Yasir Iqbal

Fracton phases are a particularly exotic type of quantum spin liquids where the elementary quasiparticles are intrinsically immobile. These phases may be described by unconventional gauge theories known as tensor or multipolar gauge theories, characteristic for so-called type-I or type-II fracton phases, respectively. Both variants have been associated with distinctive singular patterns in the spin structure factor, such as multifold pinch points for type-I and quadratic pinch points for type-II fracton phases. Here, we assess the impact of quantum fluctuations on these patterns by numerically investigating the spin S=1/2 quantum version of a classical spin model on the octahedral lattice featuring exact realizations of multifold and quadratic pinch points, as well as an unusual pinch line singularity. Based on large scale pseudofermion and pseudo-Majorana functional renormalization group calculations, we take the intactness of these spectroscopic signatures as a measure for the stability of the corresponding fracton phases. We find that in all three cases, quantum fluctuations significantly modify the shape of pinch points or lines by smearing them out and shifting signal away from the singularities in contrast to effects of pure thermal fluctuations. This indicates possible fragility of these phases and allows us to identify characteristic fingerprints of their remnants.

We theoretically investigate the lowerature phase of the recently synthesized Lu2Mo2O5N2 material, an extraordinarily rare realization of a S=1/2 three-dimensional pyrochlore Heisenberg antiferromagnet in which Mo5+ are the S=1/2 magnetic species. Despite a Curie-Weiss temperature (ΘCW) of -121(1) K, experiments have found no signature of magnetic ordering or spin freezing down to T∗≈0.5 K. Using density functional theory, we find that the compound is well described by a Heisenberg model with exchange parameters up to third nearest neighbors. The analysis of this model via the pseudofermion functional renormalization group method reveals paramagnetic behavior down to a temperature of at least T=|ΘCW|/100, in agreement with the experimental findings hinting at a possible three-dimensional quantum spin liquid. The spin susceptibility profile in reciprocal space shows momentum-dependent features forming a "gearwheel" pattern, characterizing what may be viewed as a molten version of a chiral noncoplanar incommensurate spiral order under the action of quantum fluctuations. Our calculated reciprocal space susceptibility maps provide benchmarks for future neutron scattering experiments on single crystals of Lu2Mo2O5N2.

Renormalization group methods are well-established tools for the (numerical) investigation of the low-energy properties of correlated quantum many-body systems, allowing us to capture their scale-dependent nature. The functional renormalization group (FRG) allows us to continuously evolve a microscopic model action to an effective low-energy action as a function of decreasing energy scales via an exact functional flow equation, which is then approximated by some truncation scheme to facilitate computation. Here, we report on our implementation of multiloop FRG, an extended truncation scheme recently developed for electronic FRG calculations, within the pseudofermion functional renormalization group (pf-FRG) framework for interacting quantum spin systems. We discuss in detail the conceptual intricacies of the flow equations generated by the multiloop truncation, as well as essential refinements to the integration scheme for the resulting integrodifferential equations. To benchmark our approach, we analyze antiferromagnetic Heisenberg models on the pyrochlore, simple cubic, and face-centered cubic lattice, discussing the convergence of physical observables for higher-loop calculations and comparing with existing results where available. Combined, these methodological refinements systematically improve the pf-FRG approach to one of the numerical tools of choice when exploring frustrated quantum magnetism in higher spatial dimensions.

Pinch point singularities, associated with flat band magnetic excitations, are tell-tale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary nonanalytic features - shaped as half moons and stars - arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin S=1/2 Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state characterized by flat bands to one that is governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudofermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram of the model. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half moons in its structure factor. Our Letter thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, and He, Nat. Commun. 10, 4254 (2019)2041-172310.1038/s41467-019-11727-3]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by starlike patterns.

