arXiv subjects

Karlo Penc

Publications and source records attributed to Karlo Penc.

At least 19 recordsLinked to original sources

arXiv2026

Chiral Color Ice: Exact Local Handedness Constraints and M\"obius Zero Modes in Frustrated Magnets

Local constraints govern the low-energy physics of frustrated matter, but familiar ice-type rules constrain flux-like quantities and are insensitive to handedness. Here we show that handedness itself can be imposed as an exact local quantum constraint without selecting an axis in spin space. We construct positive-semidefinite, SU(2)-invariant parent Hamiltonians whose complete zero-energy space on a tetrahedron has a prescribed chirality sign, rather than selecting a particular chiral wave function. For spin-1/2 the local term is a rank-one projector onto a chiral tetrahedral singlet, while for arbitrary spin it factorizes as $B^\dagger B$ through a singlet-annihilation operator, with a completely characterized kernel given by the span of the globally rotated chiral color-ice states. For coherent states, the same zero-energy condition becomes an $S$-independent nonlinear constraint in which three spin directions determine the fourth through a M\"obius transformation; compositions of these maps define constraint holonomies on extended lattices. Connecting the same local constraint in different ways produces qualitatively different collective regimes: corner-sharing lattices retain exponentially large quantum ground-state kernels, with rigorous lower bounds exceeding conventional ice benchmarks; edge-sharing lattices support subdimensional plane or line zero modes; while triangular constructions suppress nonuniform coherent deformations and contain the complete Anderson tower of tetrahedral magnetic order at exactly zero energy. Two inequivalent triangular coverings further show that harmonic zero-mode counting does not determine the size of the quantum kernel. These results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled and related directly to the connectivity of the constraint network.

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arXiv2026

Chiral enhancement of two-magnon bound states in an $S=1/2$ triangular-lattice magnet

We study one- and two-magnon excitations above the fully polarized state of the spin-$1/2$ triangular-lattice $J_1$-$J_2$-$J_3$ Heisenberg model with a uniform scalar-chirality interaction. In the Heisenberg model, we identify two special manifolds of one-magnon minima by rewriting the dispersion in complete-square form. The chirality term cancels exactly in the one-magnon sector, leaving the dispersion and instability field unchanged, but survives in the two-magnon sector as an oriented interaction between neighboring magnons. Using symmetry-adapted lattice harmonics, we show that scalar chirality splits two-magnon states of opposite relative-motion chirality and selectively enhances the binding of one of them. It can strengthen an existing bound state, change the symmetry of the lowest magnon pair, or induce binding where none occurs without chirality. Exact diagonalization further shows that two-magnon pairing can also occur at finite total momentum. Our results identify scalar chirality as a microscopic mechanism for enhancing two-magnon pairing without modifying the one-magnon spectrum.

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arXiv2026

Classical Kitaev model in a magnetic field

Motivated by experiments on spin-orbit coupled magnets with Kitaev exchange in magnetic fields, we present an analysis of the classical Kitaev honeycomb model in the presence of a magnetic field. We show that there is a spin liquid regime that exists within a finite window of fields from zero up to a finite threshold before transitioning into the polarized paramagnet. We uncover constraints that spins need to satisfy in the ground state and show that they determine the exact limiting zero temperature behavior of the heat capacity and magnetic susceptibility within the spin liquid as a function of field. When the field is finite, both the two-point spin and the quadrupolar correlations are short-ranged, in contrast to the zero-field case. We rationalize an effective mass for the quadrupolar correlations in terms of a coarse-grained theory with fluctuating effective charge degrees of freedom. Finally, we show that weak site-dilution does not change the magnetization within the spin liquid -- a kind of "perfect" compensation of the site dilution.

