arXiv:0903.4242

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

Li Wang, Shi-Jian Gu, Shu Chen

Published Mar 25, 2009• 0 citations

Abstract

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.

DOI: 10.48550/arxiv.0903.4242

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arXiv:0903.4242

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

Li Wang, Shi-Jian Gu, Shu Chen

Published Mar 25, 2009• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.0903.4242

Related papers

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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.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.

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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.

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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.