Nature of the metal-insulator transition in the half--filled t-t' Hubbard chain

TL;DR

This paper investigates the quantum phase transition from insulator to metal in a half-filled Hubbard chain with next-nearest-neighbor hopping, combining analytical and numerical methods to map the phase diagram and transition characteristics.

Contribution

It derives an effective low-energy Hamiltonian and analytical transition line, providing new insights into the insulator-metal transition in the Hubbard chain.

Findings

Phase diagram well-described by commensurate-incommensurate transition theory

Analytical expression for the transition line t'_c(U,t)

Numerical evidence for separation of spin and charge transitions

Abstract

We study the quantum phase transition from an insulator to a metal realized at t'=t'_c > 0.5t in the ground state of the half-filled Hubbard chain with both nearest-neighbor (t) and next-nearest-neighbor (t') hopping. The study is carried out using the bosonization approach and density matrix renormalization group calculations. An effective low-energy Hamiltonian that describes the insulator-metal transition is derived. We find that the gross features of the phase diagram are well-described by the standard theory of commensurate-incommensurate transitions in a wide range of parameters. We also obtain an analytical expression for the insulator-metal transition line t'_c(U,t). We argue that close to the insulator-metal transition line, a crossover to a regime corresponding to an infinite-order transition takes place.We present results of density-matrix-renormalization-group calculations of spin and charge distribution in various sectors of the phase diagram. The numerical results support the picture derived from the effective theory and give evidence for the complete separation of the transitions involving spin and charge degrees of freedom.