the symmetry object More...

#include <Symmetry.hpp>

Public Member Functions
Symmetry	clone () const
	return a clone instance of current Symmetry object.

int	stype () const
	return the symmetry type-id of current Symmetry object, see cytnx::SymmetryType::

int &	n () const
	return the discrete n of current Symmetry object.

std::string	stype_str () const
	return the symmetry type name of current Symmetry object in string form, see cytnx::SymmetryType::

bool	check_qnum (const cytnx_int64 &qnum)
	check the quantum number `qnum` is within the valid value range of current Symmetry.

bool	check_qnums (const std::vector< cytnx_int64 > &qnums)
	check all the quantum numbers \qnums are within the valid value range of current Symmetry.

std::vector< cytnx_int64 >	combine_rule (const std::vector< cytnx_int64 > &inL, const std::vector< cytnx_int64 > &inR)
	apply combine rule of current symmetry to two quantum number lists.

void	combine_rule_ (std::vector< cytnx_int64 > &out, const std::vector< cytnx_int64 > &inL, const std::vector< cytnx_int64 > &inR)
	apply combine rule of current symmetry to two quantum number lists, and store it into parameter `out`.

cytnx_int64	combine_rule (const cytnx_int64 &inL, const cytnx_int64 &inR, const bool &is_reverse=false) const
	apply combine rule of current symmetry to two quantum numbers.

void	combine_rule_ (cytnx_int64 &out, const cytnx_int64 &inL, const cytnx_int64 &inR, const bool &is_reverse=false)
	apply combine rule of current symmetry to two quantum numbers, and store the combined quntun number into parameter

void	reverse_rule_ (cytnx_int64 &out, const cytnx_int64 &in)
	Apply reverse rule of current symmetry to a given quantum number and store in parameter `out`.

cytnx_int64	reverse_rule (const cytnx_int64 &in) const
	Apply reverse rule of current symmetry to a given quantum number and return the result.

fermionParity	get_fermion_parity (const cytnx_int64 &in_qnum) const
	fermionic parity for a given quantum number

bool	is_fermionic () const
	check if the Symmetry is fermionic or not

void	Save (const std::string &fname) const
	Save the current Symmetry object to a file.

void	Save (const char *fname) const
	Same as Save(const std::string &fname) const;.

void	print_info () const
	Print the information of current Symmetry object.

bool	operator== (const Symmetry &rhs) const
	the equality operator of the Symmetry object.

bool	operator!= (const Symmetry &rhs) const
	the inequality operator of the Symmetry object.

Static Public Member Functions
static Symmetry	U1 ()
	create a U1 symmetry object

static Symmetry	Zn (const int &n)
	create a Zn discrete symmetry object with \(n\in\mathbb{N}\)

static Symmetry	FermionParity ()
	create a fermionic parity symmetry object

static Symmetry	FermionNumber ()
	create a fermionic occupation number symmetry object

static Symmetry	Load (const std::string &fname)
	Load a Symmetry object from a file.

static Symmetry	Load (const char *fname)
	Same as static Symmetry Load(const std::string &fname);.

Detailed Description

the symmetry object

Member Function Documentation

◆ check_qnum()

bool cytnx::Symmetry::check_qnum ( const cytnx_int64 & qnum )

inline

check the quantum number qnum is within the valid value range of current Symmetry.

Parameters

[in] qnum a singule quantum number.

Returns: [bool]

◆ check_qnums()

bool cytnx::Symmetry::check_qnums ( const std::vector< cytnx_int64 > & qnums )

inline

check all the quantum numbers \qnums are within the valid value range of current Symmetry.

Parameters

[in] qnums the list of quantum numbers

Returns: [bool]

◆ clone()

Symmetry cytnx::Symmetry::clone ( ) const

inline

return a clone instance of current Symmetry object.

