HMC force class for rectangular gauge action with the SF BC. More...

#include <force_G_Rectangle_SF.h>

Inheritance diagram for Force_G_Rectangle_SF:

Public Member Functions
	Force_G_Rectangle_SF ()

	Force_G_Rectangle_SF (const Parameters &params)

	~Force_G_Rectangle_SF ()

void	set_parameters (const Parameters &params)

void	set_parameters (const double beta, const double c_plaq, const double c_rect, double phi, double phipr, const double ct, const double ctr)

void	get_parameters (Parameters &params) const

void	force_core (Field &)

Public Member Functions inherited from Force_G
	Force_G ()

virtual	~Force_G ()

void	set_config (Field *U)

void	set_config (Field_G *U)

virtual void	force_core (Field &v, Field *U)

virtual void	force_core (Field &v, Field_G *U)

Static Public Attributes
static const std::string	class_name = "Force_G_Rectangle_SF"

Private Attributes
Bridge::VerboseLevel	m_vl

int	m_Nc

double	m_beta

double	m_c_plaq

double	m_c_rect

std::string	m_label

Staple_SF	m_staple

ShiftField_lex	m_shift

Mat_SU_N	m_wk
	SF boundary condition. More...

Mat_SU_N	m_wkpr

double	m_ct
	SF boundary improvement coefficient for the plaquatte action. More...

double	m_ctr
	SF boundary improvement coefficient for the rectangle action. More...

std::vector< double >	m_phi

std::vector< double >	m_phipr

Additional Inherited Members
Protected Attributes inherited from Force_G
Field_G *	m_U

Detailed Description

HMC force class for rectangular gauge action with the SF BC.

Gauge action with plaquette and rectangular Wilson loops. Iwasaki, Luscher-Weisz, DBW2 are examples of this type of action.

SF boundary condition is intrduced accrdong to the following policy.

The total size of temporal links is Nt with the Dirichlet BC.
We need t=0, ..., Nt sites for Nt links.
The boundary spatial link at t=0 is dummy.
- Calculation of the Hamiltonian and force is overridden to given the correct result without using the spatial link at t=0 stored in the Field_G object.
- The spatial link at t=0 is updated by a randomly given conjugate momentum but is not used for the Hamiltoniand nor the force.
- The corresponding force for the spatial conjugate momentum at t=0 is set to zero. This conjugate momentum is not updated at the boundary.
The boundary spatial sites at t=Nt does not exist in the Field_G object.
- Calculation of the Hamiltonian and force is overridden to given the correct result using an approriate matrix for the spatial link at t=Nt.

The rectangle improved gauge action is given by

$S[U]= \frac{\beta}{N_c}\sum_{{\cal C}\in{\cal S}_0}W_0({\cal C}) {\rm Re}{\rm Tr}\left(-P({\cal C})\right) +\frac{\beta}{N_c}\sum_{{\cal C}\in{\cal S}_1}W_1({\cal C}) {\rm Re}{\rm Tr}\left(-R({\cal C})\right)$

where ${\cal C}$ is an oriented plaquette or rectangle. One needs to choose the weight factors appropriately to achieve the O(a) improvement.

$W_0({\cal C}) = \left\{ \begin{array}{ll} c_0 c^P_{\rm{t}}(g^2_0) & \mbox{for } {\cal C} \in P_{\rm{t}} : \mbox{Set of temporal plaquettes that just touch} \\ & \mbox{\hspace{19mm} one of the boundaries, } \\ c_0 & \mbox{for } {\cal C} \in P_{\rm{other}} : \mbox{otherwise, } \end{array} \right.$

$W_1({\cal C}) = \left\{ \begin{array}{ll} c_1 c^R_{\rm{t}}(g^2_0) & \mbox{for } {\cal C} \in R^2_{\rm{t}} : \mbox{Set of temporal rectangles that have exactly} \\ & \mbox{\hspace{19mm} two links on a boundary, } \\ c_1 & \mbox{for } {\cal C} \in R_{\rm{other}} : \mbox{otherwise, } \end{array} \right.$

A major difference from Action_G_Rectangle class is to override a calculation of the Hamltonian and the force.
Boundary condition can be accessed with m_phi and m_phipr.
Boundary improvement factor is stored in m_ct, m_ctr.
[03 Feb. 2012 Y.Taniguchi]

(Coding history will be recovered from trac.) YAML is implemented. [14 Nov 2012 Y.Namekawa]

Definition at line 103 of file force_G_Rectangle_SF.h.

Constructor & Destructor Documentation

◆ Force_G_Rectangle_SF() [1/2]

Force_G_Rectangle_SF::Force_G_Rectangle_SF ( )

inline

Definition at line 138 of file force_G_Rectangle_SF.h.

◆ Force_G_Rectangle_SF() [2/2]

Force_G_Rectangle_SF::Force_G_Rectangle_SF ( const Parameters & params )

inline

Definition at line 143 of file force_G_Rectangle_SF.h.

◆ ~Force_G_Rectangle_SF()

Force_G_Rectangle_SF::~Force_G_Rectangle_SF ( )

inline

Definition at line 149 of file force_G_Rectangle_SF.h.

Member Function Documentation

◆ force_core()

void Force_G_Rectangle_SF::force_core ( Field & force )

virtual

The force for the rectangle improved gauge action with the SF boundary.

