Finite Density Condensation and Scattering Data: A Study in 
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>ϕ</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>
 Lattice Field Theory

Gattringer, Christof; Giuliani, Mario; Orasch, Oliver

doi:10.1103/physrevlett.120.241601

Cited by 5 publications

(8 citation statements)

References 23 publications

(33 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We show that we can use worm algorithms to update the worldline configurations efficiently in any particle-number sector by tuning the chemical potential carefully [32]. While worldline methods to study bosonic quantum field theories are well known by now [33][34][35], and have been used in several studies so far [36][37][38][39][40][41], their applicability to bosonic quantum many-body physics has remained relatively unexplored [42,43]. Thus, our work can be viewed as an attempt to fill this gap.…”

Section: Introductionmentioning

confidence: 99%

Few-body physics on a spacetime lattice in the worldline approach

Singh¹,

Chandrasekharan²

2019

Phys. Rev. D

View full text Add to dashboard Cite

We formulate the physics of two species of nonrelativistic hard-core bosons with attractive or repulsive delta function interactions on a spacetime lattice in the worldline approach. We show that worm algorithms can efficiently sample the worldline configurations in any fixed particle-number sector if the chemical potential is tuned carefully. Since fermions can be treated as hard-core bosons up to a permutation sign, we apply this approach to study nonrelativistic fermions. The fermion permutation sign is an observable in this approach and can be used to extract energies in each particle-number sector. In one dimension, nonrelativistic fermions can only permute across boundaries, and so our approach does not suffer from sign problems in many cases, unlike the auxiliary field method. Using our approach, we discover limitations of the recently proposed complex Langevin calculations in one spatial dimension for some parameter regimes. In higher dimensions, our method suffers from the usual fermion sign problem. Here we provide evidence that it may be possible to alleviate this problem for few-body physics.

show abstract

Section: Introductionmentioning

confidence: 99%

Few-body physics on a spacetime lattice in the worldline approach

Singh¹,

Chandrasekharan²

2019

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…replaced by the corresponding values m(L). This gives rise to a value of a = −0.078 (7) for the scattering length in lattice units and a value of a m ∞ = −0.013(1) for the dimensionless product of a and m ∞ . The functions (3.1) and (3.2) with the fit values for m ∞ , A and a are shown as full red curves in Fig.…”

Section: (33)mentioning

confidence: 99%

“…Thus we conclude from (1.1) that the condensation thresholds µ n (L) are governed by the scattering data. Demonstrating and analyzing the connection between low temperature condensation and scattering data in φ 4 theory in two and four dimensions is the topic of this contribution (see also [7]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Low temperature condensation and scattering data

Orasch¹,

Gattringer²,

Giuliani³

2019

Proceedings of the 36th Annual International Symposium on Lattice Field Theory — PoS(LATTICE2018)

Self Cite

View full text Add to dashboard Cite

We study φ 4 lattice field theory at finite chemical potential µ in two and four dimensions, using a worldline representation that overcomes the complex action problem. We compute the particle number at very low temperature as a function of µ and determine the first three condensation thresholds, where the system condenses 1, 2 and 3 particles. The corresponding critical values of the chemical potential can be related to the 1-, 2-and 3-particle energies of the system, and we check this relation with a direct spectroscopy determination of the n-particle energies from 2n-point functions. We analyze the thresholds as a function of the spatial size of the system and use the known finite volume results for the n-particle energies to relate the thresholds to scattering data. For four dimensions we determine the scattering length from the 2-particle threshold, while in two dimensions the full scattering phase shift can be determined. In both cases the scattering data computed from the 2-particle threshold already allow one to determine the 3-particle energy. In both, two and four dimensions we find very good agreement of this "prediction" with direct determinations of the 3-particle energy from either the thresholds or the 6-point functions. The results show that low temperature condensation is indeed governed by scattering data.

show abstract

“…[12,13] Significant progress has been made to predict the evolution process by computational approaches based on physical mechanisms, such as first-principles calculations, molecular dynamics, and Monte Carlo simulations. [14][15][16][17][18][19] Alternative approaches within the category of dynamic Bayesian models (DBMs), such as hidden Markov model (HMM) and long short-term memory (LSTM), have been developed in parallel to predict time series from statistical perspectives. [20][21][22][23][24] Such capability of inferring future response patterns enables us to understand the evolution mechanism and to conduct virtual experiments.…”

Section: Introductionmentioning

confidence: 99%

Intelligent Generation of Evolutionary Series in a Time‐Variant Physical System via Series Pattern Recognition

Liang

Jiang

Lin

et al. 2020

Advanced Intelligent Systems

View full text Add to dashboard Cite

Intelligent generation of time‐variant control series remains the critical challenge for acquiring the desired system evolution, due to the difficulties in perceiving temporal correlation and conducting appropriate feedback propagation. A machine learning (ML) algorithm named time‐series generative adversarial network (TSGAN) is developed to overcome the difficulties, by incorporating a long short‐term memory (LSTM) kernel for recognizing multirange temporal patterns beyond the Markovian approximation and an adversarial training mechanism for efficient optimization. A variety of time series are examined by temperature‐control experiments, and the results demonstrate an exceptional accuracy (>95%, 35% higher than prevalent ML methods) as well as strong transferability and stability of the TSGAN algorithm. The dependence of generation performance on underlying statistical mechanisms associated with different ML algorithms, including the deep neural network (DNN), hidden Markov model (HMM), LSTM, and TSGAN, is elucidated by analyzing the generation quality of characteristic temporal patterns. The capability of generating arbitrarily complex response series opens an opportunity for inverse design of time‐variant functionals as strenuously pursued in material science and modern technology.

show abstract

Finite Density Condensation and Scattering Data: A Study in ϕ4 Lattice Field Theory

Cited by 5 publications

References 23 publications

Few-body physics on a spacetime lattice in the worldline approach

Few-body physics on a spacetime lattice in the worldline approach

Low temperature condensation and scattering data

Intelligent Generation of Evolutionary Series in a Time‐Variant Physical System via Series Pattern Recognition

Contact Info

Product

Resources

About