Physical review. B./Physical review. B

Robust approach to study the effect on quantum phase transitions of various perturbations at finite temperatures

Cheng-Pu Lv, Yanchao Li, Hai‐Qing Lin

Published Feb 22, 2022• 5 citations

Abstract

We propose using maximum coherence (${\mathrm{QC}}_{\mathrm{max}}$) to study quantum phase transition (QPT). We investigate several well-known models, such as the XXZ model, ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ model, and one-dimensional spin Kitaev model. The results show that ${\mathrm{QC}}_{\mathrm{max}}$ can be used to detect different types of QPTs, including the Berezinskii-Kosterlitz-Thouless and topological types. In addition, ${\mathrm{QC}}_{\mathrm{max}}$ is more robust against interferences, such as thermal fluctuations and measurement interferences, than any existing detector. This property enables ${\mathrm{QC}}_{\mathrm{max}}$ to identify QPTs in experiments, where temperature effects and measurement interferences always exist. Thus, ${\mathrm{QC}}_{\mathrm{max}}$ might be an ideal tool for studying QPTs because of its measurability, universality, and robustness against interferences.

DOI: 10.1103/physrevb.105.054424

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Physical review. B./Physical review. B

Robust approach to study the effect on quantum phase transitions of various perturbations at finite temperatures

Cheng-Pu Lv, Yanchao Li, Hai‐Qing Lin

Published Feb 22, 2022• 5 citations

Publisher

Abstract

We propose using maximum coherence (

{\mathrm{QC}}_{\mathrm{max}}

) to study quantum phase transition (QPT). We investigate several well-known models, such as the XXZ model,

{J}_{1}\text{\ensuremath{-}}{J}_{2}

model, and one-dimensional spin Kitaev model. The results show that

{\mathrm{QC}}_{\mathrm{max}}

can be used to detect different types of QPTs, including the Berezinskii-Kosterlitz-Thouless and topological types. In addition,

{\mathrm{QC}}_{\mathrm{max}}

is more robust against interferences, such as thermal fluctuations and measurement interferences, than any existing detector. This property enables

{\mathrm{QC}}_{\mathrm{max}}

to identify QPTs in experiments, where temperature effects and measurement interferences always exist. Thus,

{\mathrm{QC}}_{\mathrm{max}}

might be an ideal tool for studying QPTs because of its measurability, universality, and robustness against interferences.

DOI: 10.1103/physrevb.105.054424

Related papers

Quantum coherence spectrum and quantum phase transitions

Yanchao Li, Jing Zhang, Hai‐Qing Lin

We review the internal connection between quantum coherence (QC) and quantum phase transitions (QPTs). We propose two quantities ${L}_{\text{QC}}$ and ${S}_{\text{QC}}$ to detect QPTs of different orders by analyzing the spectrum of QC. Our results show that the two quantities not only can detect different types of QPT but can also exhibit a remarkable robustness against thermal fluctuations. In comparison with other detectors, such as quantum entanglement and QD, ${L}_{\text{QC}}$ and ${S}_{\text{QC}}$ can show more effective and reliable behaviors in characterizing a QPT at zero and finite temperatures. In light of this property and the fundamental role of QC in quantum information processing, QC spectrum-related ${L}_{\text{QC}}$ and ${S}_{\text{QC}}$ have considerable importance in detecting QPTs at a real finite-temperature experimental environment.We review the internal connection between quantum coherence (QC) and quantum phase transitions (QPTs). We propose two quantities ${L}_{\text{QC}}$ and ${S}_{\text{QC}}$ to detect QPTs of different orders by analyzing the spectrum of QC. Our results show that the two quantities not only can detect different types of QPT but can also exhibit a remarkable robustness against thermal fluctuations. In comparison with other detectors, such as quantum entanglement and QD, ${L}_{\text{QC}}$ and ${S}_{\text{QC}}$ can show more effective and reliable behaviors in characterizing a QPT at zero and finite temperatures. In light of this property and the fundamental role of QC in quantum information processing, QC spectrum-related ${L}_{\text{QC}}$ and ${S}_{\text{QC}}$ have considerable importance in detecting QPTs at a real finite-temperature experimental environment.

