arXiv subjects

Yasir Iqbal

Publications and source records attributed to Yasir Iqbal.

At least 37 records · Page 2Linked to original sources

arXiv2026

Unified gauge-theory description of quantum spin liquids on square-based frustrated lattices

Quantum spin liquids are commonly thought to be highly sensitive to lattice geometry, symmetry, and microscopic exchange patterns, leading to a proliferation of seemingly distinct phases across frustrated magnets. Here, we provide a framework that unifies phases that appear distinct from the viewpoint of this intuition. We postulate that the spin-$\tfrac{1}{2}$ Heisenberg antiferromagnets on the square, Shastry-Sutherland, and checkerboard lattices can realize a single unified quantum phase: a gapless $\mathbb{Z}_2$ Dirac quantum spin liquid, despite their markedly different lattice symmetries. Using a systematic projective symmetry group analysis, we identify a checkerboard spin-liquid state that completes a closed set of adiabatically connected phases linking the well-established square-lattice and Shastry-Sutherland spin liquids. Crucially, we show that this lattice-level unification is mirrored exactly in the continuum description. In all three cases, the spin liquids descend from a common SU(2) $π$-flux parent state and are governed by the same gauge theory, QED$_3$ with two Dirac fermion flavors coupled to two adjoint Higgs fields. As a result, we postulate that the surrounding Néel and valence-bond-solid phases and their confinement transitions admit a unified interpretation within the framework of deconfined quantum criticality. More broadly, our results suggest that quantum spin liquids are most fundamentally classified not by lattice geometry or microscopic couplings, but by the emergent gauge theory and its Higgs structure. Distinct frustrated lattices can thus host the same quantum phase and exhibit the same confinement mechanisms, despite substantial differences in their microscopic symmetries.

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arXiv2026

Crystal structure, magnetic and resonant properties of decorated spin kagome system (CsCl)Cu$_5$As$_2$O$_{10}$

We report the synthesis and investigation of the crystal structure and physical properties of the averievite-like arsenate, $(\mathrm{CsCl})\mathrm{Cu}_5\mathrm{As}_2\mathrm{O}_{10}$. Just above room temperature, this compound undergoes a structural phase transition from the high-temperature trigonal $P\bar{3}m1$ $(a=b=a_0$ and $c=c_0)$ to the low-temperature monoclinic $I2/a$ phase $(a \approx \sqrt{3}a_0$, $b=a_0$, $c \approx 2c_0$ and $β\approx 90.6^\circ)$. According to thermodynamic and nuclear magnetic resonance measurements, it experiences a phase transition into a canted antiferromagnetic state at $T_N = 21~\mathrm{K}$. The density functional theory calculations place the energy scale of kagome exchange interaction parameter in $(\mathrm{CsCl})\mathrm{Cu}_5\mathrm{As}_2\mathrm{O}_{10}$ in between those in V- and P-analogs.

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arXiv2026

Engineering altermagnetic orders on the square-kagome lattice through sublattice interference

We investigate the emergence of altermagnetic (AM) phases on the square-kagome lattice. Our analysis reveals that matrix element effects due to an orthogonal sublattice weight decomposition of Fermi level eigenstates known as sublattice interference enable decoupled magnetic ordering tendencies on distinct sublattices. Depending on which sublattice undergoes a magnetic instability, we identify a $d_{xy}$-type AM phase and a $d_{x^{2}-y^{2}}$-type AM phase originating from different sublattice polarization patterns. Using the Kotliar-Ruckenstein slave boson formalism we explore the stability of these AM phases as a function of interaction strength. Our findings demonstrate that sublattice-selective magnetic instabilities provide a versatile route to engineer the nature of AM order.

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arXiv2026

Dzyaloshinskii-Moriya-driven instabilities in square-kagome quantum antiferromagnets

