https://www.quanty.org/ 2026-04-26T10:08:51+00:00 https://www.quanty.org/ https://www.quanty.org/_media/wiki/dokuwiki.svg text/html 2025-11-20T03:20:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/calculatehybridizationfunction?rev=1763608828&do=diff CalculateHybridizationFunction Responsefunction.CalculateHybridizationFunction(G0,Sigma) calculates the interacting impurity bath Green's function. Given a lattice with local Green's function $G_0(\omega)$ and a local self energy $\Sigma(\omega)$. The full Green's function then is $G(\omega) = G_0(\omega-\Sigma(\omega))$$$G_{Bath} = \frac{1}{G_0(\omega-\Sigma(\omega))^{-1} + \Sigma(\omega)}$$$G_0$$\Sigma$$G_{Bath}(\omega)$$G_{Bath}(\omega)$$G_0$$\Sigma$responsefunction index text/html 2025-11-20T03:20:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/calculateselfenergy?rev=1763608831&do=diff CalculateSelfEnergy ResponseFunction.CalculateSelfEnergy($G_0$,$G$) calculates \begin{equation} \Sigma = G_0^{-1} - G^{-1} \end{equation} Input $G_0$ : ResponseFunction object$G$ : ResponseFunction objectPossible options are:“epsilon” : minimal distance between two poles to be considered different in energy (default value 2.3E-13)$\Sigma$$H_0$$G_0$$H_1$responsefunction index text/html 2025-11-20T03:20:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/changetype?rev=1763608831&do=diff ChangeType The function ResponseFunction.ChangeType(G, type, ...) can be used to transform the representation of a response function. In Quanty, there are 4 different types for the response function: list of poles (ListOfPoles)tri-diagonal (Tri)Anderson (responsefunction index text/html 2025-11-20T03:20:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/chop?rev=1763608828&do=diff Chop G2 = ResponseFunction.Chop(G1) removes (sets to zero) all numbers form $G_1$ that are in absolute value smaller than epsilon. Chop does not change the type of the response function. Input G : a response functionepsilon : (optional) the smallest number considered different from zero. If not given the standard value is 10 times machine precision. responsefunction index text/html 2025-11-20T03:20:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/createbitmasks?rev=1763608830&do=diff CreateBitMasks alligned paragraph text Example description text Input -- some example code Result text produced as output Table of contents responsefunction index text/html 2025-11-20T03:20:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/invertenergy?rev=1763608829&do=diff InvertEnergy InvertEnergy(G) takes response function $G(\omega)$ as an argument and returns $-G(-\omega)^*$. As we only store the poles and their residues we can do this by negating the energy of the poles without the need to change the size of the residue Example This example initializes a response function in the responsefunction index text/html 2025-11-20T03:20:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/mergepolesininterval?rev=1763608829&do=diff MergePolesInInterval Gnew = ResponseFunction.MergePolesInInterval(Gold, Emin, Emax) converts $G_{old}$ into a list of poles format and merges all poles in the interval $[ E_{min}$ , $E_{max} ]$ (boundaries included) into a single pole, thereby conserving the zeroth and first moment. $G_{old}$$E_{min}$$E_{max}$$G_{new}$responsefunction index text/html 2025-11-20T03:20:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/new?rev=1763608832&do=diff ResponseFunction.New ResponseFunction.New(Table) creates a new response function object according to the values in Table. Response functions can be of 4 different types (ListOfPoles, Tri, And, or Nat) and single-valued or matrix-valued. Below 8 examples for creating each of these response functions by hand at some arbitrary values.