We use Wk, Wk' for the boundary spatial link.
The boundary improvement factor ct, ctr is implemented.

ctr is multiplied to the following temporal rectangle staple

       +---+---+        +---+---+
       |  ctr              ctr  |
   t=0 +---+---x        x---+---+

       x   <---+        +---x   ^
       |  ctr  |        |  ctr  |
   t=0 +---+---+        +---+---+

       +---+---+        +---+---+
       |  ctr              ctr  |
t=Nt-1 +---+---x        x---+---+

       +---+---+        +---+---+
       |  ctr  |        |  ctr  |
t=Nt-1 x   <---+        +---x   v

Force for the boundary spatial link is set to zero.
```
       +---+---+             +---+---+
       |       |  --> 0      |       |  --> 0
   t=0 x   <---+         t=0 +---x   v
```
```
   t=0 x   <---+         t=0 +---x   ^
       |       |  --> 0      |       |  --> 0
       +---+---+             +---+---+
 
```
- We notice that the upper and lower staple accompanied with the boundary spatial link is set to zero by Staple_SF::upper() and Staple_SF::lower(). Corresponding contributions to the boundary spatial link are automaticaly zero.

Contribution from the non existing rectangle is automatically zero by Staple_SF::upper() and Staple_SF::lower().

       +---+        +---+
           |        |
   t=0 ^   +    t=0 +   ^  --> 0
       |   |        |   |
       +---+        +---+

       +---+        +---+
       |   |        |   |
  t=Nt +   +   t=Nt +   +  --> 0
           |        |
       <---+        +--->

Implements Force_G.

Definition at line 230 of file force_G_Rectangle_SF.cpp.

◆ get_parameters()

void Force_G_Rectangle_SF::get_parameters ( Parameters & params ) const

virtual

Implements Force_G.

Definition at line 69 of file force_G_Rectangle_SF.cpp.

◆ set_parameters() [1/2]

void Force_G_Rectangle_SF::set_parameters	(	const double	beta,
		const double	c_plaq,
		const double	c_rect,
		double *	phi,
		double *	phipr,
		const double	ct,
		const double	ctr
	)

Set parameters for the improved gauge action with the SF boundary.

m_beta
m_c_plaq, m_c_rect: plaquette and rectangle factor.
- Iwasaki action: c_plaq = 3.648, c_rect = -0.331
m_phi, m_phipr: boundary spatial link
m_ct: improvement factor for the boundary temporal plaquette.
m_ctr: improvement factor for the boundary temporal rectangle with two links attached to the boundary.

Definition at line 108 of file force_G_Rectangle_SF.cpp.

◆ set_parameters() [2/2]

void Force_G_Rectangle_SF::set_parameters ( const Parameters & params )

virtual

Implements Force_G.

Definition at line 25 of file force_G_Rectangle_SF.cpp.

Member Data Documentation

◆ class_name

const std::string Force_G_Rectangle_SF::class_name = "Force_G_Rectangle_SF"

static

Definition at line 106 of file force_G_Rectangle_SF.h.

◆ m_beta

double Force_G_Rectangle_SF::m_beta

private

Definition at line 116 of file force_G_Rectangle_SF.h.

◆ m_c_plaq

double Force_G_Rectangle_SF::m_c_plaq

private

Definition at line 117 of file force_G_Rectangle_SF.h.

◆ m_c_rect

double Force_G_Rectangle_SF::m_c_rect

private

Definition at line 118 of file force_G_Rectangle_SF.h.

◆ m_ct

double Force_G_Rectangle_SF::m_ct

private

SF boundary improvement coefficient for the plaquatte action.

Definition at line 130 of file force_G_Rectangle_SF.h.

◆ m_ctr

double Force_G_Rectangle_SF::m_ctr

private

SF boundary improvement coefficient for the rectangle action.

Definition at line 132 of file force_G_Rectangle_SF.h.

◆ m_label

std::string Force_G_Rectangle_SF::m_label

private

Definition at line 120 of file force_G_Rectangle_SF.h.

◆ m_Nc

int Force_G_Rectangle_SF::m_Nc

private

Definition at line 114 of file force_G_Rectangle_SF.h.

◆ m_phi

std::vector<double> Force_G_Rectangle_SF::m_phi

private

Definition at line 135 of file force_G_Rectangle_SF.h.

◆ m_phipr

std::vector<double> Force_G_Rectangle_SF::m_phipr

private

Definition at line 135 of file force_G_Rectangle_SF.h.

◆ m_shift

ShiftField_lex Force_G_Rectangle_SF::m_shift

private

Definition at line 123 of file force_G_Rectangle_SF.h.

◆ m_staple

Staple_SF Force_G_Rectangle_SF::m_staple

private

Definition at line 122 of file force_G_Rectangle_SF.h.

◆ m_vl

Bridge::VerboseLevel Force_G_Rectangle_SF::m_vl

private

Definition at line 109 of file force_G_Rectangle_SF.h.

◆ m_wk

Mat_SU_N Force_G_Rectangle_SF::m_wk

private

SF boundary condition.

Definition at line 126 of file force_G_Rectangle_SF.h.

◆ m_wkpr

Mat_SU_N Force_G_Rectangle_SF::m_wkpr

private

Definition at line 126 of file force_G_Rectangle_SF.h.

The documentation for this class was generated from the following files:

src/lib/Force/Gauge/force_G_Rectangle_SF.h
src/lib/Force/Gauge/force_G_Rectangle_SF.cpp

Public Member Functions

Static Public Attributes

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Force_G_Rectangle_SF() [1/2]

◆ Force_G_Rectangle_SF() [2/2]

◆ ~Force_G_Rectangle_SF()

Member Function Documentation

◆ force_core()

◆ get_parameters()

◆ set_parameters() [1/2]

◆ set_parameters() [2/2]

Member Data Documentation

◆ class_name

◆ m_beta

◆ m_c_plaq

◆ m_c_rect

◆ m_ct

◆ m_ctr

◆ m_label

◆ m_Nc

◆ m_phi

◆ m_phipr

◆ m_shift

◆ m_staple

◆ m_vl

◆ m_wk

◆ m_wkpr