Decorated square-kagome quantum antiferromagnets provide a natural setting in which strong frustration, lattice decoration, and spin-orbit-induced anisotropy compete on comparable energy scales. Here we show that in Na$_6$Cu$_7$BiO$_4$(PO$_4$)$_4$Cl$_3$ the coupling ($J_{10}$) which links the decorating Cu(3) sites to the square-kagome backbone, stabilizes the gapped quantum-paramagnetic regime, while symmetry-allowed Dzyaloshinskii-Moriya (DM) interactions systematically suppress the minimum spinon gap $Δ_{\mathrm{spinon}}$ and drive the system toward magnetic condensation. To establish this, we combine ab initio calculation of the DM vectors with a generalized Schwinger-boson self-consistent mean-field theory that treats singlet and triplet hopping/pairing channels on equal footing. As a benchmark, the isotropic square-kagome Heisenberg model exhibits four competing low-energy saddle points distinguished by their Wilson-loop fluxes and by characteristic static and dynamical structure-factor fingerprints. A minimal DM perturbation does not qualitatively reshape this competing landscape, but already enhances the tendency towards order. For the realistic decorated Hamiltonian, finite-size scaling of $Δ_{\mathrm{spinon}}$ together with momentum-resolved structure factors identifies $J_{10}$ (exchange with decorating Cu) as the control parameter of the gapped regime and shows that the full symmetry-allowed DM pattern shifts the system further toward condensation. Our results place Na$_6$Cu$_7$BiO$_4$(PO$_4$)$_4$Cl$_3$ in close proximity to a magnetic instability and provide experimentally testable predictions for anisotropy-enhanced soft modes in decorated square-kagome materials.

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arXiv2026

Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice

Geometrical frustration in quantum magnets provides a fertile setting for unconventional phases of matter, including quantum spin liquids (QSLs). The trellis lattice, with its complex site arrangements and edge-sharing triangular motifs, presents a promising platform for such physics. In this work, we undertake a comprehensive classification of all fully symmetric QSLs on the trellis lattice using the projective symmetry group approach within the Abrikosov-fermion representation. We find 7 U(1) and 25 $Z_2$ short-ranged Ansätze and analyze the phase diagram in the mean-field parameter space, uncovering both gapped and Dirac QSLs as well as a semi-Dirac spin liquid that emerges at the level of projective symmetry group classification and mean-field band structure, in which the spinon dispersion is linear along one momentum direction but quadratic along the orthogonal one. We demonstrate that such dispersions can occur only at high-symmetry points in the Brillouin zone with $C_{2v}$ little groups and analyze their characteristic correlation signatures. Moreover, by optimizing over all symmetry-allowed mean-field states, we map out a phase diagram -- featuring six distinct phases -- of the nearest-neighbor Heisenberg Hamiltonian on the trellis lattice. Among these, we find four quasi-one-dimensional QSL phases, one dimer phase, and one Dirac QSL phase. Going beyond mean field, we also assess equal-time and dynamical spin structure factors of these phases using density-matrix renormalization group and Keldysh pseudofermion functional renormalization group calculations and compare qualitative momentum-space features of these spectra with those obtained at the mean-field level. Finally, we identify four cuprate and vanadate compounds as promising experimental realizations and provide spectroscopic predictions, based on first-principles Hamiltonians, as a guide for neutron-scattering studies.

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arXiv2026

Quantum Coulomb Liquids of Different Rank in the Breathing Pyrochlore Antiferromagnet

Emergent gauge fields and Coulomb liquids have long been central to the physics of frustrated pyrochlore magnets, yet their realization beyond conventional, i.e. rank-1 $U(1)$, spin ice and into fully quantum higher-rank regimes has remained elusive. Here we provide a controlled demonstration of this physics in the spin-$\tfrac{1}{2}$ quantum Heisenberg antiferromagnet on the breathing pyrochlore lattice with symmetry-allowed Dzyaloshinskii--Moriya interactions, using the pseudofermion functional renormalization group. We show that tuning the breathing asymmetry stabilizes extended quantum analogues of both rank-1 and rank-2 $U(1)$ Coulomb liquids within a single microscopic model, directly distinguished by their characteristic pinch-point morphologies in momentum space. This provides the first controlled quantum realization in three dimensions where gauge theories of different rank emerge within a single microscopic spin Hamiltonian. In addition, quantum fluctuations qualitatively reshape the classical nearest-neighbor atlas of phases, causing an incommensurate spiral instability and an extended quantum-disordered regime without dipolar order, both absent from the classical model. Our results establish the breathing pyrochlore as a timely and experimentally relevant platform where higher-rank gauge constraints, conventional magnetic order, and fluctuation-driven quantum phases compete on equal footing, opening a direct route to diagnosing emergent gauge structure in three-dimensional quantum magnets.