We assess the ground-state phase diagram of the Heisenberg model on the Kagome lattice by employing Gutzwiller-projected fermionic wave functions. Within this framework, different states can be represented, defined by distinct unprojected fermionic Hamiltonians that include hopping and pairing terms, as well as a coupling to local Zeeman fields to generate magnetic order. For , the so-called U(1) Dirac state, in which only hopping is present (such as to generate a -flux in the hexagons), has been shown to accurately describe the exact ground state [Y. Iqbal, F. Becca, S. Sorella, and D. Poilblanc, Phys. Rev. B87, 060405(R) (2013)10.1103/PhysRevB.87.060405; Y.-C. He, M. P. Zaletel, M. Oshikawa, and F. Pollmann, Phys. Rev. X7, 031020 (2017)10.1103/PhysRevX.7.031020.]. Here we show that its accuracy improves in the presence of a small antiferromagnetic superexchange , leading to a finite region where the gapless spin liquid is stable; then, for , a first-order transition to a magnetic phase with pitch vector is detected by allowing magnetic order within the fermionic Hamiltonian. Instead, for small ferromagnetic values of , the situation is more contradictory. While the U(1) Dirac state remains stable against several perturbations in the fermionic part (i.e., dimerization patterns or chiral terms), its accuracy clearly deteriorates on small systems, most notably on 36 sites where exact diagonalization is possible. Then, on increasing the ratio , a magnetically ordered state with periodicity eventually overcomes the U(1) Dirac spin liquid. Within the ferromagnetic regime, evidence is shown in favor of a first-order transition at .

We investigate the nature of the ground state of the spin-12 Heisenberg antiferromagnet on the shuriken lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multivariable variational Monte Carlo (mVMC), and pseudofermion/pseudo-Majorana functional renormalization group (PFFRG/PMFRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence bond crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.

We investigate the ground-state properties of the spin-1/2 pyrochlore Heisenberg antiferromagnet using pseudofermion functional renormalization group techniques. The first part of our analysis is based on an enhanced parton mean-field approach, which takes into account fluctuation effects from renormalized vertex functions. Our implementation of this technique extends earlier approaches and resolves technical difficulties associated with a diagrammatic overcounting. Using various parton ansätze for quantum spin liquids, dimerized and nematic states our results indicate a tendency for lattice symmetry breaking in the ground state. While overall quantum spin liquids seem unfavorable in this system, the recently proposed monopole state still shows the strongest support among all spin liquid ansätze that we have tested, which is further confirmed by our complementary variational Monte Carlo calculations. In the second part of our investigation, we probe lattice symmetry breaking more directly by applying the pseudofermion functional renormalization group to perturbed systems. Our results from this technique confirm that the system's ground state either exhibits broken C3 rotation symmetry, or a combination of inversion and C3 symmetry breaking.

Motivated by recent experiments on Cs2Cu3SnF12 and YCu3(OH)6Cl3, we consider the S = 1/2 Heisenberg model on the kagome lattice with nearest-neighbor superexchange J and (out-of-plane) Dzyaloshinskii-Moriya interaction JD, which favors (in-plane) Q = (0, 0) magnetic order. By using both variational Monte Carlo and tensor-network approaches, we show that the ground state develops a finite magnetization for JD/J ≳ 0.03−0.04; instead, for smaller values of the Dzyaloshinskii-Moriya interaction, the ground state has no magnetic order and, according to the fermionic wave function, develops a gap in the spinon spectrum, which vanishes for JD → 0. The small value of JD/J for the onset of magnetic order is particularly relevant for the interpretation of low-temperature behaviors of kagome antiferromagnets, including ZnCu3(OH)6Cl2. For this reason, we assess the spin dynamical structure factor and the corresponding low-energy spectrum, by using the variational Monte Carlo technique. The existence of a continuum of excitations above the magnon modes is observed within the magnetically ordered phase, with a broad peak above the lowest-energy magnons, similarly to what has been detected by inelastic neutron scattering on Cs2Cu3SnF12

We perform a projective symmetry group (PSG) classification of symmetric quantum spin liquids with different gauge groups on the square-octagon lattice. Employing the Abrikosov fermion representation for spin 12, we obtain 32SU(2), 1808U(1), and 384Z2 algebraic PSGs. Constraining ourselves to mean-field parton ansätze with short-range amplitudes, the classification reduces to a limited number, with 4 SU(2), 24 U(1), and 36 Z2, distinct phases. We discuss their ground-state properties and spinon dispersions within a self-consistent treatment of the Heisenberg Hamiltonian with frustrating couplings.

We investigate the quantum phases of the frustrated spin-12J1-J2-J3 Heisenberg model on the square lattice with ferromagnetic J1 and antiferromagnetic J2 and J3 interactions. Using the pseudofermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry-breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time-reversal invariance, these phases either break spin-rotation symmetry, lattice-rotation symmetry, or a combination of both. We therefore propose the J1-J2-J3 Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematic orders emerge in the same model.