
Temperature flow in pseudo-Majorana functional renormalization for quantum spins
B. Schneider, J. Reuther, M. G. Gonzalez, B. Sbierski, N. Niggemann
Physical Review B 109 (12), 195109 (2024).
We implement the temperature flow scheme first proposed by Honerkamp and Salmhofer [Phys. Rev. B 64, 184516 (2001)] into the pseudo-Majorana functional renormalization group method for quantum spin systems. Since the renormalization group parameter in this approach is a physical quantity, the temperature T, the numerical efficiency increases significantly compared to more conventional renormalization group parameters, especially when computing finite-temperature phase diagrams. We first apply this method to determine the finite-temperature phase diagram of the J1-J2 Heisenberg model on the simple cubic lattice, where our findings support claims of a vanishingly small nonmagnetic phase around the high frustration point J2 = 0.25J1. Perhaps most importantly, we find the temperature flow scheme to be advantageous in detecting finite-temperature phase transitions as, by construction, a phase transition is never encountered at an artificial, unphysical cutoff parameter. Finally, we apply the temperature flow scheme to the dipolar XXZ model on the square lattice, where we find a rich phase diagram with a large nonmagnetic regime down to the lowest accessible temperatures. Wherever a comparison with error-controlled (quantum) Monte Carlo methods is applicable, we find excellent quantitative agreement with less than 5% deviation from the numerically exact results.

Magnetism in the two-dimensional dipolar XY model
B. Sbierski, M. Bintz, S. Chatterjee, M. Schuler, N. Y. Yao, L. Pollet
Physical Review B 109 (14), 144411 (2024).
Motivated by a recent experiment on a square-lattice Rydberg atom array realizing a long-range dipolar properties. We obtain the phase diagram, critical properties, entropies, variance of the magnetization, and site-resolved correlation functions. We consider both ferromagnetic and antiferromagnetic interactions and apply quantum Monte Carlo and pseudo-Majorana functional renormalization group techniques, generalizing the latter to a U (1) symmetric setting. Our simulations perform extensive thermometry in dipolar Rydberg atom arrays and establish conditions for adiabaticity and thermodynamic equilibrium. On the ferromagnetic side of the experiment, we determine the entropy per particle S/N approximate to 0.5, close to the one at the critical temperature, Sc/N = 0.585(15). The simulations suggest the presence of an out-of-equilibrium plateau at large distances in the correlation function, thus motivating future studies on the nonequilibrium dynamics of the system.

Pseudo-fermion functional renormalization group for spin models
T. Mueller, D. Kiese, N. Niggemann, B. Sbierski, J. Reuther, S. Trebst, R. Thomale, Y. Iqbal
Reports on Progress in Physics 87 (3), 36501 (2024).
For decades, frustrated quantum magnets have been a seed for scientific progress and innovation in condensed matter. As much as the numerical tools for low-dimensional quantum magnetism have thrived and improved in recent years due to breakthroughs inspired by quantum information and quantum computation, higher-dimensional quantum magnetism can be considered as the final frontier, where strong quantum entanglement, multiple ordering channels, and manifold ways of paramagnetism culminate. At the same time, efforts in crystal synthesis have induced a significant increase in the number of tangible frustrated magnets which are generically three-dimensional in nature, creating an urgent need for quantitative theoretical modeling. We review the pseudo-fermion (PF) and pseudo-Majorana (PM) functional renormalization group (FRG) and their specific ability to address higher-dimensional frustrated quantum magnetism. First developed more than a decade ago, the PFFRG interprets a Heisenberg model Hamiltonian in terms of Abrikosov pseudofermions, which is then treated in a diagrammatic resummation scheme formulated as a renormalization group flow of m-particle pseudofermion vertices. The article reviews the state of the art of PFFRG and PMFRG and discusses their application to exemplary domains of frustrated magnetism, but most importantly, it makes the algorithmic and implementation details of these methods accessible to everyone. By thus lowering the entry barrier to their application, we hope that this review will contribute towards establishing PFFRG and PMFRG as the numerical methods for addressing frustrated quantum magnetism in higher spatial dimensions.