scholarly journals Tensor network study of two dimensional lattice $\phi^{4}$ theory

2019 ◽  
Author(s):  
Ryo Sakai ◽  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Yoshifumi Nakamura ◽  
Shinji Takeda ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Network

scholarly journals Loop-TNR analysis of CP(1) model with theta term

2018 ◽  
Vol 175 ◽  
pp. 11015
Author(s):  
Hikaru Kawauchi ◽  
Shinji Takeda
Keyword(s):  
Renormalization Group ◽  
Phase Structure ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Networks ◽  
Tensor Network ◽  
Network Methods ◽  
Renormalization Method ◽  
Future Work

The phase structure of the two dimensional lattice CP(1) model in the presence of the θ term is analyzed by tensor network methods. The tensor renormalization group, which is a standard renormalization method of tensor networks, is used for the regions θ = 0 and θ ≠ 0. Loop-TNR, which is more suitable for the analysis of near criticality, is also implemented for the region θ = 0. The application of Loop-TNR for the region θ ≠ 0 is left for future work.

scholarly journals Application of tensor network method to two dimensional lattice N = 1 Wess–Zumino model

2018 ◽  
Vol 175 ◽  
pp. 11019
Author(s):  
Ryo Sakai ◽  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Yoshifumi Nakamura ◽  
Shinji Takeda ◽  
...  
Keyword(s):  
Majorana Fermions ◽  
Two Dimensional ◽  
Scalar Boson ◽  
Boson Systems ◽  
Dimensional Lattice ◽  
Sign Problem ◽  
Tensor Network ◽  
Network Method ◽  
Basic Ideas ◽  
Zumino Model

We study a tensor network formulation of the two dimensional lattice N = 1 Wess–Zumino model with Wilson derivatives for both fermions and bosons. The tensor renormalization group allows us to compute the partition function without the sign problem, and basic ideas to obtain a tensor network for both fermion and scalar boson systems were already given in previous works. In addition to improving the methods, we have constructed a tensor network representation of the model including the Yukawatype interaction of Majorana fermions and real scalar bosons. We present some numerical results.

scholarly journals Tensor network formulation for two-dimensional lattice $$ \mathcal{N} $$ = 1 Wess-Zumino model

2018 ◽  
Vol 2018 (3) ◽  
Author(s):  
Daisuke Kadoh ◽  
Yoshinobu Kuramashi ◽  
Yoshifumi Nakamura ◽  
Ryo Sakai ◽  
Shinji Takeda ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Dimensional Lattice ◽  
Tensor Network ◽  
Zumino Model

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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