_{z}.
We analyze the fidelity per lattice site for two different ground states of the one-dimensional quantum Ising model in a transverse field near the critical point. It is found that, in the thermodynamic limit, the fidelity per lattice site is singular, and the derivative of its logarithmic function with respect to the transverse field strength is logarithmically divergent at the critical point. The scaling behavior is confirmed numerically by performing a finite-size scaling analysis for systems of different sizes, consistent with the conformal invariance at the critical point. This allows us to extract the correlation length critical exponent, which turns out to be universal in the sense that the correlation length critical exponent does not depend on either the anisotropic parameter or the transverse field strength.