Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field

Adelhardt, Patrick; Koziol, Jan Alexander; Schellenberger, Andreas; Schmidt, K. P.

doi:10.1103/physrevb.102.174424

Cited by 27 publications

(135 citation statements)

References 77 publications

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“…From the high-temperature extrapolation to zero temperature, the T-linear relations intersect at a point located on the field axis, so that one can get the QCP λ c = 1.0. It is worth noting that, at λ c , the dispersion presents ω| λ λc ∝ |k − k c | z with the dynamic critical exponent z = 2 for d = 1 [33,34]. Thus, one can obtain ] = 1/2.…”

Section: Resultsmentioning

confidence: 95%

“…A peak-valley structure marks two crossover temperatures fanning out a QC regime, which constitute two branches of the phase crossover boundaries. In the QC regime, it is well known that the correlation length ξ diverges as ξ ∝ |λ − λ c | −v , whereas the correlation time τ c diverges as [1], and the energy gap E g is inversely proportional to the correlation length [32,33], wherein v and z are defined as the correlation length and dynamic critical exponents, respectively. It presents a linear relation of crossover temperature T p ∝ |λ − λ c | zv with zv = 1.…”

Section: Resultsmentioning

confidence: 99%

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Critical Scaling of Entropy and Thermal Drude Weight in Anisotropic Heisenberg Antiferromagnets: A Thermodynamic Quest for Quantum Criticality

Ding

Zhong

2022

Front. Phys.

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Up to now, probing the quantum phase transition (QPT) and quantum critical (QC) phenomena at finite temperatures in one-dimensional (1D) spin systems still lacks an in-depth understanding. Herein, we study the QPT and thermodynamics of 1D spin-1/2 anisotropic Heisenberg antiferromagnetic chains by Green’s function theory. The quantum phase diagram is renormalized by the anisotropy (∆), which manifests a quantum critical point (QCP) hc = 1 + ∆ signaling the transition from gapless Tomonaga–Luttinger liquid (TLL) to gapped ferromagnetic (FM) state, demonstrated by the magnetic entropy and thermal Drude weight. At low temperatures, it is shown that two crossover temperatures fan out a QC regime and capture the QCP via the linear extrapolation to zero temperature. In addition, around QCP, the QC scaling is performed by analyzing the entropy and thermal Drude weight to extract the critical exponents (α, δ, and β) that fulfill the Essamm–Fisher scaling law, which provides a novel thermodynamic means to detect QPT for experiment. Furthermore, scaling hypothesis equations with two rescaled manners are proposed to testify the scaling analysis, for which all the data points fall on a universal curve or two independent branches for the plot against rescaled field or temperature, implying the self-consistency and reliability of the obtained critical exponents.

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Section: Resultsmentioning

confidence: 95%

Section: Resultsmentioning

confidence: 99%

Critical Scaling of Entropy and Thermal Drude Weight in Anisotropic Heisenberg Antiferromagnets: A Thermodynamic Quest for Quantum Criticality

Ding

Zhong

2022

Front. Phys.

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“…A key ingredient is that the model covers both the XX-and XY -symmetric cases, and a variety of phase transitions occur, as the transverse field and the XY -anisotropy change. Meanwhile, its extention to the long-range-interaction case has been made [7]; particularly, the limiting cases such as the transverse-field Ising and XXZ chains with the long-range interactions have been investigated in depth [8,9,10,11,12,13,14,15,16,17]. A notable point is that the effective dimensionality [8] D = 2/σ + 1,…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we investigate the transverse-field XY chain with the longrange interactions [7] by means of the exact-diagonalization method, which enables us to access to the ground state directly. We devote ourselves to the anisotropy-driven multi-criticality around the XX-symmetric point.…”

Section: Introductionmentioning

confidence: 99%

“…We devote ourselves to the anisotropy-driven multi-criticality around the XX-symmetric point. So far, the transverse-field-driven criticality with the fixed anisotropy has been explored in detail [7]. As for the large-N magnet, the multi-criticality has been studied [23], and an intriguing reentrant behavior was observed in low dimensions, 2 < D < 3.065 .…”

Section: Introductionmentioning

confidence: 99%

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Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality

Nishiyama

2021

Preprint

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The transverse-field XY chain with the long-range interactions was investigated by means of the exact-diagonalization method. The algebraic decay rate σ of the long-range interaction is related to the effective dimensionality D(σ), which governs the criticality of the transverse-field-driven phase transition at H = H c . According to the large-N analysis, the phase boundary H c (η) exhibits a reentrant behavior within 2 < D < 3.065 . . ., as the XY -anisotropy η changes. On the one hand, as for the D = (2 + 1) and (1 + 1) short-range XY magnets, the singularities have been determined as H c (η) − H c (0) ∼ |η| and 0, respectively, and the transient behavior around D ≈ 2.5 remains unclear. As a preliminary survey, setting (σ, η) = (1, 0.5), we investigate the phase transition by the agency of the fidelity, which seems to detect the singularity at H = H c rather sensitively. Thereby, under the setting σ = 4/3 (D = 2.5), we cast the fidelity data into the crossover-scaling formula with the properly scaled η, aiming to determine the multi-criticality around η = 0. Our result indicates that the multi-criticality is identical to that of the D = (2 + 1) magnet, and H c (η)'s linearity might be retained down to D > 2.

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Quantum criticality in spin-1/2 anisotropic XY model with staggered Dzyaloshinskii–Moriya interaction

Yao

Liu

Wan

et al. 2022

Physica A: Statistical Mechanics and its Applications

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Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field

Cited by 27 publications

References 77 publications

Critical Scaling of Entropy and Thermal Drude Weight in Anisotropic Heisenberg Antiferromagnets: A Thermodynamic Quest for Quantum Criticality

Critical Scaling of Entropy and Thermal Drude Weight in Anisotropic Heisenberg Antiferromagnets: A Thermodynamic Quest for Quantum Criticality

Fidelity-mediated analysis of the transverse-field $XY$ chain with the long-range interactions: Anisotropy-driven multi-criticality

Quantum criticality in spin-1/2 anisotropic XY model with staggered Dzyaloshinskii–Moriya interaction

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