Extracting signatures of quantum criticality in the finite-temperature behavior of many-body systems

TL;DR

This paper compares the finite-temperature phase diagrams of quantum and classical Ising models to identify quantum-specific effects, revealing similar regimes but different critical exponents due to quantum fluctuations.

Contribution

It provides the classical limit phase diagram of the 1D Ising model in a transverse field, highlighting quantum effects by comparison with the quantum case.

Findings

Classical and quantum phase diagrams are surprisingly similar.

Different critical exponents distinguish quantum from classical fluctuations.

Quantum fluctuations affect the nature of phase transition behavior.

Abstract

We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase transition with that of its classical limit, in order to single out the genuinely quantum effects. To this aim, we consider the one-dimensional Ising model in a transverse field: while the quantum S=1/2 Ising chain is exactly solvable and extensively studied, results for the classical limit (infinite S) of such model are lacking, and we supply them here. They are obtained numerically, via the Transfer-matrix method, and their asymptotic low-temperature behavior is also derived analytically by self-consistent spin-wave theory. We draw the classical phase-diagram according to the same procedure followed in the quantum analysis, and the two phase diagrams are found unexpectedly similar: Three regimes are detected also in the classical case, each characterized by a functional dependence of the correlation length on temperature and field analogous to that of the quantum model. What discriminates the classical from the quantum case are the different values of the exponents entering such dependencies, a consequence of the different nature of zero-temperature quantum fluctuations with respect to thermal ones.