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Quantum simulation of the Haldane phase using open shell molecules
Authors:
Suman Aich,
Ceren B. Dag,
H. A. Fertig,
Debayan Mitra,
Babak Seradjeh
Abstract:
Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the $N=0,J=1/2,F=1$ state is coupled to the $N=1,J=3/2,F=2$ manifold with circu…
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Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the $N=0,J=1/2,F=1$ state is coupled to the $N=1,J=3/2,F=2$ manifold with circularly polarized microwaves, in the presence of a small magnetic field, can lead to spin-1 quantum magnetic Hamiltonians, due to the decoupling between electron spin and orbit, that is unique to the $^2Σ$ ground state molecules. We demonstrate that in one dimension, the phase diagram associated with this Hamiltonian, computed via tensor network methods, hosts the celebrated Haldane phase. We find that the Haldane phase persists even in the presence of SU(3) correction terms that break the SU(2) algebra of the Hamiltonian. We discuss the feasibility of the proposed scheme for $^2Σ$ molecules with large rotational constants such as the directly laser cooled molecule MgF for future experiments.
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Submitted 16 March, 2026;
originally announced March 2026.
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Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
Authors:
Suman Aich,
Babak Seradjeh
Abstract:
We investigate the higher-order bulk-boundary correspondence in a family of chiral-symmetric Bloch Hamiltonians with anticommuting mirror symmetries. These models generalize the $π$-flux square lattice, the prototypical topological quadrupole insulator, and include both separable and nonseparable models with extended and diagonal hopping. For separable systems, the product of subsystem chiral wind…
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We investigate the higher-order bulk-boundary correspondence in a family of chiral-symmetric Bloch Hamiltonians with anticommuting mirror symmetries. These models generalize the $π$-flux square lattice, the prototypical topological quadrupole insulator, and include both separable and nonseparable models with extended and diagonal hopping. For separable systems, the product of subsystem chiral winding numbers correctly predicts the number of zero-energy corner states. However, this invariant fails in nonseparable models, motivating the development of new momentum-space diagnostics. We introduce gauge-independent mirror-filtered winding numbers for Wannier Hamiltonians, constructed by projecting mirror eigenstates onto the occupied subspace. Furthermore, by adapting periodicized Wilson lines from chiral Floquet theory to the case with momentum-dependent chiral operator, we define new invariants associated directly with Wannier gaps. These invariants provide a detailed characterization of Wannier band topology. Our results clarify the interplay between chiral symmetry, mirror symmetries, and Wilson loops in higher-order topological phases and point to open challenges in formulating momentum-space invariants for general nonseparable models.
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Submitted 24 July, 2026; v1 submitted 28 November, 2025;
originally announced November 2025.
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Selective bulk-boundary correspondence in higher-order topological insulators with anticommuting mirror and chiral symmetries
Authors:
Suman Aich,
Babak Seradjeh
Abstract:
We investigate higher-order topological insulators protected by chiral and anticommuting mirror symmetries. Using models in the BDI class, which include the prototypical topological quadrupole insulator, we show that breaking mirror symmetries that anticommute with the chiral operator leads to edge-selective bulk-boundary correspondence, with gap closings and bound states appearing only along a su…
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We investigate higher-order topological insulators protected by chiral and anticommuting mirror symmetries. Using models in the BDI class, which include the prototypical topological quadrupole insulator, we show that breaking mirror symmetries that anticommute with the chiral operator leads to edge-selective bulk-boundary correspondence, with gap closings and bound states appearing only along a subset of boundaries of the same orientation and codimension. We define a new edge-sensitive topological invariant that distinguishes this mechanism from previous reports of non-topological edge-selection effects.
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Submitted 13 July, 2026; v1 submitted 26 September, 2025;
originally announced September 2025.
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Multiple tunable real-space degeneracies in graphene irradiated by twisted light
Authors:
Suman Aich,
Babak Seradjeh
Abstract:
We report the theoretical discovery of multiple real-space degenerate Floquet-Bloch states in monolayer graphene coherently driven by twisted circularly-polarized light. Using Floquet theory, we characterize the real-space structure of quasienergies and Floquet modes in terms of the orbital angular momentum and radial vortex profile of light. We obtain the effective real-space Floquet Hamiltonian…
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We report the theoretical discovery of multiple real-space degenerate Floquet-Bloch states in monolayer graphene coherently driven by twisted circularly-polarized light. Using Floquet theory, we characterize the real-space structure of quasienergies and Floquet modes in terms of the orbital angular momentum and radial vortex profile of light. We obtain the effective real-space Floquet Hamiltonian and show it supports crossings of Floquet modes, especially at high-symmetry $K$ and $Γ$ points of graphene, localized at rings around the vortex center. At specific frequencies, the vortex bound states form a multiply degenerate structure in real-space. This structure is purely dynamically generated and controlled by the frequency and tuned by the intensity of twisted light. We discuss the experimental feasibility of observing and employing multiple real-space degeneracies for coherent optoelectronic quantum state engineering.
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Submitted 29 August, 2024; v1 submitted 8 November, 2023;
originally announced November 2023.
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The clash of the Titans: how preferential attachment helps the survival of the smallest
Authors:
Suman Aich,
Anita Mehta
Abstract:
We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolize th…
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We examine the effects of preferential attachment on a model of competing clusters. In the original model, cluster masses grow at the expense of their neighbours; on a lattice, this is known to result in the asymptotic survival and indefinite growth of clusters which are isolated from each other. The presence of preferential attachment results in an inhomogeneous topology, where hubs monopolize the connections, while most other nodes are sparsely connected. Interestingly, this results in the protection of the less massive clusters from annihilation, to which the hubs are doomed.
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Submitted 31 March, 2014;
originally announced March 2014.