Lifshitz phase transitions in one-dimensional Gamma model

TL;DR

This paper investigates Lifshitz phase transitions in a one-dimensional Gamma model, revealing topological changes in Weyl nodes and rich quantum phases driven by off-diagonal exchange interactions with strong spin-orbit coupling.

Contribution

It introduces an exactly solvable 1D Gamma model exhibiting Lifshitz transitions characterized by Weyl node topology changes, enriching understanding of correlated electron systems.

Findings

Identification of three gapless phases with different Weyl node configurations

Observation of type I and type II Weyl node coexistence in phase II

Entanglement measures effectively signal second-order phase transitions

Abstract

In this paper, we study quantum phase transitions and magnetic properties of a one-dimensional spin-1/2 Gamma model, which describes the off-diagonal exchange interactions between edge-shared octahedra with strong spin-orbit couplings along the sawtooth chain. The competing exchange interactions between the nearest neighbors and the second neighbors stabilize semimetallic ground state in terms of spinless fermions, and give rise to a rich phase diagram, which consists of three gapless phases. We find distinct phases are characterized by the number of Weyl nodes in the momentum space, and such changes in the topology of the Fermi surface without symmetry breaking produce a variety of Lifshitz transitions, in which the Weyl nodes situating at $k=\pi$ interchange from type I to type II. A coexistence of type-I and type-II Weyl nodes is found in phase II. The information measures including concurrence, entanglement entropy and relative entropy can effectively signal the second-order transitions. The results indicate that the Gamma model can act as an exactly solvable model to describe Lifshitz phase transitions in correlated electron systems.