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arXiv2026

Rigorous Anderson-type lower bounds on the ground-state energy of the pyrochlore Heisenberg antiferromagnet

We construct rigorous Anderson-type lower bounds on the ground-state energy of the spin-$S$ Heisenberg antiferromagnet on the pyrochlore lattice. By formulating and optimizing a hierarchy of local cluster motifs ordered by size, we generate a sequence of increasingly tight bounds. A seven-site "hourglass" cluster composed of two corner-sharing tetrahedra furnishes an optimal lower bound that admits a closed-form expression for arbitrary spin $S$. We also derive exact lower bounds for generalized models with further-neighbor exchange, ring exchange, and scalar spin-chirality interactions. For $S=1/2$ and $S=1$, numerical optimization of an 18-site "crown" cluster containing a hexagonal loop yields rigorous lower bounds on the ground-state energy per site of the nearest-neighbor Heisenberg model with unit exchange, $e_\mathrm{GS} \geq -0.549832$ and $e_\mathrm{GS} \geq -1.632985$, respectively. We compare the resulting bounds with numerical ground-state energy estimates from the literature.

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arXiv2025

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 Ans\"atze 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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arXiv2025

Spin Nernst and thermal Hall effects of topological triplons in quantum dimer magnets on the maple-leaf and star lattices

We present a comprehensive theoretical study of the topological properties of triplon excitations in spin-1/2 dimer-singlet ground states defined on the maple leaf and star lattices. Our analysis is based on a model that includes Heisenberg interactions, Dzyaloshinskii-Moriya (DM) interactions, and an external magnetic field. In the absence of an in-plane DM vector, we demonstrate that the triplon Hamiltonian maps onto the magnon Hamiltonian of the Kagome lattice, inheriting its nontrivial topological characteristics, including Berry curvature and topological invariants such as the Z2 invariant and Chern numbers. This correspondence enables us to derive analytical expressions for the spin Nernst and thermal Hall conductivities at low temperatures. Furthermore, we explore the effects of realistic finite in-plane DM interactions, uncovering multiple topological transitions and a complex thermal Hall conductivity behavior, including potential sign reversals as functions of magnetic field and temperature. Using layer groups, we also provide a symmetry classification of the star and maple leaf lattices.

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arXiv2024

Evidence for a $\mathbb{Z}_{2}$ Dirac spin liquid in the generalized Shastry-Sutherland model

We present a multimethod investigation into the nature of the recently reported quantum spin liquid (QSL) phase in the spin-$1/2$ Heisenberg antiferromagnet on the Shastry-Sutherland lattice. A comprehensive projective symmetry group classification of fermionic mean-field Ans\"atze on this lattice yields 46 U(1) and 80 $\mathbb{Z}_2$ states. Using density-matrix renormalization group (DMRG) and exact diagonalization calculations, we find that the Shastry-Sutherland model and the square-lattice $J_1$-$J_2$ Heisenberg antiferromagnet share the same QSL phase. Motivated by this observation, we establish an explicit mapping of our Ans\"atze to those on the square lattice, and identify the counterpart of the square-lattice $\mathbb{Z}_2$ Dirac QSL (Z2A$zz$13) in the Shastry-Sutherland system. Employing state-of-the-art variational Monte Carlo calculations with Gutzwiller-projected wavefunctions, further improved by L\'anczos steps, we demonstrate excellent agreement in both energies and correlation functions between a gapless (Dirac) $\mathbb{Z}_2$ spin liquid-characterized by only a few variational parameters-and results obtained from neural quantum states and DMRG. Finally, we apply the recently developed Keldysh formulation of the pseudo-fermion functional renormalization group to compute the dynamical spin structure factor. The resulting spectra exhibit features consistent with Dirac cones in the excitation spectrum, providing strong independent evidence for a Dirac QSL ground state. Our identification of a $d$-wave pairing $\mathbb{Z}_2$ Dirac QSL is consistent with recently observed signatures of QSL behavior in Pr$_2$Ga$_2$BeO$_7$ and outlines predictions for future experiments.

