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.

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.

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.

In the field of quantum many-body physics, the spectral (or Lehmann) representation simplifies the calculation of Matsubara n-point correlation functions if the eigensystem of a Hamiltonian is known. It is expressed via a universal kernel function and a system-and correlator-specific product of matrix elements. Here we provide the kernel functions in full generality, for arbitrary n, arbitrary combinations of bosonic or fermionic operators and an arbitrary number of anomalous terms. As an application, we consider bosonic 3-and 4-point correlation functions for the fermionic Hubbard atom and a free spin of length S, respectively.

The pseudofermion representation for S = 1/2 quantum spins introduces unphysical states in the Hilbert space, which can be projected out using the Popov-Fedotov trick. However, state-of-the-art implementation of the functional renormalization group method for pseudofermions have so far omitted the Popov-Fedotov projection. Instead, restrictions to zero temperature were made and the absence of unphysical contributions to the ground state was assumed. We question this belief by exact diagonalization of several small-system counterexamples where unphysical states do contribute to the ground state. We then introduce Popov-Fedotov projection to pseudofermion functional renormalization, enabling finite-temperature computations with only minor technical modifications to the method. At large and intermediate temperatures, our results are perturbatively controlled and we confirm their accuracy in benchmark calculations. At lower temperatures, the accuracy degrades due to truncation errors in the hierarchy of flow equations. Interestingly, these problems cannot be alleviated by switching to the parquet approximation. We introduce the spin projection as a method-intrinsic quality check. We also show that finite-temperature magnetic-ordering transitions can be studied via finite-size scaling.

Within the mature field of Anderson transitions, the critical properties of the integer quantum Hall transition still pose a significant challenge. Numerical studies of the transition suffer from strong corrections to scaling for most observables. In this Letter, we suggest to overcome this problem by using the longitudinal conductance g of the network model as the scaling observable, which we compute for system sizes nearly 2 orders of magnitude larger than in previous studies. We show numerically that the sizable corrections to scaling of g can be accounted for in a remarkably simple form, which leads to an excellent scaling collapse. Surprisingly, the scaling function turns out to be indistinguishable from a Gaussian. We propose a cost-function-based approach and estimate v = 2.609(7) for the localization length exponent, consistent with previous results, but considerably more precise than in most works on this problem. Extending previous approaches for Hamiltonian models, we also confirm our finding using integrated conductance as a scaling variable.

We employ a recently developed variant of the functional renormalization group method for spin systems, the so-called pseudo Majorana functional renormalization group, to investigate three-dimensional spin-1/2 Heisenberg models at finite temperatures. We study unfrustrated and frustrated Heisenberg systems on the simple cubic and pyrochlore lattices. Comparing our results with other quantum many-body techniques, we demonstrate a high quantitative accuracy of our method. Particularly, for the unfrustrated simple cubic lattice antiferromagnet ordering temperatures obtained from finite-size scaling of one-loop data deviate from error controlled quantum Monte Carlo results by similar to 5% and we confirm consistency of our data with established critical exponents nu and eta of the three-dimensional Heisenberg universality class. As the PMFRG yields results in good agreement with QMC, but remains applicable when the system is frustrated, we next treat the pyrochlore Heisenberg antiferromagnet as a paradigmatic magnetically disordered system and find nearly perfect agreement of our two-loop static homogeneous susceptibility with other methods. We further investigate the broadening of pinch points in the spin structure factor as a result of quantum and thermal fluctuations and confirm a finite width in the extrapolated limit T -> 0. While extensions towards higher loop orders 'seem to systematically improve our approach for magnetically disordered systems we also discuss subtleties when increasing ` in the presence of magnetic order. Overall, the pseudo Majorana functional renormalization group is established as a powerful many-body technique in quantum magnetism with a wealth of possible future applications. Published by the SciPost Foundation.