Returns: [Symmetry]

Example:

c++ API:

#include "cytnx.hpp"
#include <iostream>
 
using namespace cytnx;
using namespace std;
int main() {
  /* 1.
      create symmetry objects
  */
  Symmetry sym_A = Symmetry::U1();
  Symmetry sym_C = Symmetry::U1();
 
  Symmetry sym_D = sym_A;  // same instance.
 
  // using is() to check if they are the same instance.
  cout << is(sym_D, sym_A) << endl;  // true. same instance
  cout << (sym_D == sym_A) << endl;  // true, same content
 
  cout << is(sym_C, sym_A) << endl;  // false. different instance
  cout << (sym_C == sym_A) << endl;  // true, sane content
 
  return 0;
}

output>

python API:

import sys
from pathlib import Path
home = str(Path.home())
sys.path.append(home + '/Cytnx_lib')
from cytnx import *
 
sym_A = Symmetry.U1()
sym_C = Symmetry.U1()
 
sym_D = sym_A
print(sym_D is sym_A) #true
print(sym_D == sym_A) #true
print(sym_C is sym_A) #false
print(sym_C == sym_A) #true

output>

True
True
False
True

◆ combine_rule() [1/2]

cytnx_int64 cytnx::Symmetry::combine_rule	(	const cytnx_int64 &	inL,
		const cytnx_int64 &	inR,
		const bool &	is_reverse = `false`
	)		const

inline

apply combine rule of current symmetry to two quantum numbers.

Parameters

[in]	inL	the #1 quantum number.
[in]	inR	the #2 quantum number.

Returns: the combined quantum number.

◆ combine_rule() [2/2]

std::vector< cytnx_int64 > cytnx::Symmetry::combine_rule	(	const std::vector< cytnx_int64 > &	inL,
		const std::vector< cytnx_int64 > &	inR
	)

inline

apply combine rule of current symmetry to two quantum number lists.

Parameters

[in]	inL	the #1 quantum number list that is to be combined.
[in]	inR	the #2 quantum number list that is to be combined.

Returns: the combined quantum numbers.

◆ combine_rule_() [1/2]

void cytnx::Symmetry::combine_rule_	(	cytnx_int64 &	out,
		const cytnx_int64 &	inL,
		const cytnx_int64 &	inR,
		const bool &	is_reverse = `false`
	)

inline

apply combine rule of current symmetry to two quantum numbers, and store the combined quntun number into parameter

Parameters

	out.
[out]	out	the output quantum number.
[in]	inL	the #1 quantum number.
[in]	inR	the #2 quantum number.

◆ combine_rule_() [2/2]

void cytnx::Symmetry::combine_rule_	(	std::vector< cytnx_int64 > &	out,
		const std::vector< cytnx_int64 > &	inL,
		const std::vector< cytnx_int64 > &	inR
	)

inline

apply combine rule of current symmetry to two quantum number lists, and store it into parameter out.

Parameters

[out]	out	the output quantum number list.
[in]	inL	the #1 quantum number list that is to be combined.
[in]	inR	the #2 quantum number list that is to be combined.

◆ FermionNumber()

static Symmetry cytnx::Symmetry::FermionNumber ( )

inlinestatic

create a fermionic occupation number symmetry object

valid qnum value range:

\f$(-\infty , \infty)\f$

combine rule:

Q + Q

description:

create a new fermionic occupation number object that serves as a generator. This is a U1 symmetry with parity defined as EVEN for even occupation numbers and ODD for odd occupation numbers. The symmetry object is a property of Bond . It is used to identify the symmetry of the quantum number set, as well as providing the combining rule for the quantum number when Bonds are combined.

◆ FermionParity()

static Symmetry cytnx::Symmetry::FermionParity ( )

inlinestatic

create a fermionic parity symmetry object

valid qnum value range:

\f$[0 , 1]\f$

where 0 corresponds to even parity and 1 to odd parity;

combine rule:

(Q + Q)%2

description:

create a new fermionic parity symmetry object that serves as a generator. The symmetry object is a property of Bond . It is used to identify the symmetry of the quantum number set, as well as providing the combining rule for the quantum number when Bonds are combined.