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arXiv2026

Unifying Dirac Spin Liquids on Square and Shastry-Sutherland Lattices via Fermionic Deconfined Criticality

We present a fermionic gauge theory for deconfined quantum criticality on the Shastry-Sutherland lattice and reveal its shared low-energy field-theoretic structure with the square lattice. Starting from an SU(2) $π$-flux parent state, we construct a continuum theory of Dirac spinons coupled to an SU(2) gauge field and adjoint Higgs fields whose condensates drive transitions to a staggered-flux U(1) spin liquid and a gapless $\mathbb{Z}_{2}$ Dirac spin liquid. While the Shastry-Sutherland lattice permits additional symmetry-allowed fermion bilinears compared to the square lattice, the quantum field theories are identical up to additional irrelevant terms. Consequently, the Higgs potential structure and the leading low-energy theory coincide with the square-lattice case at the quantum critical point. The SO(5) critical point is expected to realize conformal deconfined criticality: we analyze it in a large flavor expansion, calculate its critical exponents, and identify the Yukawa coupling between the fermions and Higgs fields as the relevant perturbation that destabilizes it, consistent with pseudocritical behavior observed in recent Monte Carlo studies. We show that the emergent SO(5) order parameter acquires a large anomalous dimension at the critical point, leading to strongly enhanced Néel and VBS susceptibilities-a hallmark of fermionic deconfined quantum criticality consistent with numerical studies. Our results place recent numerical evidence for a gapless $\mathbb{Z}_{2}$ Dirac spin liquid on the Shastry-Sutherland lattice within a controlled field-theoretic framework and demonstrate that fermionic deconfined criticality on the square lattice-including critical exponents and stability-extends to frustrated lattices with reduced symmetry.

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arXiv2026

Competing Paramagnetic Phases in the Maple-Leaf Heisenberg Antiferromagnet

We establish a remarkably rich ground state phase diagram in the maple-leaf lattice spin-$1/2$ Heisenberg antiferromagnet as a function of the three symmetry-inequivalent nearest-neighbor bonds using exact diagonalization and tower-of-states analysis on clusters up to $N=36$ sites. Besides a hexagonal plaquette state, a star-shaped valence bond solid state is discovered in close vicinity to the (canted) $120^\circ$ magnetic phase, strongly reminiscent of a de-confined critical point or Dirac spin liquid scenario on the triangular lattice antiferromagnets. Moreover, an exact dimer product-state is observed next to a collinear Néel-state, similar to the Shastry-Sutherland model. All identified phases compete in a parameter regime close to the isotropic point, providing a promising region for spin liquids to emerge. By analyzing Gutzwiller-projected wave-functions we identify a sliver of parameter regime where a gapped $\mathbb{Z}_{2}$ spin liquid Ansatz is in astonishing agreement with the exact $N=36$ ground state. This rich competition of paramagnetic phases demonstrates that the maple-leaf antiferromagnet is a promising platform for exotic states of matter and quantum critical phenomena.

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arXiv2025

Keldysh pseudo-fermion functional renormalization group for quantum magnetism

The functional renormalization group (FRG) approach for spin models relying on a pseudo-fermionic description has proven to be a powerful technique in simulating ground state properties of strongly frustrated magnetic lattices. A drawback of the FRG framework is that it is formulated in the imaginary-time Matsubara formalism and thus only able to access static correlations, a limitation shared with most other many-body approaches. A description of the dynamical properties of magnetic systems is the key to bridging the gap between theory and neutron scattering spectra. We take the decisive step of expanding the scope of pseudo-fermion FRG to the Keldysh formalism, which, while originally developed to address non-equilibrium phenomena, enables a direct calculation of the equilibrium dynamical spin structure factors on generic lattices in arbitrary dimension. We identify the principal features characterizing the low-energy spectra of exemplary zero-, one- and two-dimensional spin-$1/2$ Heisenberg models as well as the Kitaev honeycomb model while identifying current limitations of the method that have to be improved upon.

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arXiv2025

Unconventional orders in the maple-leaf ferro-antiferromagnetic Heisenberg model

Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-$1/2$ Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons $J_h$ and ferromagnetic couplings on triangles $J_t$ and dimer $J_d$ bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around $J_{d}=J_{t}=0$, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c$120^\circ$ antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.

