State enumeration with number conservation

All functions have the name tag _conserve which means that the total particle number is conserved. The particle number within the range can be obtained by get_particle_number(start,end). The number of possible states is given by Eq. (2) which is returned by get_dim_U1(…). The constructor can be found in Constructors with indexing. We provide functions for forward and backward iteration as well as mappings from indices to the physical state and vice versa.

• Example code:

  using State = danceq::internal::State<5,4,uint64_t>;
  
  uint64_t start = 1;
  uint64_t end = 4;
  uint64_t number = 3;
  
  State state(0UL, number, start, end);
  uint64_t dim = state.get_dim_U1(number,end-start);
  std::cout << "[main] - dim  = " << dim << std::endl;
  
  for(uint64_t i = 0; i < dim; i++){
      std::cout << "[main] - |Psi_" << i << "> = " << state << std::endl;
      state.increment_U1(start,end);
  }
  

• Output:

  [main] - dim = 10
  [main] - |Psi_0> = |0;3;0;0;0>
  [main] - |Psi_1> = |0;2;1;0;0>
  [main] - |Psi_2> = |0;1;2;0;0>
  [main] - |Psi_3> = |0;0;3;0;0>
  [main] - |Psi_4> = |0;2;0;1;0>
  [main] - |Psi_5> = |0;1;1;1;0>
  [main] - |Psi_6> = |0;0;2;1;0>
  [main] - |Psi_7> = |0;1;0;2;0>
  [main] - |Psi_8> = |0;0;1;2;0>
  [main] - |Psi_9> = |0;0;0;3;0>
  

uint64_t danceq::internal::State::get_particle_number(const uint64_t start = 0, const uint64_t end = MaxSites) const

Returns the total particle number within a given range.

The particle number within the range start* and end is defined by

\[\textbf{particle_number} = \sum_{i=\textbf{start}}^{\textbf{end}-1} \sigma_i\,.\]

Parameters:

• start – Start of range

• end – End of range

Returns:

Particle number

static uint64_t danceq::internal::State::get_dim_U1(const uint64_t number, const uint64_t length = MaxSites, const uint64_t Q_ = Q)

Returns the dimension of a specific sector with number conservation.

The dimension of a particle number sector for a system of size length* and a local Hilbert space dimension Q__ with a total of number excitations is obtained by the Eq. (2).

Warning

The method produces overflow errors due the alternating sign in the equation for large values.

Parameters:

• number – Number sector

• length – Size of the system

• Q_ – Local Hilbert space dimension

Returns:

Dimension

int32_t danceq::internal::State::set_state_from_index_U1(const uint64_t index, const IntType num = -1, const uint64_t start = 0, const uint64_t end = MaxSites)

Sets a State defined by an index with number conservation.

The state refers to the index* with number conservation in the range start to end. This is the inverse function of get_index_U1. The particle number can be set by num*. Its default value is -1* which takes the current particle number, get_particle_number(start, end), as an input.

Parameters:

• index – Index to be set

• num – Particle number sector

• start – Start of range

• end – End of range

Returns:

error_code

uint64_t danceq::internal::State::get_index_U1(const uint64_t start = 0, const uint64_t end = MaxSites) const

Retrieves index from the State.

The index* is obtained by the integer counting in the range start to end with additional number conservation. This is the inverse function of set_state_from_index_U1.

Parameters:

• start – Start of range

• end – End of range

Returns:

error_code

int32_t danceq::internal::State::increment_U1(uint64_t start = 0, uint64_t end = MaxSites, bool *overflow = nullptr)

Incrementing the State with number conservation.

The state is set to its increment defined by integer counting in the range start* to end and the current particle number.

If overflow* is given, it is set to true if the state jumps from its maximal index to the minimal index.

Parameters:

• start – Start of range

• end – End of range

• overflow – Pointer to register overflow

Returns:

error_code

int32_t danceq::internal::State::decrement_U1(uint64_t start = 0, uint64_t end = MaxSites, bool *underflow = nullptr)

Decrementing the State with number conservation.

The state is set to its decrement defined by integer counting in the range start* to end and the current particle number.

If underflow* is given, it is set to true if the state jumps from its minimal index to the maximal index.

Parameters:

• start – Start of range

• end – End of range

• underflow – Pointer to register underflow

Returns:

error_code