scholarly journals Tensor renormalization group approach to four-dimensional complex ϕ4 theory at finite density

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Shinichiro Akiyama ◽  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Takumi Yamashita ◽  
Yusuke Yoshimura
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Large Volume ◽  
Numerical Algorithms ◽  
Two Dimensions ◽  
Test Bed ◽  
Finite Density ◽  
Sign Problem ◽  
Tensor Network ◽  
Volume Limit

Abstract Tensor network is an attractive approach to the field theory with negative sign problem. The complex ϕ4 theory at finite density is a test bed for numerical algorithms to verify their effectiveness. The model shows a characteristic feature called the Silver Blaze phenomenon associated with the sign problem in the large volume limit at low temperature. We analyze the four-dimensional model employing the anisotropic tensor renormalization group algorithm with a parallel computation. We find a clear signal of the Silver Blaze phenomenon on a large volume of V = 10244, which implies that the tensor network approach is effective even for four-dimensional field theory beyond two dimensions.

scholarly journals Renormalization Group evolution from on-shell SMEFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Minyuan Jiang ◽  
Teng Ma ◽  
Jing Shu
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Standard Model ◽  
Effective Field Theory ◽  
Effective Field ◽  
High Dimensional ◽  
Anomalous Dimensions ◽  
The Standard Model ◽  
Group Evolution

Abstract We describe the on-shell method to derive the Renormalization Group (RG) evolution of Wilson coefficients of high dimensional operators at one loop, which is a necessary part in the on-shell construction of the Standard Model Effective Field Theory (SMEFT), and exceptionally efficient based on the amplitude basis in hand. The UV divergence is obtained by firstly calculating the coefficients of scalar bubble integrals by unitary cuts, then subtracting the IR divergence in the massless bubbles, which can be easily read from the collinear factors we obtained for the Standard Model fields. Examples of deriving the anomalous dimensions at dimension six are presented in a pedagogical manner. We also give the results of contributions from the dimension-8 H4D4 operators to the running of V+V−H2 operators, as well as the running of B+B−H2D2n from H4D2n+4 for general n.

scholarly journals Interface Roughening in Two Dimensions

2021 ◽  
Vol 182 (3) ◽  
Author(s):  
Gernot Münster ◽  
Manuel Cañizares Guerrero
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Capillary Wave ◽  
System Size ◽  
Two Dimensions ◽  
Two Dimensional ◽  
Wave Approximation ◽  
Statistical Field ◽  
Statistical Field Theory ◽  
Interface Roughening

AbstractRoughening of interfaces implies the divergence of the interface width w with the system size L. For two-dimensional systems the divergence of $$w^2$$ w 2 is linear in L. In the framework of a detailed capillary wave approximation and of statistical field theory we derive an expression for the asymptotic behaviour of $$w^2$$ w 2 , which differs from results in the literature. It is confirmed by Monte Carlo simulations.

scholarly journals Complex Langevin calculations in QCD at finite density

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Yuta Ito ◽  
Hideo Matsufuru ◽  
Yusuke Namekawa ◽  
Jun Nishimura ◽  
Shinji Shimasaki ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Chemical Potential ◽  
Expansion Method ◽  
Finite Density ◽  
Fermi Sphere ◽  
Expectation Value ◽  
Sign Problem ◽  
Zero Momentum ◽  
Effective Theories ◽  
Severe Sign

Abstract We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with β = 5.7 and four-flavor staggered fermions with degenerate quark mass ma = 0.01 and nonzero quark chemical potential μ. We confirm that a sufficient condition for correct convergence is satisfied for μ/T = 5.2 − 7.2 on a 83 × 16 lattice and μ/T = 1.6 − 9.6 on a 163 × 32 lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to μ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) × 4 (flavor) × 2 (spin) = 24. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

scholarly journals Aspects of quantum information in finite density field theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Lucas Daguerre ◽  
Raimel Medina ◽  
Mario Solís ◽  
Gonzalo Torroba
Keyword(s):  
Field Theory ◽  
Quantum Information ◽  
Mutual Information ◽  
Fermi Surface ◽  
Relative Entropy ◽  
Chemical Potential ◽  
Operator Product ◽  
Dirac Fermions ◽  
Long Distance ◽  
Finite Density

Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

STOCHASTIC FIELD THEORY AND RENORMALIZATION GROUP APPROACH TO CRITICAL BEHAVIORS IN THERMO FIELD DYNAMICS

1989 ◽  
Vol 04 (09) ◽  
pp. 2185-2210
Author(s):  
B. BHATTACHARYA
Keyword(s):  
Field Theory ◽  
Renormalization Group ◽  
Finite Temperature ◽  
Internal Field ◽  
Point Of View ◽  
Internal Space ◽  
Theoretic Approach ◽  
Stochastic Field ◽  
Stochastic Fields ◽  
Renormalization Group Approach

We have studied here the critical behaviors in a simple model from the point of view of the renormalization group at finite temperature utilizing the Stochastic field theoretic approach towards a finite temperature field theory. To this end, thermofield dynamics has been formulated in terms of Stochastic fields in the external and internal space and the thermal average of the two-point correlation function of the internal field functions is related with the order parameter. The thermodynamical functions and the critical phenomena are then studied constructing the generating functionals involving Stochastic fields.

scholarly journals Aspects of renormalization in finite-density field theory

2015 ◽  
Vol 91 (19) ◽  
Author(s):  
A. Liam Fitzpatrick ◽  
Gonzalo Torroba ◽  
Huajia Wang
Keyword(s):  
Field Theory ◽  
Density Field ◽  
Finite Density
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