Spinless Fermions

These tutorials apply the ALPS dmrg application to one-dimensional spinless fermions. Dropping the spin degree of freedom leaves the simplest interacting fermionic chain there is, which makes it a clean setting for the features of the method that spin models never exercise. Chief among these are the Jordan-Wigner string that maps fermionic operators onto spin operators, the use of particle number rather than total $S_z$ as the conserved quantum number, and a low-energy description in terms of Luttinger-liquid parameters instead of a spin gap. The series builds on the spin-chain tutorials, so it assumes familiarity with the DMRG control parameters introduced in DMRG-01.

Introduction

• DMRG-07 Introduction — introduces the spinless-fermion chain and the parameters used throughout this series.

Simulations

• DMRG-08 Ground State Energies — computes ground state energies of the spinless-fermion chain with the dmrg application, benchmarked against exact free fermions and the Heisenberg result of DMRG-03.
• DMRG-09 Particle-Number Sectors — the fixed-$N$ blocks built by CONSERVED_QUANTUMNUMBERS="N": energies and density profiles of the $N=0$, $1$ and $2$ sectors, checked against closed-form answers.
• DMRG-10 Model — spinless fermions against hardcore bosons: why the two are the same Hamiltonian on an open chain, and why only the boson form is usable with the dmrg binary.
• DMRG-11 Boundary Conditions — open against periodic chains at equal bond dimension: the $1/L$ surface term of the open chain against the ring’s conformal $1/L^2$, and the bond dimension the ring costs in exchange.