Quantum Phase Transitions in quasi-one dimensional systems

TL;DR

This paper reviews various quantum phase transitions in quasi-one dimensional systems, including spin chains, bosons, and fermions, highlighting recent progress and open questions in the field.

Contribution

It provides a comprehensive overview of quantum phase transitions across different quasi-one dimensional systems, emphasizing the complexity and open problems especially in fermionic cases.

Findings

Coupled spin chains exhibit diverse quantum phase transitions.

Bosonic systems in quasi-one dimensions show unique transition behaviors.

Fermionic systems remain largely open with many unresolved questions.

Abstract

I review in this chapter several classes of quantum phase transitions that occur in quasi-one dimensional systems. I start by examining the simple case of coupled spin chains and ladders, then move to the case of bosons, and finally deal with the more complicated and still largely open case of fermions.