◆ get_fermion_parity()

fermionParity cytnx::Symmetry::get_fermion_parity ( const cytnx_int64 & in_qnum ) const

inline

fermionic parity for a given quantum number

Parameters

[in] in_qnum quantum number

Returns: parity of the quantum number; false for bosonic degree of freedom, true for fermionic

◆ is_fermionic()

bool cytnx::Symmetry::is_fermionic ( ) const

inline

check if the Symmetry is fermionic or not

Returns: true if Symmetry is fermionic

◆ Load() [1/2]

static Symmetry cytnx::Symmetry::Load ( const char * fname )

static

Same as static Symmetry Load(const std::string &fname);.

◆ Load() [2/2]

static Symmetry cytnx::Symmetry::Load ( const std::string & fname )

static

Load a Symmetry object from a file.

Parameters

[in] fname the file name.

Precondition: the file extension must be ".cysym".

Returns: the loaded Symmetry object.

◆ n()

int & cytnx::Symmetry::n ( ) const

inline

return the discrete n of current Symmetry object.

Returns: [int]

Note

for U1, n=1 will be returned.
for Zn, n is the discrete symmetry number. (ex: Z2, n=2)

◆ operator!=()

bool cytnx::Symmetry::operator!= ( const Symmetry & rhs ) const

the inequality operator of the Symmetry object.

◆ operator==()

bool cytnx::Symmetry::operator== ( const Symmetry & rhs ) const

the equality operator of the Symmetry object.

◆ print_info()

void cytnx::Symmetry::print_info ( ) const

inline

Print the information of current Symmetry object.

◆ reverse_rule()

cytnx_int64 cytnx::Symmetry::reverse_rule ( const cytnx_int64 & in ) const

inline

Apply reverse rule of current symmetry to a given quantum number and return the result.

that means, \( o = -i \), where \( o \) is the reverse quantum number, and \( i \) is the input quantum number in.

Parameters

[in] in the input quantum number.

Returns: the reverse quantum number.

◆ reverse_rule_()

void cytnx::Symmetry::reverse_rule_	(	cytnx_int64 &	out,
		const cytnx_int64 &	in
	)

inline

Apply reverse rule of current symmetry to a given quantum number and store in parameter out.

that means, \( o = -i \), where \( o \) is the output quantum number out, and \( i \) is the input quantum number in.

Parameters

[out]	out	the output quantum number.
[in]	in	the input quantum number.

◆ Save() [1/2]

void cytnx::Symmetry::Save ( const char * fname ) const

Same as Save(const std::string &fname) const;.

◆ Save() [2/2]

void cytnx::Symmetry::Save ( const std::string & fname ) const

Save the current Symmetry object to a file.

Parameters

[in] fname the file name.

Postcondition: the file extension will be automatically added as ".cysym".

◆ stype()

int cytnx::Symmetry::stype ( ) const

inline

return the symmetry type-id of current Symmetry object, see cytnx::SymmetryType::

Returns: [int] the symmetry type-id.

◆ stype_str()

std::string cytnx::Symmetry::stype_str ( ) const

inline

return the symmetry type name of current Symmetry object in string form, see cytnx::SymmetryType::

Returns: [std::string] the symmetry type name.

◆ U1()

static Symmetry cytnx::Symmetry::U1 ( )

inlinestatic

create a U1 symmetry object

valid qnum value range:

\f$(-\infty , \infty)\f$

combine rule:

Q + Q

description:

create a new U1 symmetry object that serves as a generator. The symmetry object is a property of Bond . It is used to identify the symmetry of the quantum number set, as well as providing the combining rule for the quantum number when Bonds are combined.

