arXiv subjects

Hari Borutta

Publications and source records attributed to Hari Borutta.

3 recordsLinked to original sources

arXiv2026

Parent Hamiltonian construction of generalized Calogero-Sutherland models

The Calogero-Sutherland model is a paradigmatic integrable system describing one-dimensional non-relativistic particles with inverse-square-type interactions. At interaction strength $λ=2$, the CSM exhibits a deep connection to anyon physics, featuring the Laughlin-Jastrow polynomial as its exact ground state. Motivated by this structure, we develop a general reverse-engineering construction of positive semidefinite continuum parent Hamiltonians for trial states admitting a rational conformal field theory description with central charge $c<1$. By leveraging the null-vector structure of the underlying primary fields and the associated Belavin-Polyakov-Zamolodchikov equations, we derive corresponding many-body annihilation operators. We then apply this construction explicitly to the Moore-Read and $k=3$ Read-Rezayi states-relating to Ising and Fibonacci anyons, respectively-obtaining continuum Hamiltonians for which these Jack-polynomial states, viewed as one-dimensional chiral spin liquid wave functions, are exact zero modes. We emphasize, however, that our construction does not by itself establish ground-state uniqueness or determine the nature of the excitation spectrum.

cond-mat.str-el↗

arXiv2026

Microscopic Spin-1 Parent Hamiltonians for Emergent Valence-Bond Loop Manifolds

We construct an exact spin-$1$ parent Hamiltonian for constrained valence-bond loop manifolds on the checkerboard and pyrochlore lattices. The Hamiltonian is local, SU(2)- and time-reversal-invariant, and built from positive-semidefinite projectors acting on triangular faces. Each projector removes only the maximally polarized state of a triangle, so the model is frustration-free. Its zero-energy states are generated by an AKLT-like construction in which each spin-$1$ moment is resolved into two virtual spin-$\tfrac12$ degrees of freedom, singlets are formed inside every crossed plaquette or tetrahedron, and the physical spin-$1$ Hilbert space is recovered by projection. The resulting ground states are fully packed singlet-loop states on the corner-sharing lattice. Thus, a loop or dimer constraint, usually introduced as part of an effective Rokhsar--Kivelson description, appears here as the exact zero-energy manifold of a microscopic spin Hamiltonian. We analyze spin correlations within this manifold and show that, for a fixed loop covering, they are determined by loop connectivity. We also project symmetry-allowed perturbations into the ground-state manifold and derive the resulting low-energy pseudospin dynamics. The checkerboard and pyrochlore cases differ sharply. On the pyrochlore lattice, tetrahedral symmetry removes simple local bias terms, and the leading nontrivial next-nearest-neighbour Heisenberg perturbation gives an emergent spin-$\tfrac12$ XY model on the diamond lattice of tetrahedron centers. These results give an exact spin-$1$ microscopic starting point for constrained valence-bond physics in two and three dimensions, and show how loop, dimer, and gauge-theoretic descriptions can be approached from a small-spin, SU(2)-invariant frustrated magnet.

cond-mat.str-el↗

arXiv2026

Crystallography-driven molecularization of a two-dimensional spin-$3/2$ magnet

Large-spin two-dimensional magnets are generally expected to develop conventional long-range order once the dominant exchange scale becomes appreciable. The layered spin-$3/2$ maple-leaf compound Na$_2$Mn$_3$O$_7$ defies this expectation: despite sizable antiferromagnetic interactions and no evident disorder, it exhibits no magnetic ordering and displays two well-separated thermodynamic crossover scales. We show that this behavior originates from a crystallography-driven molecularization of the magnetic degrees of freedom. The low-symmetry structure partitions the Mn sublattice into inequivalent exchange pathways, generating a pronounced hierarchy that nearly isolates antiferromagnetic hexagons. Magnetic correlations therefore develop in two stages: first within individual hexagons at a scale set by the dominant exchange, and only at much lower temperatures do frustrated inter-hexagon couplings attempt to establish coherence across the lattice. While isolated hexagons reproduce the two-step thermodynamic structure, the experimentally relevant temperature scales emerge only once the hexagons are embedded in the frustrated two-dimensional network. The resulting quantum ground state is magnetically disordered, characterized by strong intra-hexagon correlations and rapidly decaying inter-hexagon correlations. These results identify crystallographic inequivalence as a materials-level mechanism for stabilizing molecularized and quantum-disordered states even in large-spin two-dimensional magnets.

cond-mat.str-el↗