Dissertation Defense: Jeet Shah

Title:  Quantum Dimer Models and Mixed-State Topological Phases: Geometry and Stability
Speaker:  Jeet Shah (QuICS)
Date & Time:  July 28, 2026, 10:00am
Where to Attend:  PSC 2136 and Virtual Via Zoom: https://umd.zoom.us/j/6022663536?omn=92882108272&jst=2

Quantum many-body systems can organize into phases whose essential properties are not captured by local order parameters. Quantum spin liquids, topologically ordered states, and symmetry-protected topological (SPT) phases are instead characterized by entanglement and nonlocal correlations. Understanding when such phases arise, how they can be diagnosed, and how the system geometry and dissipation affect them is important in modern condensed matter physics and quantum information science.

This dissertation studies these questions in quantum dimer models and SPT phases under dissipation. Quantum dimer models can realize exotic phases such as topologically ordered quantum spin liquids. The Rokhsar-Kivelson (RK) construction provides exactly solvable models whose ground states are uniform superpositions of many dimer configurations. We use and extend this construction to investigate phase transitions and boundary-induced phase separation in several quantum dimer models. First, we describe a generalized RK construction for edge-weighted dimer wavefunctions and apply it to the triangular lattice. It yields an exactly solvable continuous transition between a Z2 topological quantum spin liquid and a symmetry-broken columnar phase. We characterize this transition using dimer-dimer correlations, nonlocal vison correlations, and the topological min-entropy. Next, we show that the thermodynamic limit can break down in certain quantum spin and dimer models: changing the boundary shape while keeping the Hamiltonian fixed can induce macroscopic regions with distinct quantum phases. Using Kasteleyn-matrix methods, we demonstrate this effect on the Aztec diamond and square-octagon fortress by computing dimer-dimer and vison correlators. We then study a quantum monomer-dimer model on the quasicrystalline Penrose tiling. Because Penrose tilings do not admit perfect dimer coverings, monomers occur at finite density. Mapping the model to a Z2 gauge theory with matter and computing open Wilson lines and closed Wilson loops, we find evidence that the RK point realizes a confined phase.

We next propose a way to realize a U(1) quantum spin liquid using three-dimensional Rydberg atom arrays arranged on the pyrochlore lattice. Within our analysis, tuning the Rabi frequency accesses both a confinement-deconfinement transition driven by magnetic monopoles and a Higgs transition driven by electric charges. We also identify experimentally accessible diagnostics that distinguish the deconfined phase from ordered phases.

Finally, we study the stability of steady-state mixed-state SPT order in an open system. Using the decohered cluster state, protected by a combination of strong and weak symmetries, we construct and analyze a parent Lindbladian for which it appears as a steady state.  Through exact mappings to reaction-diffusion processes and density matrix renormalization group calculations, we find that generic symmetric perturbations destabilize this order through strong-to-weak spontaneous symmetry breaking.

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