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arXiv2024

Spin Liquid Landscapes in the Kagome Lattice: A Variational Monte Carlo Study of the Chiral Heisenberg Model and Experimental Signatures

Chiral spin liquids, which break time-reversal symmetry, are of great interest due to their topological properties and fractionalized excitations (anyons). In this work, we investigate chiral spin liquids (CSL) on the kagome lattice arising from the competition between the third-nearest-neighbor Heisenberg interaction across hexagons ($J_d$) and a staggered scalar spin chirality term ($J_\chi$). Using variational Monte Carlo methods, we map out the phase diagram and identify various gapped and gapless CSL phases, each characterized by a distinct flux pattern. Notably, the interplay between $J_d$ and $J_\chi$ induces a tricritical point, which we analyze using Landau-Ginzburg theory. Additionally, we identify potential signatures of these CSLs-including distinctive spin-spin correlations, anomalies in the static spin structure factor, longitudinal thermal conductivity, and magentoelectric effects-which offer practical guidance for their future experimental detection.

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arXiv2024

The algebraic spin liquid in the SU(6) Heisenberg model on the kagome lattice

We explore the Dirac spin liquid (DSL) as a candidate for the ground state of the Mott insulating phase of fermions with six flavors on the Kagome lattice, particularly focusing on realizations using $^{173}$Yb atoms in optical lattices. Using mean-field theory and variational Monte Carlo simulations, we demonstrate that the Dirac spin liquid (DSL) has the lowest variational energy among SU(6) symmetry-preserving trial wave functions with a periodicity of a 12-site unit cell, as well as uniform chiral states with larger unit cells. It remains a local minimum even when small second-nearest neighbor and ring exchange interactions are introduced. To characterize the DSL, we calculate the static and dynamic structure factor of the Gutzwiller projected wavefunction and compare it with mean-field calculations. The static structure factor shows triangular-shaped plateaus around the $\mathrm{K}$ points in the extended Brillouin zone, with small peaks at the corners of these plateaus. The dynamical structure factor consists of a gapless continuum of fractionalized excitations. Our study also presents several complementary results, including bounds for the ground state energy, methods for calculating three-site ring exchange expectations in the projective mean field, the boundary of ferromagnetic states, and the non-topological nature of flat bands in the DSL band structure.

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arXiv2024

The dynamical structure factor of the SU(4) algebraic spin liquid on the honeycomb lattice

We compute the momentum resolved dynamical spin structure factor $S(k,ω)$ of the SU(4) Heisenberg model on the honeycomb lattice assuming the $π$-flux Dirac spin liquid ground state by two methods: (i) variationally using Gutzwiller projected particle-hole excitations of the $π$-flux Fermi sea and (ii) in the non-interacting parton mean-field picture. The two approaches produce qualitatively similar results. Based on this analogy, we argue that the energy spectrum of the projected excitations is a gapless continuum of fractional excitations. Quantitatively, the Gutzwiller projection shifts the weight from higher to lower energies, thus emphasizing the lower edge of the continuum. In the mean-field approach, we obtained the $1/\text{distance}^4$ decay of the spin correlation function, and the local correlations show $S^{33}_{\text{MF}}(ω)\propto ω^3$ behavior.

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arXiv2023

Crystalline phases and devil's staircase in qubit spin ice

Motivated by the recent realization of an artificial quantum spin ice in an array of superconducting qubits with tunable parameters [King {\it et al.}, Science 373, 576 (2021)], we scrutinize a quantum six vertex model on the square lattice that distinguishes type-I and type-II vertices. We map the zero-temperature phase diagram using numerical (exact diagonalization) and analytical (perturbation expansion, Gerschgorin theorem) methods. Following a symmetry classification, we identify three crystalline phases alongside a subextensive manifold of isolated configurations. Monte Carlo simulations at the multicritical Rokhsar-Kivelson point provide evidence for a quantum phase exhibiting a cascade of transitions with increasing flux. By comparing structure factors, we find evidence for the emergence of the fully flippable and plaquette phases in the artificial quantum spin ice.

