Dyson hierarchical long-ranged quantum spin-glass via real-space renormalization

Cécile Monthus (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We consider the Dyson hierarchical version of the quantum Spin-Glass with random Gaussian couplings characterized by the power-law decaying variance J 2 (r) ∝ r −2σ and a uniform transverse field h. The ground state is studied via real-space renormalization to characterize the spinglass-paramagnetic zero temperature quantum phase transition as a function of the control parameter h. In the spinglass phase h < hc, the typical renormalized coupling grows with the length scale L as the power-law J typ L (h) ∝ Υ(h)L θ with the classical droplet exponent θ = 1 − σ, where the stiffness modulus vanishes at criticality Υ(h) ∝ (hc − h) µ , whereas the typical renormalized transverse field decays exponentially h typ L (h) ∝ e − L ξ in terms of the diverging correlation length ξ ∝ (hc − h) −ν. At the critical point h = hc, the typical renormalized coupling J typ L (hc) and the typical renormalized transverse field h typ L (hc) display the same power-law behavior L −z with a finite dynamical exponent z. The RG rules are applied numerically to chains containing L = 2 12 = 4096 spins in order to measure these critical exponents for various values of σ in the region 1/2 < σ < 1.

Mots clés: disordered systems (theory); quantum phase transitions (theory); renormalisation group; spin glasses (theory)

Domaines: Physique [physics]

Cécile Monthus. Dyson hierarchical long-ranged quantum spin-glass via real-space renormalization. Journal of Statistical Mechanics: Theory and Experiment, 2015, 2015 (10), pp.10024. ⟨10.1088/1742-5468/2015/10/P10024⟩. ⟨cea-01321792⟩