Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations

Inglis, Stephen; Melko, Roger G.

doi:10.1103/physreve.87.013306

Cited by 39 publications

(44 citation statements)

References 37 publications

(71 reference statements)

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“…To do that, we exploit the expansion of the correlators ⟨s n s m ⟩ and ⟨p n p m ⟩ (cf. (28) and (29)). Let us first consider the negativity between site n ≡ (n x , n y , n z ) and m ≡ (m x , m y , m z ).…”

Section: Low-temperature Expansionmentioning

confidence: 94%

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Entanglement and classical fluctuations at finite-temperature critical points

Wald¹,

Arias²,

Alba³

2020

J. Stat. Mech.

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We investigate several entanglement-related quantities at finite-temperature criticality in the three-dimensional quantum spherical model, both as a function of temperature T and of the quantum parameter g, which measures the strength of quantum fluctuations. While the von Neumann and the Rényi entropies exhibit the volume-law for any g and T , the mutual information obeys an area law. The prefactors of the volume-law and of the area-law are regular across the transition, reflecting that universal singular terms vanish at the transition. This implies that the mutual information is dominated by nonuniversal contributions. This hampers its use as a witness of criticality, at least in the spherical model. We also study the logarithmic negativity. For any value of g, T , the negativity exhibits an area-law. The negativity vanishes deep in the paramagnetic phase, it is larger at small temperature, and it decreases upon increasing the temperature. For any g, it exhibits the so-called sudden death, i.e., it is exactly zero for large enough T . The vanishing of the negativity defines a "death line", which we characterise analytically at small g. Importantly, for any finite T the area-law prefactor is regular across the transition, whereas it develops a cusp-like singularity in the limit T → 0. Finally, we consider the single-particle entanglement and negativity spectra. The vast majority of the levels are regular across the transition. Only the larger ones exhibit singularities. These are related to the presence of a zero mode, which reflects the symmetry breaking. This implies the presence of sub-leading singular terms in the entanglement entropies. Interestingly, since the larger levels do not contribute to the negativity, sub-leading singular corrections are expected to be suppressed for the negativity.

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Section: Low-temperature Expansionmentioning

confidence: 94%

“…Much efforts focused on the behaviour of the mutual information. For instance, it has been suggested [25][26][27][28][29][30] that the mutual information exhibits a crossing for different sizes at a finite-temperature critical point, similar to more traditional tools in critical phenomena, such as the Binder cumulant [31].…”

Section: Introductionmentioning

confidence: 95%

Entanglement and classical fluctuations at finite-temperature critical points

Wald¹,

Arias²,

Alba³

2020

J. Stat. Mech.

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“…In practice, we consider as a condition for the flatness of H(n) a maximum deviation of 20% from the mean value. Once H(n) is flat, it is reset to zero, and f is decreased by ln( f )→ln( f old )/2 [41]. This process is repeated until convergence is achieved.…”

Section: Measuring Entanglement Entropy In Numerical Simulationsmentioning

confidence: 99%

“…This process is repeated until convergence is achieved. Here we use the convergence condition proposed in [41,42].…”

Section: Measuring Entanglement Entropy In Numerical Simulationsmentioning

confidence: 99%

Measuring von Neumann entanglement entropies without wave functions

Mendes-Santos¹,

Giudici²,

Fazio³

et al. 2020

New J. Phys.

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We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of lattice entanglement Hamiltonians-recently proposed in the paper [Dalmonte et al 2018 Nat. Phys. 14 827] via field theoretical insights-and can be performed by quantum Monte Carlo methods. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories. The protocol can also be adapted to measure entanglement in experiments via quantum quenches.

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“…The 1/t algorithm has been successfully applied to several statistical systems [24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Nonconvergence of the Wang-Landau algorithms with multiple random walkers

Belardinelli

Pereyra

2016

Phys. Rev. E

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This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and 1/t algorithms. The classical algorithms are modified by the use of m independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number π by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, t; then, the average over m walkers is performed. It is observed that the error goes as 1/ √ m. However, if the number of walkers increases above a certain critical value m > mx, the error reaches a constant value (i.e. it saturates). This occurs for both algorithms; however, it is shown that for a given system, the 1/t algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value mx, since it does not reduces the error in the calculation. Therefore, the number of walkers does not guarantee convergence.

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Wang-Landau method for calculating Rényi entropies in finite-temperature quantum Monte Carlo simulations

Cited by 39 publications

References 37 publications

Entanglement and classical fluctuations at finite-temperature critical points

Entanglement and classical fluctuations at finite-temperature critical points

Measuring von Neumann entanglement entropies without wave functions

Nonconvergence of the Wang-Landau algorithms with multiple random walkers

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