[julia] unexpected fermion density configuration in CDW phase

Question

Dear all,

As a simple exercise, I examine the CDW phase of the spinless fermion chian (with nearest neighbor interaction) at half filling.

For @@U@@ small, the fermion density configuration is almost flat, with something like Friedel oscillation at two ends.

However, for @@U@@ large, the fermion density configuration is not a standard CDW, but forming a symmetric crossing at the center site, like this:

This configuration is somehow expected, since it is more symmetric than the usual 101010,
but how can i recover this standard result?

In case needed, the code I use is given below:

using LinearAlgebra
using MKL
using ITensors
using HDF5

let
        N = 20
        t1 = 1.0
        U = 50

        sites = siteinds("Fermion", N; conserve_qns=true)

        ampo = OpSum()
        for j in 1:(N-1)
            ampo += -t1, "Cdag", j+1, "C", j
            ampo += -t1, "Cdag", j, "C", j+1
        end
        for j in 1:(N-1)
            ampo += U, "N", j, "N",j+1
        end
        H = MPO(ampo, sites)

        nthreads = 8
        BLAS.set_num_threads(nthreads)
        sweeps = Sweeps(300)
        etol = 1E-9
        obs1 = DMRGObserver(;energy_tol=etol,minsweeps=20)
        obs2 = DMRGObserver(;energy_tol=etol,minsweeps=10)
        obs3 = DMRGObserver(;energy_tol=etol,minsweeps=10)
        setmaxdim!(sweeps, 20, 30, 50, 100, 200, 300, 500, 1000, 2000)
        setcutoff!(sweeps, 1E-10)
        vnoi = [1E-5 for i in 1:10]
        setnoise!(sweeps, 1E-3, 1E-4, vnoi...,
                  1E-6, 1E-7, 1E-8, 1E-9, 1E-10,
                  1E-11, 1E-12, 0.0)

        state = [isodd(n) ? "Emp" : "Occ" for n in 1:N]
           psii = randomMPS(sites, state, 10)
        energy0, psi0 = dmrg(H, psii, sweeps;observer=obs1)
            n = expect(psi0,"N")
end

Answer 1

I have found the solution by myself: using a pinning field at both ends.

In case this problem also bothers someone else in the future, I will keep this thread.

Comments

Glad you found the solution and thanks for posting your answer.