Reconstructing the quantum critical fan of strongly correlated systems via quantum correlations

TL;DR

This paper demonstrates that quantum correlations, specifically quantum variance of the order parameter, can be used to identify and reconstruct the quantum critical fan in strongly correlated systems, bridging theory and experimental spectroscopy.

Contribution

It introduces a method to detect the quantum critical fan via quantum variance, providing a broader and more accessible signature than traditional correlations.

Findings

Quantum variance exhibits temperature scaling of the quantum critical regime.

Quantum variance shows clear crossovers to other regimes in the phase diagram.

The approach enables experimental reconstruction of the quantum critical fan using spectroscopy.

Abstract

Albeit occurring at zero temperature, quantum critical phenomena are known to have a huge impact on the finite-temperature phase diagram of strongly correlated systems -- an aspect which gives experimental access to their observation. In particular the existence of a gapless, zero-temperature quantum critical point is known theoretically to induce the existence of an extended region in parameter space -- the so-called quantum critical fan -- characterized by power-law temperature dependences of all observables, with exponents related to those of the quantum critical point. Identifying experimentally the quantum critical fan and its crossovers to the other regions (renormalized classical, quantum disordered) remains nonetheless a big challenge. Focusing on paradigmatic models of quantum phase transitions, here we show that quantum correlations - captured by the quantum variance of the order parameter (I. Fr\'erot and T. Roscilde, Phys. Rev. B {\bf 94}, 075121 (2016)) - exhibit the temperature scaling associated with the quantum critical regime over an extended parameter region, much broader than that revealed by ordinary correlations, and with well-defined crossovers to the other regimes. The link existing between the quantum variance and the dynamical order-parameter susceptibility paves the way to an experimental reconstruction of the quantum critical fan using \emph{e.g.} spectroscopy on strongly correlated quantum matter.