Emergent Kardar-Parisi-Zhang Phase in Quadratically Driven Condensates

Diessel, Oriana K.; Diehl, Sebastian; Chiocchetta, Alessio

doi:10.1103/physrevlett.128.070401

Cited by 9 publications

(6 citation statements)

References 70 publications

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“…7, we present the β function for various γ, and (+) α = 0.6, (×) 1, ( * ) 1.4, and (✷) 1.8, with η = 0.2 and N = 22. Here, the dynamical critical exponent z = 1 (2D-Ising universality class) was put into the formula (19) tentatively, and the γ < γ c data is eliminated because of the irregularity due to the oscillatory-Ising-ordered phase. As mentioned above, from the condition β(γ c ) = 0, the critical points are estimated as γ c ≈ 1.23, 1.38, 1.5, and 1.6, respectively.…”

Section: Multi-criticality Around the Xx-symmetric Point η = 0: Small...mentioning

confidence: 99%

“…Meanwhile, the transverse-field XY chain with competing antiferromagnetic longrange interactions was studied with the series expansion method [9]; notable features of the Heisenberg and Kitaev magnets are emphasized in Ref. [18,19,20]. The Ising case has been studied rather extensively [21,22,23,24].…”

Section: Introductionmentioning

confidence: 99%

“…The β function (19) is plotted for various γ, and (+) α = 0.6, (×) 1, ( * ) 1.4, and (✷) 1.8, with η = 0.2 and N = 22. The dynamical critical exponent z = 1 (2D-Ising universality class) was put into the formula(19) tentatively. The zero points of β locate the critical points as γ c = 1.23, 1.38, 1.5, and 1.6, respectively, and the slope 1/ν at each γ c seems to obey the the 2D-Ising-universality-class behavior, i.e., 1/ν = 1, as indicated by the dotted line.…”

mentioning

confidence: 99%

“…Figure 8. The β function(19) is plotted for various γ, and (+) N = 26, (×) 28, and ( * ) 30, with η = 0.4 and α = 0.6 fixed. As a dotted line, the slope 1/ ν = α (16) is shown.…”

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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

Eur. Phys. J. B

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The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J r ∝ 1/r α (r: distance between spins), and the exponent α was investigated numerically. The main concern is to clarify the character of the transversefield-driven phase transition for the small-α regime around the XX-symmetric point, η = 0 (η: XY -anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility χ F . Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the XXsymmetric point in a systematic manner. As a preliminary survey, with η = 0.5 and α = 2 fixed, we made the scaling analysis of χ F . The scaling behavior of χ F shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled η, the χ F data is cast into the crossover scaling formula for the small-α regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

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Section: Multi-criticality Around the Xx-symmetric Point η = 0: Small...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

“…Figure 8. The β function(19) is plotted for various γ, and (+) N = 26, (×) 28, and ( * ) 30, with η = 0.4 and α = 0.6 fixed. As a dotted line, the slope 1/ ν = α (16) is shown.…”

mentioning

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

Eur. Phys. J. B

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“…Meanwhile, the transverse-field XY chain with competing antiferromagnetic longrange interactions was studied with the series expansion method [9]; notable features of the Heisenberg and Kitaev magnets are emphasized in [18][19][20]. The Ising case has been studied rather extensively [21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Transverse-field XY spin chain with the competing long-range interactions: multi-criticality around the XX-symmetric point

Nishiyama¹

2023

J. Stat. Mech.

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The transverse-field XY spin chain with competing antiferromagnetic long-range interactions, J r ∝ 1 / r α (r: distance between spins), and the exponent α was investigated numerically. The main concern is to clarify the character of the transverse-field-driven phase transition for the small-α regime around the XX-symmetric point, η = 0 (η: XY-anisotropy parameter). To cope with the negative-sign problem, we employed the exact-diagonalization method, which enables us to evaluate the fidelity susceptibility χ F . Because the fidelity susceptibility does not assume any order parameter after a phase transition, it detects the multi-criticality around the XX-symmetric point in a systematic manner. As a preliminary survey, with η = 0.5 and α = 2 fixed, we made the scaling analysis of χ F . The scaling behavior of χ F shows that the transverse-field-driven phase transition belongs to the 2D-Ising universality class. Thereby, with the properly crossover-scaled η, the χ F data is cast into the crossover scaling formula for the small-α regime. The multi-critical exponents fed into the scaling formula are argued through referring to related studies.

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Universality of Bose–Einstein condensation and quenched formation dynamics

Proukakis

2024

Encyclopedia of Condensed Matter Physics

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Emergent Kardar-Parisi-Zhang Phase in Quadratically Driven Condensates

Cited by 9 publications

References 70 publications

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

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

Transverse-field XY spin chain with the competing long-range interactions: multi-criticality around the XX-symmetric point

Universality of Bose–Einstein condensation and quenched formation dynamics

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