Lattice Monte Carlo calculations for unitary fermions in a finite box

Endres, Michael G.; Kaplan, David B.; Lee, Jong-Wan; Nicholson, Amy

doi:10.1103/physreva.87.023615

Cited by 61 publications

(66 citation statements)

References 66 publications

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“…This agreement is insensitive to the form of the extrapolation used, as the Hadron Spectrum σ-meson mass result at m π ∼ 391 MeV is itself less that one standard deviation smaller than the best-fit nucleon excitation scale. Fits where δE = M σ is explicitly assumed can be performed more precisely and lead to consistent results with smaller uncertainties for the nucleon mass M N = 0.7226 (18), as shown in Fig. 35.…”

Section: An Improved Estimatormentioning

confidence: 91%

“…They presented general arguments, that are discussed below, suggesting that this behavior might be a generic feature of quantum field theories. Knowledge of the approximate form of the correlation function distribution was exploited to construct an improved estimator, the cumulant expansion, that was productively applied to subsequent studies of unitary fermions [15][16][17][18]. Correlation function distributions have been studied analytically in the Nambu-Jona-Lasinio model [13,19], where it was found that real correlation functions were approximately log-normal but complex correlation functions in a physically equivalent formulation of the theory were broad and symmetric at large times with qualitative similarities to the QCD nucleon distribution.…”

Section: Introductionmentioning

confidence: 99%

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Statistics of baryon correlation functions in lattice QCD

Wagman

Savage²

2017

Phys. Rev. D

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A systematic analysis of the structure of single-baryon correlation functions calculated with lattice QCD is performed, with a particular focus on characterizing the structure of the noise associated with quantum fluctuations. The signal-to-noise problem in these correlation functions is shown, as long suspected, to result from a sign problem. The log-magnitude and complex phase are found to be approximately described by normal and wrapped normal distributions respectively. Properties of circular statistics are used to understand the emergence of a large time noise region where standard energy measurements are unreliable. Power-law tails in the distribution of baryon correlation functions, associated with stable distributions and "Lévy flights", are found to play a central role in their time evolution. A new method of analyzing correlation functions is considered for which the signal-to-noise ratio of energy measurements is constant, rather than exponentially degrading, with increasing source-sink separation time. This new method includes an additional systematic uncertainty that can be removed by performing an extrapolation, and the signal-to-noise problem re-emerges in the statistics of this extrapolation. It is demonstrated that this new method allows accurate results for the nucleon mass to be extracted from the large-time noise region inaccessible to standard methods. The observations presented here are expected to apply to quantum Monte Carlo calculations more generally. Similar methods to those introduced here may lead to practical improvements in analysis of noisier systems.

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Section: An Improved Estimatormentioning

confidence: 91%

Section: Introductionmentioning

confidence: 99%

Statistics of baryon correlation functions in lattice QCD

Wagman

Savage²

2017

Phys. Rev. D

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“…It is suitable for studying hadronic physics as well as atomic physics in a finite volume (see Refs. [66,67] for examples of the Lüscher method applied on atomic systems).…”

Section: Introductionmentioning

confidence: 99%

Two-particle multichannel systems in a finite volume with arbitrary spin

2014

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The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin, momentum, and masses in a finite volume with either periodic or twisted boundary conditions is presented. Although emphasis is placed in cubic volumes, the result holds for asymmetric volumes. The result is relativistic, holds for all momenta below the three-and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. For hadronic systems the range of the interaction is set by the inverse of the pion mass, mπ, and as a result the formalism presented is suitable for mπL 1. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.

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“…An example is seen in the evolution [10] of the determination of the so-called Bertsch parameter at unitarity. Quantitative comparisons have allowed validation of our understanding and provided an impetus for developments of both experimental and theoretical techniques.…”

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confidence: 99%

Ground-state properties of strongly interacting Fermi gases in two dimensions

2015

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Exact calculations are performed on the two-dimensional strongly interacting, unpolarized, uniform Fermi gas with a zero-range attractive interaction. Two auxiliary-field approaches are employed which accelerate the sampling of imaginary-time paths using BCS trial wave functions and a force bias technique. Their combination enables calculations on large enough lattices to reliably compute ground-state properties in the thermodynamic limit. A new equation of state is obtained, with a parametrization provided, which can serve as a benchmark and allow accurate comparisons with experiments. The pressure, contact parameter, and condensate fraction are determined systematically vs. kF a. The momentum distribution, pairing correlation, and the structure of the pair wave function are computed. The use of force bias to accelerate the Metropolis sampling of auxiliary-fields in determinantal approaches is discussed. Exact results on fundamental models are uncommon, especially for strongly interacting fermion systems. In the rare cases where they exist (for example in onedimensional models by Bethe ansatz or density matrix renormalization group [1, 2]), they have invariably played an integral role in bringing about physical insights, advancing our understanding, and serving as benchmarks for the development of new theoretical and computational approaches.The Fermi gas with a zero-range attractive interactions is a model for strongly interacting fermions which has generated a great deal of research activities [3,4]. The model is of interest in both condensed matter and nuclear physics. As a model it is rather unique in that, thanks to advances in experimental techniques using ultracold atoms, it can be realized in a laboratory with great precision and control [4,5].In three-dimensions (3D) the interplay between experiment, theory and computation has lead to rapid advances [6][7][8][9]. An example is seen in the evolution [10] of the determination of the so-called Bertsch parameter at unitarity. Quantitative comparisons have allowed validation of our understanding and provided an impetus for developments of both experimental and theoretical techniques. The remarkable level of agreement achieved recently between calculation [8] and experiment [7] demonstrates the tremendous progress towards precise understanding and control of strongly correlated quantum matter.The two-dimensional (2D) Fermi gas has attracted considerable recent interest [11][12][13][14][15][16][17][18][19], especially with its experimental realization using highly anisotropic trapping potentials [20]. In 2D a bound state always exists, and the BCS-BEC cross-over offers rich possibilities between the interplay of inter-particle spacing (density) and interaction strength, where effects beyond the mean-field description will be more pronounced than in 3D. Interest in this model is further enhanced by the 2D nature of many of the most interesting and complex materials, including high-T c cuprate superconductors and topological superconductors [21].In this paper, ...

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Lattice Monte Carlo calculations for unitary fermions in a finite box

Cited by 61 publications

References 66 publications

Statistics of baryon correlation functions in lattice QCD

Statistics of baryon correlation functions in lattice QCD

Two-particle multichannel systems in a finite volume with arbitrary spin

Ground-state properties of strongly interacting Fermi gases in two dimensions

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