Finite-temperature critical behavior of long-range quantum Ising models

Lazo, Eduardo González; Heyl, Markus; Dalmonte, Marcello; Angelone, Adriano

doi:10.21468/scipostphys.11.4.076

Cited by 14 publications

(19 citation statements)

References 50 publications

(75 reference statements)

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“…( 33) and ϟ = d/d uc for d > d uc , the rounding of finite systems with respect to the bulk behavior is characterized in terms of a universal scaling function Ψ and the critical exponents. It can be used to extract critical exponents in a mean-field regime from finite systems [52,64]. In Ref.…”

Section: O(r H T Lmentioning

confidence: 99%

Scaling at quantum phase transitions above the upper critical dimension

et al. 2022

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The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension following the recently introduced Q-FSS formalism for thermal phase transitions. Contrary to long-standing belief, the correlation sector is affected by dangerous irrelevant variables. The presented formalism recovers a generalized hyperscaling relation and FSS form. Using this new FSS formalism, we determine the full set of critical exponents for the long-range transverse-field Ising chain in all criticality regimes ranging from the nearest-neighbor to the long-range mean-field regime. For the same model, we also explicitly confirm the effect of dangerous irrelevant variables on the characteristic length scale.

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Section: O(r H T Lmentioning

confidence: 99%

Scaling at quantum phase transitions above the upper critical dimension

et al. 2022

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“…As we will discuss below, the finite-size classical system involves a compact direction among those appearing in the non-local kernel, while the field theoretic description of the finite-temperature quantum system requires the introduction of one extra compact direction with local interaction. This observation is not really new, but with few exceptions [22,23] it is often only left implicit in the details of numerical simulations [24,25], and it has not been explored much at an analytical level.…”

Section: Jhep02(2024)078mentioning

confidence: 99%

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Benedetti,

Gurau,

Harribey

et al. 2024

J. High Energ. Phys.

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In this paper we consider classical and quantum versions of the critical long-range O(N) model, for which we study finite-size and finite-temperature effects, respectively, at large N. First, we consider the classical (isotropic) model, which is conformally invariant at criticality, and we introduce one compact spatial direction. We show that the finite size dynamically induces an effective mass and we compute the one-point functions for bilinear primary operators with arbitrary spin and twist. Second, we study the quantum model, mapped to a Euclidean anisotropic field theory, local in Euclidean time and long-range in space, which we dub fractional Lifshitz field theory. We show that this model admits a fixed point at zero temperature, where it displays anisotropic Lifshitz scaling, and show that at finite temperature a thermal mass is induced. We then compute the one-point functions for an infinite family of bilinear scaling operators.In both the classical and quantum model, we find that, as previously noted for the short-range O(N) model in [1], the large-N two-point function contains information about the one-point functions, not only of the bilinear operators, but also of operators that appear in the operator product expansion of two fundamental fields only at subleading order in 1/N, namely powers of the Hubbard-Stratonovich intermediate field.

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“…the Kac normalization [96,97] makes the energy scale to be the same for all α ≤ 2 which somehow suppresses the effect of different decaying exponent α and the phase transition temperature T c is thus scaled to be the same for all α. This point should be further examined by more robust analysis.…”

Section: B Kac Normalization and Phase Diagram At α mentioning

confidence: 99%

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

Zhao

Meng

et al. 2023

Preprint

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The well-known Mermin-Wagner theorem prohibits the existence of finite-temperature spontaneous continuous symmetry breaking phase in systems with short-range (SR) interactions at spatial dimension $D\le 2$. For long-range (LR) interaction with monotonic power-law form ($1/r^{\alpha}$), the theorem further forbids a ferro- or antiferromagnetic order at finite temperature when $\alpha\ge 2D$. However, the situation for $\alpha \in (2,4)$ at $D=2$ is beyond the predicting power of the theorem and the situation is still unclear. Here we address this question by large-scale quantum Monte Carlo (QMC) simulations, accompanied with field theoretical analysis. We find the spontaneous breaking of the $SU(2)$ symmetry for $\alpha \in (2,4)$ in ferromagnetic Heisenberg model with $1/r^{\alpha}$ interaction at $D=2$, and obtain the accurate critical exponents by finite-size analysis for $\alpha<3$ where the system is above the upper critical dimension with Gaussian fixed point and for $3\le\alpha<4$ where the system is below the upper critical dimension with non-Gaussian fixed point. Our results reveal the novel critical behaviors in 2D LR Heisenberg models and will intrigue further experimental studies of quantum materials with LR interaction beyond the realm of the Mermin-Wagner theorem.

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Finite-temperature critical behavior of long-range quantum Ising models

Cited by 14 publications

References 50 publications

Scaling at quantum phase transitions above the upper critical dimension

Scaling at quantum phase transitions above the upper critical dimension

Finite-size versus finite-temperature effects in the critical long-range O(N) model

Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model

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