arXiv:0706.0072 · Physical Review E

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

Shu Chen, Li Wang, Shi-Jian Gu, Yupeng Wang

Published Dec 7, 2007• 139 citations

Abstract

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.

DOI: 10.1103/physreve.76.061108

Related papers

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

Li Wang, Shi-Jian Gu, Shu Chen

arXiv:0903.4242Mar 25, 20090 citations

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

Heng-Na Xiong, Jian Ma, Yan Wang +1 more

arXiv:0808.1817Journal of Physics A Mathematical and TheoreticalJan 15, 20099 citations

A quantum fidelity study of the anisotropic next-nearest-neighbour triangular lattice Heisenberg model

Mischa Thesberg, Erik Schwartz Sørensen

arXiv:1409.1405Journal of Physics Condensed MatterOct 2, 20143 citations

Estimating phase transition of perturbed J1−J2 Heisenberg quantum chain in mixtures of ground and first excited states

Sayan Mondal, George Biswas, Ahana Ghoshal +2 more

arXiv:2211.00623New Journal of PhysicsNov 22, 20234 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

arXiv:1208.0706Journal of Physics Condensed MatterFeb 19, 201311 citations

General quantum fidelity susceptibilities for the J1 - J2 chain

Mischa Thesberg, Erik Schwartz Sørensen

arXiv:1110.0353Physical Review BDec 28, 201124 citations

arXiv:0706.0072 · Physical Review E

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

Shu Chen, Li Wang, Shi-Jian Gu, Yupeng Wang

Published Dec 7, 2007• 139 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physreve.76.061108

Related papers

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.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:0903.4242Mar 25, 20090 citations

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

Heng-Na Xiong, Jian Ma, Yan Wang +1 more

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.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.

arXiv:0808.1817Journal of Physics A Mathematical and TheoreticalJan 15, 20099 citations

A quantum fidelity study of the anisotropic next-nearest-neighbour triangular lattice Heisenberg model

Mischa Thesberg, Erik Schwartz Sørensen

Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.

arXiv:1409.1405Journal of Physics Condensed MatterOct 2, 20143 citations

Estimating phase transition of perturbed J1−J2 Heisenberg quantum chain in mixtures of ground and first excited states

Sayan Mondal, George Biswas, Ahana Ghoshal +2 more

Abstract We show that the nearest neighbour entanglement in a mixture of ground and first excited states—a subjacent state—of the J 1 − J 2 Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small finite probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to separate introductions of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point in the former case. The anisotropic J 1 − J 2 chain has a richer phase diagram which is also clearly visible by using the same order parameter.Abstract We show that the nearest neighbour entanglement in a mixture of ground and first excited states—a subjacent state—of the J 1 − J 2 Heisenberg quantum spin chain can be used as an order parameter to detect the phase transition of the chain from a gapless spin fluid to a gapped dimer phase. We study the effectiveness of the order parameter for varying relative mixing probabilities between the ground and first excited states in the subjacent state for different system sizes, and extrapolate the results to the thermodynamic limit. We observe that the nearest neighbour concurrence can play a role of a good order parameter even if the system is in the ground state, but with a small finite probability of leaking into the first excited state. Moreover, we apply the order parameter of the subjacent state to investigate the response to separate introductions of anisotropy and of glassy disorder on the phase diagram of the model, and analyse the corresponding finite-size scale exponents and the emergent tricritical point in the former case. The anisotropic J 1 − J 2 chain has a richer phase diagram which is also clearly visible by using the same order parameter.

arXiv:2211.00623New Journal of PhysicsNov 22, 20234 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.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:1208.0706Journal of Physics Condensed MatterFeb 19, 201311 citations

General quantum fidelity susceptibilities for the J1 - J2 chain

Mischa Thesberg, Erik Schwartz Sørensen

We study slightly generalized quantum fidelity susceptibilities where the differential change in the fidelity is measured with respect to a different term than the one used for driving the system toward a quantum phase transition. As a model system we use the spin- $1/2$ ${J}_{1}$ - ${J}_{2}$ antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, ${\ensuremath{\chi}}_{\ensuremath{\rho}}$, ${\ensuremath{\chi}}_{D}$, and ${\ensuremath{\chi}}_{\mathrm{AF}}$, which are related to the spin stiffness, the dimer order, and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the ${J}_{1}$ - ${J}_{2}$ model. We show that they all can accurately identify a quantum critical point in this model occurring at ${J}_{2}^{c}\ensuremath{\sim}0.241{J}_{1}$ between a gapless Heisenberg phase for ${J}_{2}<{J}_{2}^{c}$ and a dimerized phase for ${J}_{2}>{J}_{2}^{c}$ . This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.We study slightly generalized quantum fidelity susceptibilities where the differential change in the fidelity is measured with respect to a different term than the one used for driving the system toward a quantum phase transition. As a model system we use the spin-$1/2$ ${J}_{1}$-${J}_{2}$ antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, ${\ensuremath{\chi}}_{\ensuremath{\rho}}$, ${\ensuremath{\chi}}_{D}$, and ${\ensuremath{\chi}}_{\mathrm{AF}}$, which are related to the spin stiffness, the dimer order, and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the ${J}_{1}$-${J}_{2}$ model. We show that they all can accurately identify a quantum critical point in this model occurring at ${J}_{2}^{c}\ensuremath{\sim}0.241{J}_{1}$ between a gapless Heisenberg phase for ${J}_{2}<{J}_{2}^{c}$ and a dimerized phase for ${J}_{2}>{J}_{2}^{c}$. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.

arXiv:1110.0353Physical Review BDec 28, 201124 citations

1/2

{J}_{1}

{J}_{2}

antiferromagnetic Heisenberg chain. For this model, we study three fidelity susceptibilities, ${\ensuremath{\chi}}_{\ensuremath{\rho}}$, ${\ensuremath{\chi}}_{D}$, and ${\ensuremath{\chi}}_{\mathrm{AF}}$, which are related to the spin stiffness, the dimer order, and antiferromagnetic order, respectively. All these ground-state fidelity susceptibilities are sensitive to the phase diagram of the

{J}_{1}

{J}_{2}

model. We show that they all can accurately identify a quantum critical point in this model occurring at ${J}_{2}^{c}\ensuremath{\sim}0.241{J}_{1}$ between a gapless Heisenberg phase for

{J}_{2}<{J}_{2}^{c}

and a dimerized phase for

{J}_{2}>{J}_{2}^{c}

. This phase transition, in the Berezinskii-Kosterlitz-Thouless universality class, is controlled by a marginal operator and is therefore particularly difficult to observe.