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arXiv2025

Tensor network analysis of the maple-leaf antiferromagnet spangolite

Spangolite (Cu$_6$Al(SO$_4$)(OH)$_{12}$Cl$\cdot$3H$_2$O) is a hydroxy-hydrated copper sulfate mineral with a one-seventh depleted triangular lattice of Cu$^{2+}$ ions in each layer. Experimental measurements revealed a non-magnetic ground state at $T \sim 8\, \text{K}$ with magnetic properties dominated by dimerization. We propose a spatially anisotropic Heisenberg model for the Cu$^{2+}$ spin-$1/2$ degrees of freedom on this geometrically frustrated and effectively two-dimensional maple-leaf lattice, featuring five symmetry inequivalent couplings with ferromagnetic bonds on hexagons and antiferromagnetic triangular bonds. The validity of the proposed Hamiltonian is demonstrated by state-of-the-art tensor network calculations, which can assess both the nature of the ground state as well as low-temperature thermodynamics, including the effects of a magnetic field. We provide theoretical support for a picture of a non-trivially correlated dimer ground state, which accounts for the appreciable reduction of the magnetic moment at high temperatures observed in experiment, thereby resolving a long-standing puzzle. We predict the static spin structure factor as well as the emergence of magnetisation plateaus at high values of an external magnetic field, explore the nature of the quantum states in them, and study their melting with increasing temperature.

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arXiv2025

Quantum effects on pyrochlore higher-rank U(1) spin liquids: Pinch-line singularities, spin nematics, and connections to oxide materials

Motivated by the magnetism of pyrochlore oxides, we consider the effect of quantum fluctuations in the most general symmetry-allowed nearest-neighbor Kramers exchange Hamiltonian on the pyrochlore lattice. At the classical level, this Hamiltonian exhibits a rich landscape of classical spin liquids and a variety of nonconventional magnetic phases. In contrast, much remains unclear for the quantum model, where quantum fluctuations have the potential to alter the classical landscape and stabilize novel magnetic phases. Employing state-of-the-art pseudo-fermion functional renormalization group calculations for the spin-$1/2$ model, we determine the quantum phase diagram at relevant cross-sections, where the classical model hosts an algebraic nodal rank-2 spin liquid and a spin nematic order. We find large regions in parameter space on which dipolar magnetic order is absent and, based on known fingerprints in the correlation functions, we suggest that this nonconventional region is composed of an ensemble of distinct phases stabilized by quantum fluctuations. Our results hint at the existence of a spin nematic phase, and we identify the quantum analog of the classical rank-2 spin liquid. Furthermore, we highlight the importance of assessing the subtle interplay of quantum and thermal fluctuations in reconciling the experimental findings on the nature of magnetic order in Yb$_2$Ti$_2$O$_7$.

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arXiv2025

Chiral Gapless Spin Liquid in Hyperbolic Space

We analyze the Kitaev model on the $\{9,3\}$ hyperbolic lattice. The $\{9,3\}$ is formed by a regular tricoordinated tiling of nonagons, where the 3-color coding of bonds according to the inequivalent Kitaev Ising spin couplings yields the natural generalization of the original Kitaev model for Euclidean regular honeycomb tiling. Upon investigation of the bulk spectrum for large finite size droplets, we identify a gapless chiral $\mathbb{Z}_2$ spin liquid state featuring spontaneous time reversal symmetry breaking. Due to its non-commutative translation group structure, such type of hyperbolic spin liquid is conjectured to feature chiral quasiparticles with a potentially non-Abelian Bloch profile.

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arXiv2025

Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu$_7$TeO$_4$(SO$_4$)$_5$Cl

Quantum antiferromagnets based on the square-kagome lattice are proving to be a fertile platform for realizing nontrivial phenomena in frustrated magnetism. Recently, several decorated square-kagome compounds of the nabokoite family have been synthesized, allowing for experimental exploration of model Hamiltonians. Here, we carry out a theoretical analysis of KCu$_7$TeO$_4$(SO$_4$)$_5$Cl nabokoite using a Heisenberg Hamiltonian derived from density functional theory energy mapping. We employ classical Monte Carlo simulations to explain the two transitions experimentally observed in the low-temperature magnetization curve. Interestingly, the intermediate-field phase is also found in a purely two-dimensional model and is described by a spin liquid featuring subextensive degeneracy with a ferrimagnetic component. We show that this phase can be approximated by a checkerboard lattice in a magnetic field. Finally, we assess the effects of quantum fluctuations in zero fields using the pseudo-Majorana functional renormalization group method.