Example:

c++ API:

#include "cytnx.hpp"
#include <iostream>
 
using namespace cytnx;
using namespace std;
int main() {
  /* 1.
      create a U1 symmetry object
  */
  Symmetry sym_u1 = Symmetry::U1();
 
  /* 2.
      using with Bond to define a bond with symmetry.
  */
  Bond bd_sym_u1_a = Bond(4, BD_KET, {{0}, {-4}, {-2}, {3}}, {sym_u1});
  Bond bd_sym_u1_b = Bond(4, BD_KET, {{0}, {-4}, {-2}, {3}});  // default is U1 symmetry
  cout << bd_sym_u1_a << endl;
  cout << bd_sym_u1_b << endl;
  cout << (bd_sym_u1_a == bd_sym_u1_b) << endl;  // true
 
  Bond bd_sym_u1_c = Bond(5, BD_KET, {{-1}, {1}, {2}, {-2}, {0}});
  cout << bd_sym_u1_c << endl;
 
  /* 3.
      new qnums will be calculated using Symmetry::combine_rule.
  */
  Bond bd_sym_all = bd_sym_u1_a.combineBond(bd_sym_u1_c);
  cout << bd_sym_all << endl;
 
  return 0;
}

output>

Dim = 4 |type: KET>
 U1::  +0 -4 -2 +3

Dim = 4 |type: KET>
 U1::  +0 -4 -2 +3

1
Dim = 5 |type: KET>
 U1::  -1 +1 +2 -2 +0

Dim = 20 |type: KET>
 U1::  -1 +1 +2 -2 +0 -5 -3 -2 -6 -4 -3 -1 +0 -4 -2 +2 +4 +5 +1 +3

python API:

import sys
from pathlib import Path
home = str(Path.home())
sys.path.append(home + '/Cytnx_lib')
from cytnx import *
 
sym_u1 = Symmetry.U1();
 
bd_sym_u1_a = Bond(4,BD_KET,[[0],[-4],[-2],[3]],[sym_u1])
bd_sym_u1_b = Bond(4,BD_KET,[[0],[-4],[-2],[3]]) #default is U1 symmetry
print(bd_sym_u1_a)
print(bd_sym_u1_b)
print(bd_sym_u1_a == bd_sym_u1_b,flush=True) #true
 
bd_sym_u1_c = Bond(5,BD_KET,[[-1],[1],[2],[-2],[0]])
print(bd_sym_u1_c)
 
bd_sym_all = bd_sym_u1_a.combineBond(bd_sym_u1_c)
print(bd_sym_all)
 
 
new_bd_sym_u1_a = Bond(BD_KET,[[0],[-4],[-2],[3]], [1,1,1,1],[sym_u1])
new_bd_sym_u1_b = Bond(BD_KET,[[0],[-4],[-2],[3]], [1,1,1,1]) #default is U1 symmetry
print(new_bd_sym_u1_a)
print(new_bd_sym_u1_b)
print(new_bd_sym_u1_a == new_bd_sym_u1_b,flush=True) #true
 
new_bd_sym_u1_c = Bond(BD_KET,[[-1],[1],[2],[-2],[0]], [1,1,1,1,1])
print(new_bd_sym_u1_c)
 
new_bd_sym_all = new_bd_sym_u1_a.combineBond(new_bd_sym_u1_c)
print(new_bd_sym_all)

output>

Dim = 4 |type: KET>
 U1::   +0  -4  -2  +3


Dim = 4 |type: KET>
 U1::   +0  -4  -2  +3


True
Dim = 5 |type: KET>
 U1::   -1  +1  +2  -2  +0


Dim = 20 |type: KET>
 U1::   -1  +1  +2  -2  +0  -5  -3  -2  -6  -4  -3  -1  +0  -4  -2  +2  +4  +5  +1  +3


Dim = 4 |type: KET>
 U1::   +0  -4  -2  +3
Deg>>    1   1   1   1


Dim = 4 |type: KET>
 U1::   +0  -4  -2  +3
Deg>>    1   1   1   1


True
Dim = 5 |type: KET>
 U1::   -1  +1  +2  -2  +0
Deg>>    1   1   1   1   1


Dim = 20 |type: KET>
 U1::   -6  -5  -4  -3  -2  -1  +0  +1  +2  +3  +4  +5
Deg>>    1   1   2   2   3   2   2   2   2   1   1   1

◆ Zn()

static Symmetry cytnx::Symmetry::Zn ( const int & n )

inlinestatic

create a Zn discrete symmetry object with \(n\in\mathbb{N}\)

valid qnum value range:

\f$[0 , n)\f$

combine rule:

(Q + Q)%n

description:

create a new Zn discrete symmetry object with integer \( n \) that serves as a generator. The symmetry object is a property of Bond . It is used to identify the symmetry of the quantum number set, as well as providing the combining rule for the quantum number when Bonds are combined.

