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Phase diagram of the XXZ spin-1/2 model on the pyrochlore lattice and its relation to the Programmable Rydberg Atoms Simulator
Nikita Astrakhantsev - University of Zürich
Wednesday, November 9, 2022, 1:00-2:00 pm Calendar
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The spin-1/2 nearest-neighbor XXZ model on the pyrochlore lattice is an iconic frustrated three-dimensional spin system with a rich phase diagram on the λ axis, where λ is the XXZ interaction anisotropy.

In the first part of the talk, I will focus on the Heisenberg case λ=1, in which the model is debated to possess a quantum spin-liquid (QSL) ground state. In [Phys. Rev. X 11, 041021 (2021)], we contested this hypothesis with an extensive numerical investigation using both exact diagonalization and complementary variational techniques. Specifically, we employed an RVB-like many-variable Monte Carlo ansatz and convolutional neural network quantum states for (variational) calculations with up to 4×43 and 4×33 spins, respectively. We demonstrated that these techniques yield consistent results, allowing for reliable extrapolations to the thermodynamic limit. In addition, we found clear indications of a dimer order with spontaneously broken inversion and rotational symmetry, calling the scenario of a featureless QSL into question.

In the second part of the talk, I will consider the region λ≪1, corresponding to the Ising model with small exchange interaction. At the λ=0 Ising case, the model possesses a thermodynamically-degenerate ground state, described by the {\it two-in, two-out} spin ice rule. Introduction of finite λ≪1 exchange interaction couples the spin ice ground states and generates the U(1) QSL with emergent U(1) electrodynamics. In this talk, I will demonstrate that this QSL can be embedded into the system of Rydberg atoms governed by the Sengupta-Sachdev Hamiltonian. I will show the preliminary results of the simulation of this embedding within the quantum Monte Carlo approach. This embedding continues the line of QSL-Rydberg mappings [see, for instance, Ruben Verresen et al., Phys. Rev. X 11, 031005] and allows one to simulate the U(1) QSL on the pyrochlore lattice using the analog Rydberg simulator on the system sizes that are otherwise intractable for classical numerical approaches.

This talk is organized by Andrea F. Svejda