Quantum Critical Phenomena, Entanglement Entropy and Hubbard Model in 1d with the Boundary Site with a Negative Chemical Potential -p and the Hubbard Coupling U Positive

TL;DR

This paper investigates a phase transition in the 1d Hubbard model with a boundary site having negative chemical potential, revealing a first-order surface phase transition characterized by entanglement entropy analysis.

Contribution

It introduces an analytic approach to identify the order of surface phase transitions in the 1d Hubbard model using entanglement entropy.

Findings

Surface phase transition occurs at a critical chemical potential p_c

Transition is of the first order, indicated by entropy discontinuity

Massless charge mode appears for p > p_c

Abstract

Recently the ground state and some excited states of the half-filled case of the 1d Hubbard model were discussed for an open chain with L sites. Authors considered the case when the boundary site has a negative chemical potential -p and the Hubbard coupling U is positive. They have shown by an analytic method that when p is larger than the transfer integral some of the ground-state solutions of the Bethe ansatz equations become complex-valued. They have found that there is a surface phase transition at some critical value p_c; when p < p_c all the charge excitations have the gap for this case, while there exists a massless charge mode when p > p_c. To find whether this surface phase transition is of the first order or of the second order we have used the entanglement entropy concept. The entropy and its derivative has a discontinuity there, so this transition is of the first order.