Lee-Yang zeros and large-deviation statistics of a molecular zipper

Deger, Aydin; Brandner, Kay; Flindt, Christian

doi:10.1103/physreve.97.012115

Cited by 41 publications

(84 citation statements)

References 63 publications

(83 reference statements)

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“…The relation between high-order cumulants of the energy and the Fisher zeros in statistical mechanics systems was also pointed out recently in Refs. [31][32][33].…”

Section: B Fisher Zeros and Cumulants Of The Gauge Actionmentioning

confidence: 99%

“…The radius of convergence of a Taylor expansion of log P is determined by the position of the zeros of P, and it is clearly the same as that of log Z, so that we can simply ignore the exponential prefactor in Eq. (33). On such a small lattice, it was possible to find all roots of P using standard methods.…”

Section: B Calculation Of the Cumulants Of The Quark Number To Arbitmentioning

confidence: 99%

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Reliable estimation of the radius of convergence in finite density QCD

Giordano

Pásztor

2019

Phys. Rev. D

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We study different estimators of the radius of convergence of the Taylor series of the pressure in finite density QCD. We adopt the approach in which the radius of convergence is estimated first in a finite volume, and the infinite-volume limit is taken later. This requires an estimator for the radius of convergence that is reliable in a finite volume. Based on general arguments about the analytic structure of the partition function in a finite volume, we demonstrate that the ratio estimator cannot work in this approach, and propose three new estimators, capable of extracting reliably the radius of convergence, which coincides with the distance from the origin of the closest Lee-Yang zero. We also provide an estimator for the phase of the closest Lee-Yang zero, necessary to assess whether the leading singularity is a true critical point. We demonstrate the usage of these estimators on a toy model, namely 4 flavors of unimproved staggered fermions on a small 6 3 × 4 lattice, where both the radius of convergence and the Taylor coefficients to any order can be obtained by a direct determination of the Lee-Yang zeros. Interestingly, while the relative statistical error of the Taylor expansion coefficients steadily grows with order, that of our estimators stabilizes, allowing for an accurate estimate of the radius of convergence. In particular, we show that despite the more than 100% error bars on high-order Taylor coefficients, the given ensemble contains enough information about the radius of convergence.

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“…The relation between high-order cumulants of the energy and the Fisher zeros in statistical mechanics systems was also pointed out recently in Refs. [31][32][33].…”

Section: B Fisher Zeros and Cumulants Of The Gauge Actionmentioning

confidence: 99%

Section: B Calculation Of the Cumulants Of The Quark Number To Arbitmentioning

confidence: 99%

Reliable estimation of the radius of convergence in finite density QCD

Giordano

Pásztor

2019

Phys. Rev. D

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“…This situation is changing now as Lee-Yang zeros have been determined in several experiments [16][17][18][19][20][21][22][23]. Recently, partition function zeros were measured using carefully engineered nano-structures involving the precession of interacting molecular spins [17][18][19], Cooper pair tunneling in superconducting devices [20][21][22], or fermionic atoms in driven optical lattices [23]. In parallel with these experiments, several theoretical proposals have been put forward for the detection of partition function zeros [24][25][26][27][28].…”

mentioning

confidence: 99%

“…With increasing system size, the partition function zeros approach the real value of the control parameter for which a phase transition occurs in the thermodynamic limit. From the definition of the cumulants, we now obtain the relation [20][21][22] U n = (−1) (n−1)…”

mentioning

confidence: 99%

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Determination of universal critical exponents using Lee-Yang theory

Deger

Flindt

2019

Phys. Rev. Research

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Lee-Yang zeros are complex values of an external control parameter at which the partition function vanishes for a many-body system of finite size. In the thermodynamic limit, the Lee-Yang zeros approach the critical value on the real-axis where a phase transition occurs. Partition function zeros have for many years been considered a purely theoretical concept, however, the situation is changing now as Lee-Yang zeros have been determined in several recent experiments. Motivated by these developments, we here devise a direct pathway from measurements of partition function zeros to the determination of critical points and universal critical exponents of continuous phase transitions. To illustrate the feasibility of our approach, we extract the critical exponents of the Ising model in two and three dimensions from the fluctuations of the total energy and the magnetization in surprisingly small lattices. Importantly, the critical exponents can be determined even if the system is away from the phase transition, for example at a high temperature. As such, our method provides an intriguing perspective for investigations of phase transitions that may be hard to reach experimentally, for instance at very low temperatures or at very high pressures.

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Quantum Fisher Information and Lee‐Yang Zeros with Quantum Coherence of the Isotropic XY$XY$ Model and the Energy Scale

et al. 2022

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Lee-Yang zeros lie on the complex plane of the control parameters for many-body systems with finite size, such as the transverse magnetic field and the inverse temperature. Here, an anisotropic spin system with nearest-neighbor interactions for finite-size parity space is considered. The Lee-Yang zeros are obtained in anisotropic XY model for the complex plane of the transverse magnetic field and in the isotropic XY model for the complex fugacity plane of the quantum coherence. A characteristic function to represent the probe spin coherence for the isotropic XY model, and study on Lee-Yang zeros, quantum coherence, and quantum Fisher information at the complex fugacity plane is presented. The relationship between quantum Fisher information and quantum coherence in decoherence channels is demonstrated and it is illustrated that information cannot be acquired at high temperatures. Meanwhile, the ground-state energy on the complex plane for the anisotropic XY model is studied and the free energy cumulants with the partition function of the anisotropic XY model for parity space is calculated.

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Lee-Yang zeros and large-deviation statistics of a molecular zipper

Cited by 41 publications

References 63 publications

Reliable estimation of the radius of convergence in finite density QCD

Reliable estimation of the radius of convergence in finite density QCD

Determination of universal critical exponents using Lee-Yang theory

Quantum Fisher Information and Lee‐Yang Zeros with Quantum Coherence of the Isotropic XY$XY$ Model and the Energy Scale

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