Tag - Ising model

Brett Min: Bath-engineering magnetic order in quantum spin chains

22nd March, 2024

Dissipative processes can drive different magnetic orders in quantum spin chains. Using a non-perturbative analytic mapping framework, we systematically show how to structure different magnetic orders in spin systems by controlling the locality of the attached baths. Our mapping approach reveals analytically the impact of spin-bath couplings, leading to the suppression of spin splittings, bath-dressing and mixing of spin-spin interactions, and emergence of non-local ferromagnetic interactions between spins coupled to the same bath, which become long-ranged for a global bath. Our general mapping method can be readily applied to a variety of spin models: We demonstrate (i) a bath-induced transition from antiferromagnetic (AFM) to ferromagnetic ordering in a Heisenberg spin chain, (ii) AFM to extended Neel phase ordering within a transverse-field Ising chain with pairwise couplings to baths, and (iii) a quantum phase transition in the fully-connected Ising model. We also demonstrate how the mapping approach can be applied to higher dimensions, larger spin systems, and fermionic systems.

Zohreh Davoudi: Quantum simulating hadronic scattering: From confining spin models to gauge theories

1st March, 2024

An exciting promise of quantum simulators is to enable a first-principles look into the real-time dynamics of matter after high-energy collisions of hadrons and nuclei, which mimic conditions in the early universe. To realize such a promise, first the gauge theories of the Standard Model should be mapped to quantum simulators. Then complex initial states, in the form of moving wave packets of composite (bound) states of elementary constituents, need to be prepared. While much progress has happened in the former in recent years, developments in the latter are just starting to gain momentum. In this talk, I will provide three examples from our recent work to demonstrate concrete proposals and algorithms for hadronic wave-packet preparations in confining models, from Ising spin systems to the low-dimensional abelian lattice gauge theories. These examples involve a range of platforms, from (solid-state and atomic) analogue quantum simulators to digital quantum computers. I will further present results for numerical studies of expected scattering outcomes, and conditions for observing inelastic channels, along with a demonstration of a high-fidelity meson wave packet generated on a trapped-ion quantum computer.

Sky Yang Cao: Recent Results on Finite Group Lattice Gauge Theories

20th March, 2023

The rigorous study of spin systems such as the Ising model is currently one of the most active research areas in probability theory. In this talk, I will introduce one particular class of such models, known as lattice gauge theories (LGTs), and go over its origins, motivations, and then some recent results. Along the way, I will also try to highlight some of the key differences between LGTs and the usual spin systems. The general theme is that LGTs are spin systems with topological considerations.

Reimundo Heluani: The singular support of the Ising model

10th September, 2020

We prove three new q-series identities of the Rogers-Ramanujan-Slater type. We find a PBW basis for the Ising model as a consequence of one of these identities. If time permits it will be shown that the singular support of the Ising model is a hyper-surface (in the differential sense) on the arc space of its associated scheme.