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RealOperatorFermiParam

Represents a named fermionic operator acting on specified sites. Create instances using factory functions like Create(), Destroy(), Number(), or Hop().

Factories​

ModeRotation(real angle, integer i, integer j) -> RealOperatorFermiParam​

Returns the mode rotation operator exp⁡(iθ(fi†fj+fj†fi))\exp(i \theta (f_{i}^\dagger f_{j} + f_{j}^\dagger f_{i})) with support on the specified sites.

Parameters​

  • angle: The rotation angle heta heta in radians.
  • i: The first site index.
  • j: The second site index.

Example​

ModeRotation(pi/2,0,1)*Fbit("1000") // Returns (0 + 1i)|0100>

NumberNumberPhase(real angle, integer i, integer j) -> RealOperatorFermiParam​

Returns the two-site number-number phase operator exp⁡(iϕninj)\exp(i \phi n_{i} n_{j}) with support on the specified sites.

Parameters​

  • angle: The phase angle ϕ\phi in radians.
  • i: The first site index.
  • j: The second site index.

Example​

NumberNumberPhase(pi,0,1)*Fbit("1100") // Returns (-1 + 0i)|1100>

NumberPhase(real angle, integer i) -> RealOperatorFermiParam​

Returns the site number phase operator exp⁡(iϕni)\exp(i \phi n_i) with support on the specified site.

Parameters​

  • angle: The phase angle ϕ\phi in radians.
  • i: The site index where the operator acts.

Example​

NumberPhase(pi,0)*Fbit("1000") // Returns (-1 + 0i)|1000>

NumberPotential(const List<real> coefficients) -> RealOperatorFermiParam​

Returns an operator representing a weighted sum of number operators ∑i=0N−1αini\sum_{i=0}^{N-1} \alpha_i n_i, where the site indices are implicitly 0,1,…,N−10, 1, \dots, N-1. If a subset of sites or a different ordering is desired, use the factory overload that accepts an explicit list of site indices.

Parameters​

  • coefficients: The coefficients αi\alpha_i.

Example​

var coefficients = [1.0,3.0,4.0,0.0]
NumberPotential(coefficients)*Fbit("0110") // Returns (7 + 0i)|0110>

NumberPotential(const List<real> coefficients, const List<integer> sites) -> RealOperatorFermiParam​

Returns an operator representing a weighted sum of number operators ∑i∈sitesαini\sum_{i \in \mathrm{sites}} \alpha_i n_i.

Parameters​

  • coefficients: The coefficients αi\alpha_i.
  • sites: The site indices where the operator acts.

Example​

var sites = [0,2,3]
var coefficients = [1.0,3.0,4.0]
NumberPotential(coefficients,sites)*Fbit("0110") // Returns (3 + 0i)|0110>

PairRotation(real angle, integer i, integer j) -> RealOperatorFermiParam​

Returns the pair rotation operator exp⁡(iθ(fi†fj†+fjfi))\exp(i \theta (f_{i}^\dagger f_{j}^\dagger + f_{j} f_{i})) with support on the specified sites.

Parameters​

  • angle: The rotation angle heta heta in radians.
  • i: The first site index.
  • j: The second site index.

Example​

PairRotation(pi/2,0,1)*Fbit("0000") // Returns (0 + 1i)|1100>

PhaseHop(real angle, integer i, integer j) -> RealOperatorFermiParam​

Returns the complex phase-hop operator eiϕfi†fj+e−iϕfj†fie^{i \phi} f_{i}^\dagger f_{j} + e^{-i \phi} f_{j}^\dagger f_{i} with support on the specified sites.

Parameters​

  • angle: The phase angle ϕ\phi in radians.
  • i: The first site index.
  • j: The second site index.

Example​

PhaseHop(0.0,0,1)*Fbit("1000") // Returns (1 + 0i)|0100>

Symbols​

NameDescription
=Assignment operator for symbolic fermionic operators.