Physical review. B./Physical review. BMar 25, 202027 citations

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Fidelity study of the quantum phase transition in the one-dimensional spin-1 XXZ model in the thermodynamic limit

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Scientific ReportsMay 19, 201698 citations

INTERPLAY BETWEEN QUANTUM PHASE TRANSITIONS AND THE BEHAVIOR OF QUANTUM CORRELATIONS AT FINITE TEMPERATURES

T. Werlang, G. A. P. RIBEIRO, GUSTAVO RIGOLIN

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Reduced State Stabilizer Rényi Entropy as a Probe of Quantum Phase Transitions in Frustrated J_1-J_2 Spin Models

George Biswas, Santanu Sarkar, Jun-Yi Wu +1 more

We investigate whether the second-order purity-corrected stabilizer Rényi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic $J_1-J_2$ Heisenberg model, the one-dimensional XXZ $J_1-J_2$ model, and the two-dimensional $J_1-J_2$ Heisenberg model on a $4\times4$ square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding $α_c(\infty)=0.24116$ , in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding $α_c(\infty)=0.2681$ . For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at $α_c(4\times4)=0.40781$ and $0.6208$ , while the ground-state SRE identifies the second at $0.6230$ . Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.We investigate whether the second-order purity-corrected stabilizer Rényi entropy (SRE) of reduced two-qubit density matrices can serve as a reliable local indicator of quantum phase transitions (QPTs) in frustrated quantum spin systems. We consider the one-dimensional isotropic $J_1-J_2$ Heisenberg model, the one-dimensional XXZ $J_1-J_2$ model, and the two-dimensional $J_1-J_2$ Heisenberg model on a $4\times4$ square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding $α_c(\infty)=0.24116$, in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding $α_c(\infty)=0.2681$. For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at $α_c(4\times4)=0.40781$ and $0.6208$, while the ground-state SRE identifies the second at $0.6230$. Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.

quant-pharXiv:2608.17313Aug 19, 20260 citations

We propose using maximum coherence (

{\mathrm{QC}}_{\mathrm{max}}

) to study quantum phase transition (QPT). We investigate several well-known models, such as the XXZ model,

{J}_{1}\text{\ensuremath{-}}{J}_{2}

model, and one-dimensional spin Kitaev model. The results show that

{\mathrm{QC}}_{\mathrm{max}}

can be used to detect different types of QPTs, including the Berezinskii-Kosterlitz-Thouless and topological types. In addition,

{\mathrm{QC}}_{\mathrm{max}}

is more robust against interferences, such as thermal fluctuations and measurement interferences, than any existing detector. This property enables

{\mathrm{QC}}_{\mathrm{max}}

to identify QPTs in experiments, where temperature effects and measurement interferences always exist. Thus,

{\mathrm{QC}}_{\mathrm{max}}

might be an ideal tool for studying QPTs because of its measurability, universality, and robustness against interferences.

We review the internal connection between quantum coherence (QC) and quantum phase transitions (QPTs). We propose two quantities

{L}_{\text{QC}}

and

{S}_{\text{QC}}

to detect QPTs of different orders by analyzing the spectrum of QC. Our results show that the two quantities not only can detect different types of QPT but can also exhibit a remarkable robustness against thermal fluctuations. In comparison with other detectors, such as quantum entanglement and QD,

{L}_{\text{QC}}

and

{S}_{\text{QC}}

can show more effective and reliable behaviors in characterizing a QPT at zero and finite temperatures. In light of this property and the fundamental role of QC in quantum information processing, QC spectrum-related

{L}_{\text{QC}}

and

{S}_{\text{QC}}

have considerable importance in detecting QPTs at a real finite-temperature experimental environment.

\frac{1}{2}

XXZ model, and the interacting Su-Schrieffer-Heeger model. The fidelity map can capture a wide range of phase transitions accurately even in small systems, thus providing a convenient tool to study QPTs in unseen models without prior knowledge of the symmetry of the system.

J_1-J_2

Heisenberg model, the one-dimensional XXZ

J_1-J_2

model, and the two-dimensional

J_1-J_2

Heisenberg model on a

4\times4

square lattice. Unlike several previously studied quantum information measures, which fail to detect QPTs in the ground state of these frustrated systems, the reduced ground-state purity-corrected SRE successfully identifies most transitions. For the remaining cases, we consider a low temperature subjacent state, modeled as a statistical mixture of the ground and first excited states with a Maxwell--Boltzmann-type occupation probability. For the 1D isotropic model, the subjacent-state SRE shows a discontinuity at the critical point, yielding

α_c(\infty)=0.24116

, in excellent agreement with established values; the ground-state SRE shows a point of inflection, yielding

α_c(\infty)=0.2681

. For the 1D XXZ model, the subjacent-state SRE reproduces the full anisotropy dependent phase diagram, while the ground-state SRE captures transitions only at low anisotropy. For the 2D model, the subjacent-state SRE detects two transitions, at

α_c(4\times4)=0.40781

and

0.6208

, while the ground-state SRE identifies the second at

0.6230

. Compared with conventional two-qubit entanglement, purity-corrected SRE shows a clear advantage in revealing otherwise-invisible phase transitions, establishing it as a robust, efficient, local probe of frustrated quantum criticality.