[1] Breakdown of the thermodynamic limit in quantum spin and dimer models (arXiv:2503.15588)

Authors: Jeet Shah, Laura Shou, Jeremy Shuler, and Victor Galitski1

Abstract: The thermodynamic limit is foundational to statistical mechanics, underlying our understanding of manybody phases. It assumes that, as the system size grows infinitely at fixed density of particles, unambiguous macroscopic phases emerge that are independent of the system’s boundary shape. We present explicit quantum spin and dimer Hamiltonians whose ground states violate this principle. Our construction relies on the previous mathematical work on classical dimers on the Aztec diamond and the square-octagon fortress, where geometry-dependent phase behaviors are observed in the infinite-size limit. We reverse engineer quantum spin Hamiltonians on the square and the square-octagon lattices whose ground states at the Rokhsar–Kivelson points are described by classical dimer coverings. On diamond-shaped domains, we find macroscopic boundary regions exhibiting distinct quantum phases from those on square-shaped domains. We study the nature of these phases by calculating the dimer-dimer and vison correlators and adapt Kasteleyn matrix based analytical and numerical methods for computing the vison correlator, which are significantly more efficient than standard Monte Carlo techniques. Our results show that the square-octagon lattice supports a single gapped short-range entangled phase, with exponentially decaying dimer correlators and a constant vison correlator. When the same model is considered on a diamond-shaped domain, an additional ordered phase emerges near the corners, where the dimers are in a staggered pattern.

[2] A quantum monomer-dimer model on Penrose tilings (arXiv:2503.15588)

Authors: Jeet Shah, Gautam Nambiar, Alexey V. Gorshkov, and Victor Galitski

Abstract: We define a quantum monomer-dimer model in the space of maximal dimer coverings of quasicrystalline Penrose tilings. Since Penrose tilings do not admit perfect dimer coverings, as shown by F. Flicker et al., PRX 10, 011005 (2020), monomers are necessarily present in our model. The model features a frustration-free Rokhsar-Kivelson (RK) point where the ground state is a uniform superposition of all the exponentially many maximal dimer coverings, despite the presence of a finite density of monomers. We map our model to a ℤ2 gauge theory with matter and calculate various correlators to characterize the phase of the system at the RK point using classical Monte Carlo calculations. Specifically, we compute the dimer-dimer and vison-vison correlators, as well as open Wilson lines and closed Wilson loops corresponding to the monomers and the visons. We find that both the dimer-dimer and vison-vison correlators decay exponentially with distance. The open Wilson lines and closed Wilson loops decay exponentially with the same correlation length, indicating that the gauge theory is in the confined phase, which implies that the system is likely in an ordered phase.

[3] Quantum spin ice in three-dimensional Rydberg atom arrays (Phys. Rev. X 15 011025 (2025))

Authors: Jeet Shah, Gautam Nambiar, Alexey V. Gorshkov, and Victor Galitski

Abstract: Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of ℤ2 topological order [G. Semeghini et al., Science 374, 1242 (2021)], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.

[4] Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking (arXiv:2410.12900)

Authors: Jeet Shah, Christopher Fechisin, Yu-Xin Wang, Joseph T. Iosue, James D. Watson, Yan-Qi Wang, Brayden Ware, Alexey V. Gorshkov, and Cheng-Ju Lin

Abstract: Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

[5] Renormalization group study of systems with quadratic band touching (Phys. Rev. B 103 195118 (2021))

Authors: Jeet Shah, and Subroto Mukerjee

Abstract: Lifshitz transitions in two 2D systems with a single quadratic band touching point as the chemical potential is varied have been studied here. The effects of interactions have been studied using the renormalization group (RG) and it is found that at the transition a repulsive interaction is marginally relevant and an attractive interaction is marginally irrelevant. We corroborate the results obtained from the RG calculation by studying a microscopic model whose ground state and Green’s functions can be obtained exactly. We find that away from the transition, the system displays an instability towards forming and excitonic condensate.

[6] Gauging the Kitaev chain (SciPost Phys. 10, 148 (2021))

Authors: Umberto Borla, Ruben Verresen, Jeet Shah, and Sergej Moroz

Abstract: We gauge the fermion parity symmetry of the Kitaev chain. While the bulk of the model becomes an Ising chain of gauge-invariant spins in a tilted field, near the boundaries the global fermion parity symmetry survives gauging, leading to local gauge-invariant Majorana operators. In the absence of vortices, the Higgs phase exhibits fermionic symmetry-protected topological (SPT) order distinct from the Kitaev chain. Moreover, the deconfined phase can be stable even in the presence of vortices. We also undertake a comprehensive study of a gently gauged model which interpolates between the ordinary and gauged Kitaev chains. This showcases rich quantum criticality and illuminates the topological nature of the Higgs phase. Even in the absence of superconducting terms, gauging leads to an SPT phase which is intrinsically gapless due to an emergent anomaly.