$\mu=0$$\mu$$-\mu$$A$$B$$G(\omega,\Gamma)$$A$$B$$A$$B$$$ G(\omega,\Gamma) = A_0 + \sum_{i=1}^{n} \frac{B_{i-1}}{\omega + \mathrm{i}\Gamma/2 - a_i} $$$$ G(\omega,\Gamm… text/html 2025-11-20T03:20:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/placeonmesh?rev=1763608828&do=diff PlaceOnMesh Gnew = ResponseFunction.PlaceOnMesh(Gold, EnergyTable) takes a response function $G_{old}$ and a list doubles, EnergyTable. The poles of $G_{new}$ are given by the EnergyTable. All poles of $G_{old}$ are copied to $G_{new}$ whereby the residue of a pole at $E_{old}$ is shared between the poles in $G_{new}$$E_{old}$$G_{new}$$G_{old}$responsefunction index text/html 2025-11-20T03:20:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/reducepoles?rev=1763608830&do=diff ReducePoles Gout = ResponseFunction.ReducePoles(Gin, NPoles) or Gout = ResponseFunction.ReducePoles(Gin, NPolesVal, NPolesCon) reduces the number of poles in $G_{in}$ to $N_{Poles}$ or to $N_{Poles}^{Val} + N_{Poles}^{Con}$ by merging poles close to each other with small spectral weight (residue) (see appendix of $N_{Poles}^{Val}$$N_{Poles}^{Con}$responsefunction index text/html 2025-11-20T03:20:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/start?rev=1763608830&do=diff Functions alligned paragraph text Example description text Input -- some example code text/html 2025-11-20T03:20:30+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/tomatrix?rev=1763608830&do=diff ToMatrix M = ResponseFunction.ToMatrix(G) returns a matrix representation of $G$ such that $$ G(\omega,\Gamma) = A_0 + B_0^* \left( \frac{1}{(\omega+\mathrm{i}\Gamma/2) - M} \right)_{[1..Blocksize,1..Blocksize]} B_0^T$$We only need the left top matrix of dimension Blocksize of the inverse of the matrix $(\omega+\mathrm{i}\Gamma/2) - M$. As a result the matrix $M$ is not uniquely determined. Any unitary transformation of the bath, i.e. all rows and columns with index larger than $G$$M$$M$response… text/html 2025-11-20T03:20:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/tooperator?rev=1763608831&do=diff ToOperator H, BitMasks = ResponseFunction.ToOperator(G) Creates a tight binding Hamiltonian $H$ in operator form from a response function $G$. See ResponseFunction.ToTigthbinding for more information on how the Hamiltonian is obtained from $G$. BitMasks contains a table relating the indices to physical meaningful subspaces. See responsefunction index text/html 2025-11-20T03:20:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/tospectra?rev=1763608831&do=diff ToSpectra Spec = ResponseFunction.ToSpectra(G,options) creates a spectrum object from a response function object. For response functions represented as matrices Spectra are stored row first in a single list. See also CreateSpectraPossible options areEnergyShift: double - a shift of the energyresponsefunction index text/html 2025-11-20T03:20:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/totable?rev=1763608828&do=diff ResponseFunction.ToTable T = ResponseFunction.ToTable(G) creates a table $T$ that can be used as input for ResponseFunction.New such that G = ResponseFunctionNew(T).The table $T$ has the metatable set to “ResponseFunctionMeta”. This defines several functions one can use on the table similar to response functions stored as user data.responsefunction index text/html 2025-11-20T03:20:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/totightbinding?rev=1763608829&do=diff ToTightBinding ResponseFunction.ToTightBinding(G) transforms a response function object to a tight binding object that, when solved, has the response function $G$ as its one particle Green's function.Depending on the representation used for the response function (Tridiagonal, Anderson, or Natural impurity orbitals) one finds a different layout of the tight binding Hamiltonian that it represents. Transformations between the different layouts are given by unitary basis transformations. In all case… text/html 2025-11-20T03:20:29+00:00 Anonymous (anonymous@undisclosed.example.com) https://www.quanty.org/documentation/language_reference/objects/responsefunction/functions/touserdata?rev=1763608829&do=diff Responsefunctions.ToUserdata Responsefunctions can be represented by tables or by user data. ResponseFunction.ToUserdata transforms a table that defines a response function to a user data that can be efficiently handled internally. ResponseFunction.ToUserdata(table) gives the same result as responsefunction index