0 votes
asked by (230 points)
closed ago by

Hi,

I'm running tDMRG for a simple anderson impurity coupled to two semi-infinite chain at different chemical potential, but get different dynamics for different spin states. Details are following:

First in the DMRG part, I decouple left chain, impurity, right chain to calculate the ground state of the decoupled system. Left chain and right chain are both half filled with same number of spin-up and spin-down electrons, and impurity is empty. My DMRG results are correct compared with analytic results (for a finite chain with even number of sites, the ground state of half filling has exactly local occupation of 0.5 for both spin-up and spin-down states.)

Secondly, I quench the whole system by coupling the impurity site and chains, and measure the dynamics of local occupation of spin-up and spin-down states. But these two occupations deviate very fast, which is unphysical considering that the Hamiltonian is symmetric under spin inversion). See the following results

t=0.01, Nup = 0.000945655, Ndn = 0.000945656
t=0.02, Nup = 0.00370455, Ndn = 0.0037134
t=0.03, Nup = 0.00812654, Ndn = 0.00818666
t=0.04, Nup = 0.0140243, Ndn = 0.0142351
t=0.05, Nup = 0.0211824, Ndn = 0.0217184
t=0.06, Nup = 0.0293665, Ndn = 0.03049
t=0.07, Nup = 0.0383324, Ndn = 0.0404003
t=0.08, Nup = 0.0478346, Ndn = 0.0512999
t=0.09, Nup = 0.057634, Ndn = 0.0630419
t=0.10, Nup = 0.0675047, Ndn = 0.0754844

My code is:
#include"itensor/all.h"
#include <math.h>
#include
using namespace itensor;

int main(int argc, char *argv[])
{
  float U=4;
  float e0=-2;
  float  tb=10;
  float  td=3.1623;
  float V=4;

  int L=101;
  double tau=0.01;
  float t_tot=3;

  auto Nc=L/2+1;//center site, impurity

  double el=V/2;
  double er=-V/2;

  //Read ground-state

  Electron sites;
  readFromFile("site_file",sites);
  MPS psi(sites);
  readFromFile("ground_state",psi);
  auto ampo = AutoMPO(sites);

//Right Chain

   for(int j=Nc+1;j <=L-1; j+=1)
    {
      ampo += -tb,"Cdagup",j,"Cup",j+1;
      ampo += -tb,"Cdagup",j+1,"Cup",j;
      ampo += -tb,"Cdagdn",j,"Cdn",j+1;
      ampo += -tb,"Cdagdn",j+1,"Cdn",j;
      ampo += er,"Ntot",j;
    }
   ampo+=er,"Ntot",L;

 //Left chain

   for(int j=1;j < Nc-1; j+=1)
    {
      ampo += -tb,"Cdagup",j,"Cup",j+1;
      ampo += -tb,"Cdagup",j+1,"Cup",j;
      ampo += -tb,"Cdagdn",j,"Cdn",j+1;
      ampo += -tb,"Cdagdn",j+1,"Cdn",j;
      ampo += el,"Ntot",j;
    }
   ampo+=el,"Ntot",Nc-1;

 //Impurity site

   ampo+=e0,"Ntot",Nc;
   ampo+=U,"Nup",Nc,"Ndn",Nc;

   //Coupling

   ampo+= -td,"Cdagup",Nc-1,"Cup",Nc;
   ampo+= -td,"Cdagup",Nc,"Cup",Nc-1;
   ampo+= -td,"Cdagdn",Nc-1,"Cdn",Nc;
   ampo+= -td,"Cdagdn",Nc,"Cdn",Nc-1;

   ampo+= -td,"Cdagup",Nc+1,"Cup",Nc;
   ampo+= -td,"Cdagup",Nc,"Cup",Nc+1;
   ampo+= -td,"Cdagdn",Nc+1,"Cdn",Nc;
   ampo+= -td,"Cdagdn",Nc,"Cdn",Nc+1;

  auto nt=round(t_tot/tau);
  auto expH=toExpH(ampo,tau*Cplx_i);
  auto args=Args("Method=","DensityMatrix","Cutoff=",1E-9,"MaxDim=",1000);

  Real Ild, Ilu, Ird, Iru, nu, nd;

  for(int j=1;j<=nt;j++){
      psi=applyMPO(expH,psi,args);
      psi.noPrime().normalize();

      printf("t=%g\n",tau*j);

      psi.position(Nc);
      //Occu
      nu=std::real(eltC(psi(Nc)*Nu*dag(prime(psi(Nc),"Site"))));
      nd=std::real(eltC(psi(Nc)*Nd*dag(prime(psi(Nc),"Site"))));
      printf("Nu=%g, Nd=%g, ",nu,nd);
   return 0;
}

Can anyone help? THANK YOU!

closed with the note: no longer needs answer
commented by (6.1k points)
edited by
It looks like the occupations match up to a certain time. Perhaps this is due to truncation or timestep error? Have you tried decreasing the timestep or the cutoff?
Welcome to ITensor Support Q&A, where you can ask questions and receive answers from other members of the community.

Formatting Tips:
  • To format code, indent by four spaces
  • To format inline LaTeX, surround it by @@ on both sides
  • To format LaTeX on its own line, surround it by $$ above and below
  • For LaTeX, it may be necessary to backslash-escape underscore characters to obtain proper formatting. So for example writing \sum\_i to represent a sum over i.
If you cannot register due to firewall issues (e.g. you cannot see the capcha box) please email Miles Stoudenmire to ask for an account.

To report ITensor bugs, please use the issue tracker.

Categories

...