Example:

c++ API:

#include "cytnx.hpp"
#include <iostream>
 
using namespace cytnx;
using namespace std;
int main() {
  // example of Z2 symmetry object
  //------------------------------------
  //  1. create Z2 object
  Symmetry sym_z2 = Symmetry::Zn(2);
 
  /* 2.
      using with Bond to define a bond with symmetry.
      Note that the qnums should obey the valid value range of the correspond symmetry.
      with Z2 = [0,2)
  */
  Bond bd_sym_z2_A = Bond(4, BD_KET, {{0}, {0}, {1}, {1}}, {sym_z2});
  Bond bd_sym_z2_B = Bond(3, BD_KET, {{0}, {1}, {1}}, {sym_z2});
  cout << bd_sym_z2_A << endl;
  cout << bd_sym_z2_B << endl;
 
  /* 3.
      new qnums will be calculated internally using Symmetry::combine_rule.
  */
  Bond bd_sym_z2all = bd_sym_z2_A.combineBond(bd_sym_z2_B);
  cout << bd_sym_z2all << endl;
 
  // example of Z4 symmetry object
  //------------------------------------
  //  1. create Z4 object
  Symmetry sym_z4 = Symmetry::Zn(4);
 
  /* 2.
      using with Bond to define a bond with symmetry.
      Note that the qnums should obey the valid value range of the correspond symmetry.
      with Z4 = [0,4)
  */
  Bond bd_sym_z4_A = Bond(4, BD_KET, {{0}, {3}, {1}, {2}}, {sym_z4});
  Bond bd_sym_z4_B = Bond(3, BD_KET, {{2}, {3}, {1}}, {sym_z4});
  cout << bd_sym_z4_A << endl;
  cout << bd_sym_z4_B << endl;
 
  /* 3.
      new qnums will be calculated internally using Symmetry::combine_rule.
  */
  Bond bd_sym_z4all = bd_sym_z4_A.combineBond(bd_sym_z4_B);
  cout << bd_sym_z4all << endl;
 
  return 0;
}

output>

Dim = 4 |type: KET>
 Z2::  +0 +0 +1 +1

Dim = 3 |type: KET>
 Z2::  +0 +1 +1

Dim = 12 |type: KET>
 Z2::  +0 +1 +1 +0 +1 +1 +1 +0 +0 +1 +0 +0

Dim = 4 |type: KET>
 Z4::  +0 +3 +1 +2

Dim = 3 |type: KET>
 Z4::  +2 +3 +1

Dim = 12 |type: KET>
 Z4::  +2 +3 +1 +1 +2 +0 +3 +0 +2 +0 +1 +3

python API:

import sys
from pathlib import Path
home = str(Path.home())
sys.path.append(home + '/Cytnx_lib')
from cytnx import *
#example of Z2 symmetry object
#------------------------------------
sym_z2 = Symmetry.Zn(2);
 
bd_sym_z2_A = Bond(4,BD_KET,[[0],[0],[1],[1]],[sym_z2])
bd_sym_z2_B = Bond(3,BD_KET,[[0],[1],[1]],[sym_z2])
print(bd_sym_z2_A)
print(bd_sym_z2_B)
 
bd_sym_z2all = bd_sym_z2_A.combineBond(bd_sym_z2_B)
print(bd_sym_z2all)
 