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arXiv2025

Monopole excitations in the $U(1)$ Dirac spin liquid on the triangular lattice

The $U(1)$ Dirac spin liquid might realize an exotic phase of matter whose low-energy properties are described by quantum electrodynamics in $2+1$ dimensions, where gapless modes exists but spinons and gauge fields are strongly coupled. Its existence has been proposed in frustrated Heisenberg models in presence of frustrating super-exchange interactions, by the (Abrikosov) fermionic representation of the spin operators [X.-G. Wen, \href{https://doi.org/10.1103/PhysRevB.65.165113}{Phys. Rev. B {\bf 65}, 165113 (2002)}], supplemented by the Gutzwiller projection. Here, we construct charge-$Q$ monopole excitations in the Heisenberg model on the triangular lattice with nearest- ($J_1$) and next-neighbor ($J_2$) couplings. In the highly frustrated regime, singlet and triplet monopoles with $Q=1$ become gapless in the thermodynamic limit; in addition, the energies for generic $Q$ agree with field-theoretical predictions, obtained for a large number of gapless fermion modes. Finally, we consider localized gauge excitations, in which magnetic $π$-fluxes are concentrated in the triangular plaquettes (in analogy with $\mathbb{Z}_2$ visons), showing that these kind of states do not play a relevant role at low energies. All our findings lend support to a stable $U(1)$ Dirac spin liquid in the $J_1-J_2$ Heisenberg model on the triangular lattice.

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arXiv2025

Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid

We study the Kitaev model on the trivalent heptagonal Hurwitz hyperbolic tiling. The presence of odd-length loops in the tiling is responsible for a spontaneous time-reversal symmetry breaking. Interestingly, at the isotropic point, the two degenerate ground states (Kramers pair) are shown to be gapped chiral spin liquids and the elementary excitations are non-Abelian Ising anyons.

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arXiv2025

Spin-Peierls transition in the frustrated spinels ZnCr2O4 and MgCr2O4

The chromium spinels MgCr2O4 and ZnCr2O4 are prime examples of the highly frustrated pyrochlore lattice antiferromagnet. Experiment has carefully established that both materials, upon cooling, distort to lower symmetry and order magnetically. We study the nature of this process by a combination of density-functional-theory based energy mapping and classical Monte Carlo simulations. We first computationally establish precise Heisenberg Hamiltonian parameters for the high temperature cubic and the low temperature tetragonal and orthorhombic structures of both spinels. We then investigate the respective ordering temperatures of high symmetry and low symmetry structures. We carefully compare our results with experimental facts and find that our simulations are remarkably consistent with a type of spin-Peierls mechanism, adapted to three dimensions, where the structural distortion is mediated by a magnetic energy gain due to a lower degree of frustration.

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arXiv2024

Gapped and gapless quantum spin liquids on the ruby lattice

The ruby lattice has been the subject of much interest recently due its realization in Rydberg atom arrays, where its rich variety of frustrated interactions gives rise to topologically ordered quantum spin liquids. Similarly, numerical studies of ruby-lattice spin models, with both isotropic and anisotropic interactions, have provided evidence of gapped and gapless spin-liquid ground states with different low-energy gauge structures. Motivated by these findings, we perform a projective symmetry group (PSG) classification of U(1) and $\mathbb{Z}_{2}$ fermionic spinon mean-field theories$\unicode{x2014}$respecting space-group and time-reversal symmetries$\unicode{x2014}$for $S=1/2$ spins. We obtain a total of 50 U(1) and 64 $\mathbb{Z}_{2}$ PSGs, and upon restricting their realization via mean-field $\textit{Ansätze}$ with up to second-nearest-neighbor singlet amplitudes (relevant to the models studied here), only 8 U(1) and 18 $\mathbb{Z}_{2}$ distinct states are obtained. We present the singlet fields for all $\textit{Ansätze}$ up to third-nearest-neighboring bonds and discuss their spinon dispersions as well as their dynamical spin structure factors. Building on this information, we also obtain the phase diagram of the Heisenberg model in the presence of first ($J_{1}$), second ($J_{1}'$), and third ($J_{2}$) neighbor antiferromagnetic couplings within a self-consistent mean-field approximation.

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