arXiv subjects

Tobias F. Maier

Publications and source records attributed to Tobias F. Maier.

4 recordsLinked to original sources

arXiv2026

Topological phase transition in a symmetric blockade structure

We present a numerical study of a blockade Hamiltonian with a local $\mathbb{Z}_2$ symmetry. For such models, the existence of a topologically ordered ground state has been proven rigorously for weak Rabi driving [T. F. Maier et al., PRX Quantum 6, 030340 (2025)]. However, the phase diagram beyond weak driving is still an open question. We perform large-scale infinite-size density matrix renormalization group (iDMRG) simulations on a cylinder and map out the full phase diagram of the model. We find a single continuous phase transition between the topologically ordered phase and a trivial paramagnetic phase, and confirm numerically the stability of the topologically ordered phase up to Rabi drives comparable to the characteristic energy scale of the system. Furthermore, we compute the excitation gaps and show that the charge gap remains open across the phase transition and charges become confined in the trivial phase. On the other hand, the gap in the symmetric sector closes at the transition, consistent with the condensation of flux excitations.

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arXiv2026

Excitation gap of a blockade structure with $\mathbb{Z}_2$ topological order

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove -- yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

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arXiv2025

Topological order in symmetric blockade structures

The bottom-up design of strongly interacting quantum materials with prescribed ground state properties is a highly nontrivial task, especially if only simple constituents with realistic two-body interactions are available on the microscopic level. Here we study two- and three-dimensional structures of two-level systems that interact via a simple blockade potential in the presence of a coherent coupling between the two states. For such strongly interacting quantum many-body systems, we introduce the concept of blockade graph automorphisms to construct symmetric blockade structures with strong quantum fluctuations that lead to equal-weight superpositions of tailored states. Drawing from these results, we design a quasi-two-dimensional periodic quantum system that - as we show rigorously - features a topological $\mathbb{Z}_2$ spin liquid as its ground state. Our construction is based on the implementation of a local symmetry on the microscopic level in a system with only two-body interactions.

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arXiv2025

Quantum doubles in symmetric blockade structures

Exactly solvable models of topologically ordered phases with non-abelian anyons typically require complicated many-body interactions which do not naturally appear in nature. This motivates the "inverse problem" of quantum many-body physics: given microscopic systems with experimentally realistic two-body interactions, how to design a Hamiltonian that realizes a desired topological phase? Here we solve this problem on a platform motivated by Rydberg atoms, where elementary two-level systems couple via simple blockade interactions. Within this framework, we construct Hamiltonians that realize topological orders described by non-abelian quantum double models. We analytically prove the existence of topological order in the ground state, and present efficient schemes to prepare these states. We also introduce protocols for the controlled adiabatic braiding of anyonic excitations to probe their non-abelian statistics. Our construction is generic and applies to quantum doubles $\mathcal{D}(G)$ for arbitrary finite groups $G$. We illustrate braiding for the simplest non-abelian quantum double $\mathcal{D}(S_3)$.

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