 
#example of Z4 symmetry object
#------------------------------------
sym_z4 = Symmetry.Zn(4)
 
bd_sym_z4_A = Bond(4,BD_KET,[[0],[3],[1],[2]],[sym_z4])
bd_sym_z4_B = Bond(3,BD_KET,[[2],[3],[1]],[sym_z4])
print(bd_sym_z4_A)
print(bd_sym_z4_B)
 
bd_sym_z4all = bd_sym_z4_A.combineBond(bd_sym_z4_B)
print(bd_sym_z4all)
 
#bk example of Z2 symmetry object
#------------------------------------
new_sym_z2 = Symmetry.Zn(2);
 
new_bd_sym_z2_A = Bond(BD_KET,[[0],[0],[1],[1]],[1,1,1,1],[new_sym_z2])
new_bd_sym_z2_B = Bond(BD_KET,[[0],[1],[1]],[1,1,1],[new_sym_z2])
print(new_bd_sym_z2_A)
print(new_bd_sym_z2_B)
 
new_bd_sym_z2all = new_bd_sym_z2_A.combineBond(new_bd_sym_z2_B)
print(new_bd_sym_z2all)
 
 
#bk example of Z4 symmetry object
#------------------------------------
new_sym_z4 = Symmetry.Zn(4)
 
new_bd_sym_z4_A = Bond(BD_KET,[[0],[3],[1],[2]],[1,1,1,1],[new_sym_z4])
new_bd_sym_z4_B = Bond(BD_KET,[[2],[3],[1]],[1,1,1],[new_sym_z4])
print(new_bd_sym_z4_A)
print(new_bd_sym_z4_B)
 
new_bd_sym_z4all = new_bd_sym_z4_A.combineBond(new_bd_sym_z4_B)
print(new_bd_sym_z4all)

output>

Dim = 4 |type: KET>
 Z2::   +0  +0  +1  +1


Dim = 3 |type: KET>
 Z2::   +0  +1  +1


Dim = 12 |type: KET>
 Z2::   +0  +1  +1  +0  +1  +1  +1  +0  +0  +1  +0  +0


Dim = 4 |type: KET>
 Z4::   +0  +3  +1  +2


Dim = 3 |type: KET>
 Z4::   +2  +3  +1


Dim = 12 |type: KET>
 Z4::   +2  +3  +1  +1  +2  +0  +3  +0  +2  +0  +1  +3


Dim = 4 |type: KET>
 Z2::   +0  +0  +1  +1
Deg>>    1   1   1   1


Dim = 3 |type: KET>
 Z2::   +0  +1  +1
Deg>>    1   1   1


Dim = 12 |type: KET>
 Z2::   +0  +1
Deg>>    6   6


Dim = 4 |type: KET>
 Z4::   +0  +3  +1  +2
Deg>>    1   1   1   1


Dim = 3 |type: KET>
 Z4::   +2  +3  +1
Deg>>    1   1   1


Dim = 12 |type: KET>
 Z4::   +0  +1  +2  +3
Deg>>    3   3   3   3

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

include/Symmetry.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ check_qnum()

◆ check_qnums()

◆ clone()

Example:

c++ API:

output>

python API:

output>

◆ combine_rule() [1/2]

◆ combine_rule() [2/2]

◆ combine_rule_() [1/2]

◆ combine_rule_() [2/2]

◆ FermionNumber()

valid qnum value range:

combine rule:

description:

◆ FermionParity()

valid qnum value range:

combine rule:

description:

◆ get_fermion_parity()

◆ is_fermionic()

◆ Load() [1/2]

◆ Load() [2/2]

◆ n()

◆ operator!=()

◆ operator==()

◆ print_info()

◆ reverse_rule()

◆ reverse_rule_()

◆ Save() [1/2]

◆ Save() [2/2]

◆ stype()

◆ stype_str()

◆ U1()

valid qnum value range:

combine rule:

description:

Example:

c++ API:

output>

python API:

output>

◆ Zn()

valid qnum value range:

combine rule:

description:

Example:

c++ API:

output>

python API:

output>