Characterizing quantum criticality and steered coherence in the XY-Gamma chain

TL;DR

This paper analytically explores the phase diagram and quantum critical behavior of the XY-Gamma spin chain model, revealing Lifshitz universality class transitions and scaling behaviors relevant for quantum simulation experiments.

Contribution

It introduces an exactly solvable XY-Gamma model, characterizes its quantum phase transitions, and derives explicit scaling forms and critical exponents for experimental relevance.

Findings

Identification of incommensurate spiral order in the gapless phase

Logarithmic scaling of local measures at quantum critical points

Critical exponents indicating Lifshitz universality class transition

Abstract

In this paper, we show that an effective spin Hamiltonian with various types of couplings can be engineered using quantum simulators in atomic-molecular-optical laboratories, dubbed the \emph{XY}-Gamma model. We analytically solve the one-dimensional short-range interacting case with the Jordan-Wigner transformation and establish the phase diagram. In the gapless phase, an incommensurate spiral order is manifested by the vector-chiral correlations. Between distinct gapped phases, a logarithmic scaling behavior of local measures, including spin correlations and the steered quantum coherence, is identified for the quantum critical points, yielding a compelling value of the correlation-length critical exponent. We derive explicit scaling forms of the excitation gap near the quantum critical points. The extracted critical exponents reveal the quantum phase transition on the boundary of Tomonaga-Luttinger liquid belongs to Lifshitz universality class.Our results may provide useful insights into the underlying mechanism in quantum criticality for state-of-the-art experiments of quantum simulation.