Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach

Abstract

The pseudofermion functional renormalization group (PFFRG) method has proven to be a powerful numerical approach to treat frustrated quantum spin systems. In its usual implementation, however, the complex fermionic representation of spin operators introduces unphysical Hilbert space sectors which renders an application at finite temperatures inaccurate. In this work, we formulate a general functional renormalization group approach based on Majorana fermions to overcome these difficulties. We, particularly, implement spin operators via an SO(3) symmetric Majorana representation which does not introduce any unphysical states and, hence, remains applicable to quantum spin models at finite temperatures. We apply this scheme, dubbed pseudo Majorana functional renormalization group (PMFRG) method, to frustrated Heisenberg models on small spin clusters as well as square and triangular lattices. Computing the finite temperature behavior of spin correlations and thermodynamic quantities such as free energy and heat capacity, we find good agreement with exact diagonalization and the high-temperature series expansion down to moderate temperatures. We, particularly, observe a significantly enhanced accuracy of the PMFRG compared to the PFFRG at finite temperatures. More generally, we conclude that the development of functional renormalization group approaches with Majorana fermions considerably extends the scope of applicability of such methods.

Dissipative spin dynamics in hot quantum paramagnets

“…Moreover, at finite temperatures the pseudofermion FRG becomes inaccurate because it introduces unphysical Hilbert space sectors. Although this problem can be elegantly avoided using an SO(3)-symmetric representation of the spin operators in terms of Majorana fermions [63], this pseudo-Majorana FRG exhibits an unphysical divergence in the limit of vanishing temperature. In contrast, our SFRG approach allows us to calculate the spin-spin correlation function G(k, ω) for vanishing and finite frequencies at all temperatures where the spin-rotational invariance is not spontaneously broken.…”

“…In fact, by numerically solving the flow equations (3.42) and (3.44) we can in principle obtain both the static spin self-energy Σ(k) and the dynamic dissipation energy ∆(k, iω). Although the direct numerical solution of the flow equations (3.42) and (3.44) is beyond the scope of this work, we believe that the numerical solution of these equations will be very rewarding because it will allow us to obtain the dynamic structure factor S(k, ω) of frustrated spin systems at low temperatures T |J|, a quantity which is not accessible with pseudofermion FRG methods [57][58][59][60][61][62][63].…”