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arXiv2023

Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice

Motivated by the search for chiral spin liquids (CSL), we consider a simple model defined on the kagome lattice of interacting SU(3) spins (in the fundamental representation) including two-site and three-site permutations between nearest neighbor sites and on triangles, respectively. By combining analytical developments and various numerical techniques, namely exact Lanczos diagonalizations and tensor network variational approaches, we find a rich phase diagram with non-topological (``trivial") and topological (possibly chiral) gapped spin liquids (SLs). Trivial spin liquids include an Affleck-Kennedy-Lieb-Tasaki (AKLT)-like phase and a trimerized phase, the latter breaking the inversion center between the up and down triangles of the kagome lattice. A topological SL is stabilized in a restricted part of the phase diagram by the time-reversal symmetry breaking (complex) 3-site permutation term. Analyzing the chiral edge modes of this topological SL on long cylinders or on finite disks, we have come up with two competing scenarios, either a CSL or a double Chern-Simon SL characterized by a single or by two counter-propagating Wess-Zumino-Witten SU(3)$_1$ chiral mode(s), respectively. In the vicinity of the extended ferromagnetic region we have found a magnetic phase corresponding either to a modulated canted ferromagnet or to a uniform partially magnetized ferromagnet.

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arXiv2022

The dynamical structure factor of the SU(3) Heisenberg chain: The variational Monte Carlo approach

We compute the dynamical spin structure factor $S(k,ω)$ of the SU(3) Heisenberg chain variationally using a truncated Hilbert space spanned by the Gutzwiller projected particle-hole excitations of the Fermi sea, introduced in [B. Dalla Piazza et al., Nature Physics 11, 62 (2015)], with a modified importance sampling. We check the reliability of the method by comparing the $S(k,ω)$ to exact diagonalization results for 18 sites and to the two-soliton continuum of the Bethe Ansatz for 72 sites. We get an excellent agreement in both cases. Detailed analysis of the finite-size effects shows that the method captures the critical Wess-Zumino-Witten SU(3)$_1$ behavior and reproduces the correct exponent, with the exception of the size dependence of the weight of the bottom of the conformal tower. We also calculate the single-mode approximation for the SU($N$) Heisenberg model and determine the velocity of excitations. Finally, we apply the method to the SU(3) Haldane-Shastry model and find that the variational method gives the exact wave function for the lowest excitation at $k=\pm 2π/3$.

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arXiv2021

Fragility of $\mathcal{Z}_2$ topological invariant characterizing triplet excitations in a bilayer kagome magnet

The discovery by Kane and Mele of a model of spinful electrons characterized by a $\mathcal{Z}_2$ topological invariant had a lasting effect on the study of electronic band structures. Given this, it is natural to ask whether similar topology can be found in the band-like excitations of magnetic insulators, and recently models supporting $\mathcal{Z}_2$ topological invariants have been proposed for both magnon [Kondo et al. Phys. Rev. B 99, 041110(R) (2019)] and triplet [D. G. Joshi and A. P. Schnyder, Phys. Rev. B 100, 020407 (2019)] excitations. In both cases, magnetic excitations form time--reversal (TR) partners, which mimic the Kramers pairs of electrons in the Kane-Mele model but do not enjoy the same type of symmetry protection. In this paper, we revisit this problem in the context of the triplet excitations of a spin model on the bilayer kagome lattice. Here the triplet excitations provide a faithful analog of the Kane-Mele model as long as the Hamiltonian preserves the TR$\times$U(1) symmetry. We find that exchange anisotropies, allowed by the point group and typical in realistic models, break the required TR$\times$U(1) symmetry and instantly destroy the $\mathcal{Z}_2$ band topology. We further consider the effects of TR breaking by an applied magnetic field. In this case, the lifting of spin-degeneracy leads to a triplet Chern insulator, which is stable against the breaking of TR$\times$U(1) symmetry. Kagome bands realize both a quadratic and a linear band touching, and we provide a thorough characterization of the Berry curvature associated with both cases. We also calculate the triplet-mediated spin Nernst and thermal Hall signals which could be measured in experiments. These results suggest that the $\mathcal{Z}_2$ topology of band-like excitations in magnets may be intrinsically fragile compared to their electronic counterparts.

