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

arXiv:0808.1817 · Journal of Physics A Mathematical and Theoretical

Reduced fidelity and quantum phase transitions in spin-1/2 frustrated Heisenberg chains

Heng-Na Xiong, Jian Ma, Yan Wang, Xiaoguang Wang

Published Jan 15, 2009• 9 citations
arXivHTMLPDF

Abstract

We use reduced fidelity to characterize quantum phase transitions in the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain with frustration. For the ground state and the low-lying excited states, explicit results of the reduced fidelities between the nearest-neighbor and next-nearest-neighbor spins are given in both the even-size and odd-size cases. We find the reduced fidelity is an effective tool in detecting the quantum phase transitions associated with level crossings for the finite-size systems. Interestingly, the reduced fidelity between next-nearest-neighbor spins is evidently more sensitive at the quantum phase transition points than the nearest-neighbor case. Moreover, the reduced fidelity of the low-lying excited states is a good indicator both for the first-order and infinite-order quantum phase transitions of the system.

DOI
10.1088/1751-8113/42/6/065304

Related papers

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

Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains

Yang Xian

Some rigorous results are presented for a first-order quantum phase transition between the dimerized state and Haldane-type state (i.e., a state similar to the ground state of the one-dimensional spin-1 Heisenberg chain) in the spin-1/2 coupled chains with nearest-neighbor and next-nearest-neighbor Heisenberg interactions. Also presented is a class of exact excited states in both phases. A partial phase diagram of the general spin-1/2 coupled chains is discussed.

arXiv:cond-mat/9501006•Physical review. B, Condensed matter•Nov 1, 1995•77 citations

Quantum discord and quantum phase transition in spin-1/2 frustrated Heisenberg chain

Chu-Hui Fan, Heng-Na Xiong, Yixiao Huang +1 more

By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the $SU(2)$ symmetry and $Z_{2}$ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.

arXiv:1301.6482•Quantum Information and Computation•May 1, 2013•6 citations

High-order fidelity and quantum phase transition for the Heisenberg chain with next-nearest-neighbor interaction

Li Wang, Shi-Jian Gu, Shu Chen

In this article, we study the high order term of the fidelity of the Heisenberg chain with next-nearest-neighbor interaction and analyze its connection with quantum phase transition of Beresinskii-Kosterlitz-Thouless type happened in the system. We calculate the fidelity susceptibility of the system and find that although the phase transition point can't be well characterized by the fidelity susceptibility, it can be effectively picked out by the higher order of the ground-state fidelity for finite-size systems.

arXiv:0903.4242•Mar 25, 2009•0 citations

Quantum phases of dimerized and frustrated Heisenberg spin chains with s = 1/2, 1 and 3/2: an entanglement entropy and fidelity study

V. M. L. Durga Prasad Goli, Shaon Sahoo, S. Ramasesha +1 more

We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J2) and dimerization (δ). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J2-δ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.

arXiv:1208.0706•Journal of Physics Condensed Matter•Feb 19, 2013•11 citations

Thermodynamics of the frustrated ferromagnetic spin-1/2 Heisenberg chain

Johannes Richter, M Härtel, D Ihle +1 more

We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.

arXiv:0811.3549•Journal of Physics Conference Series•Jan 1, 2009•6 citations
We use reduced fidelity to characterize quantum phase transitions in the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain with frustration. For the ground state and the low-lying excited states, explicit results of the reduced fidelities between the nearest-neighbor and next-nearest-neighbor spins are given in both the even-size and odd-size cases. We find the reduced fidelity is an effective tool in detecting the quantum phase transitions associated with level crossings for the finite-size systems. Interestingly, the reduced fidelity between next-nearest-neighbor spins is evidently more sensitive at the quantum phase transition points than the nearest-neighbor case. Moreover, the reduced fidelity of the low-lying excited states is a good indicator both for the first-order and infinite-order quantum phase transitions of the system.
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.
By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the SU(2)SU(2)SU(2) symmetry and Z2Z_{2}Z2​ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.
In this article, we study the high order term of the fidelity of the Heisenberg chain with next-nearest-neighbor interaction and analyze its connection with quantum phase transition of Beresinskii-Kosterlitz-Thouless type happened in the system. We calculate the fidelity susceptibility of the system and find that although the phase transition point can't be well characterized by the fidelity susceptibility, it can be effectively picked out by the higher order of the ground-state fidelity for finite-size systems.
We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction J2) and dimerization (δ). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the J2-δ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.
We studied the thermodynamics of the one-dimensional J 1 - J 2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J 1 < 0 and frustrating antiferromagnetic next- nearest-neighbor bonds J 2 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J 2 < | J 1 |/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J 2 . The analysis of the low-temperature behavior of the susceptibility χ leads to the conclusion that this behavior changes from χ ∝ T -2 at J 2 < | J 1 |/4 to χ ∝ T -3/2 at the quantum-critical point J 2 = | J 1 |/4. Another effect of the frustration is the appearance of an extra low- T maximum in the specific heat C v ( T ) for J 2 & | J 1 |/8, indicating its strong influence on the low-energy spectrum.