Dimensional reduction of Kitaev spin liquid at quantum criticality

TL;DR

This paper explores how a magnetic field induces a dimensional crossover in the Kitaev spin liquid, revealing a sequence of gapless phases and a transition to one-dimensional criticality, enriching understanding of quantum spin liquids.

Contribution

It uncovers a field-induced dimensional reduction and Lifshitz transition in the Kitaev spin liquid, combining numerical and theoretical methods to map the phase diagram.

Findings

Identification of a gapless-to-gapless Lifshitz transition.

Discovery of an intermediate phase composed of coupled quantum critical chains.

Observation of a dimensional crossover to one-dimensional quantum Ising criticality.

Abstract

We investigate the fate of the Kitaev spin liquid (KSL) under the influence of an external magnetic field $h$ in the [001] direction and upon tuning bond anisotropy of the Kitaev coupling $K_z$ keeping $K_x = K_y = K$. Guided by density matrix renormalization group, exact diagonalization, and with insights from parton mean field theory, we uncover a field-induced gapless-to-gapless Lifshitz transition from the nodal KSL to an intermediate gapless phase. The intermediate phase sandwiched between $h_{c1}$ and $h_{c2}$, which persists for a wide range of anisotropy $K_z/K > 0$, is composed of weakly coupled one-dimensional quantum critical chains. This intermediate phase is a dimensional crossover which asymptotically leads to the one-dimensional quantum Ising criticality characterized by the (1+1)D conformal field theory as the field reaches the phase transition at $h_{c2}$. Beyond $h_{c2}$ the system enters a partially polarized phase describable as effectively decoupled bosonic chains in which spin waves propagate along the one-dimensional zigzag direction. Our findings provide a comprehensive phase diagram and offer insights into the unusual physics of dimensional reduction generated by a uniform magnetic field in an otherwise two-dimensional quantum spin liquid.