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arXiv2020

Degenerate manifolds, helimagnets, and multi-$\mathbf{Q}$ chiral phases in the classical Heisenberg antiferromagnet on the face-centered-cubic lattice

We present a detailed study of the ground state phase diagram of the classical frustrated Heisenberg model on the face-centered-cubic lattice. By considering exchange interactions up till third nearest neighbors, we find commensurate, helimagnetic, as well as noncollinear multi-{\bf Q} orders which include noncoplanar and chiral spin structures. We reveal the presence of subextensively degenerate manifolds that appear at triple points and certain phase boundaries in the phase diagram. Within these manifolds, the spin Hamiltonian can be recast as a complete square of spins on finite motifs, permitting us to identify families of exact ground state spin configurations in real space -- these include randomly stacked ferro- or antiferromagnetically ordered planes and interacting ferromagnetic chains, among others. Finally, we critically investigate the ramifications of our findings on the example of the Ising model, where we exactly enumerate all the states numerically for finite clusters.

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arXiv2019

Affine lattice construction of spiral surfaces in classical Heisenberg models

Frustration in classical spin models can lead to degenerate ground states without long range order. In reciprocal space, these degeneracies appear as manifolds of wave vectors, their dimensionality increasing with the degree of frustration and the robustness of the disordered spin-liquid state. Here, we present a recipe to explicitly construct Heisenberg models on Bravais lattices with codimension-one manifolds, i.e., lines in two-dimensions and surfaces with different Euler characteristics in three-dimensions. Furthermore, we discuss the role of thermal and quantum fluctuations in stabilizing ordered states.

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arXiv2019

Dimensional crossover in the SU(4) Heisenberg model in the six-dimensional antisymmetric self-conjugate representation revealed by quantum Monte Carlo and linear flavor-wave theory

Using linear flavor-wave theory (LFWT) and auxiliary field quantum Monte Carlo (QMC), we investigate the properties of the SU(4) Heisenberg model on the anisotropic square lattice in the fully antisymmetric six-dimensional irreducible representation, a model that describes interacting fermions with four flavors at half-filling. Thanks to the calculations on very large systems, we have been able to convincingly demonstrate that QMC results are consistent with a small but finite antiferromagnetic moment at the isotropic point, in qualitative agreement with LFWT obtained earlier [F. H. Kim {\it{et al.}}, Phys. Rev. B {\bf 96}, 205142 (2017)], and in quantitative agreement with results obtained previously on the Hubbard model [D. Wang {\it{et al.}}, Phys. Rev. Lett. {\bf 112}, 156403 (2014)] after extrapolation to infinite $U/t$. The presence of a long-range antiferromagnetic order has been further confirmed by showing that a phase transition takes place into a valence-bond solid (VBS) phase not too far from the isotropic point when reducing the coupling constant along one direction on the way to decoupled chains.

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arXiv2017

Magnetoelectric memory function with optical readout

The ultimate goal of multiferroic research is the development of new-generation non-volatile memory devices, the so-called magnetoelectric (ME) memories, where magnetic bits are controlled via electric fields without the application of electrical currents subject to dissipation. This low-power operation exploits the entanglement of the magnetization and the electric polarization coexisting in multiferroic materials. Here we demonstrate the optical readout of ME memory states in the antiferromagnetic (AFM) and antiferroelectric (AFE) LiCoPO$_4$, based on the strong absorption difference of THz radiation between its two types of ME domains. This unusual contrast is attributed to the dynamic ME effect of the spin-wave excitations, as confirmed by our microscopic model, which also captures the characteristics of the observed static ME effect. Our proof-of-principle study, demonstrating the control and the optical readout of ME domains in LiCoPO$_4$, lays down the foundation for future ME memory devices based on antiferroelectric-antiferromagnetic insulators.

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